# Kipu Quantum — full site content > Concatenated text of every indexable page on kipu-quantum.com. Source of truth: https://kipu-quantum.com/llms.txt --- # Unlock Quantum-centric Intelligence URL: https://kipu-quantum.com/ [Latest NewsQuantum-Enhanced AI, Deployable in Production](/news/quantum-enhanced-ai-production)[New BlogReading Toxicity of Molecules with Neutral-Atom Quantum Processors](/blog/reading-toxicity-of-molecules-with-neutral-atom-quantum-processors)[Upcoming WebinarQuantum Computing for Finance · 28 July](/webinar-quantum-finance)[BlogClassical Surrogates for Quantum-Advantage Feature Extraction](/blog/classical-surrogates-for-quantum-feature-extraction)[ExploreThe Kipu Quantum Hub](/hub)[Latest NewsQuantum-Enhanced AI, Deployable in Production](/news/quantum-enhanced-ai-production)[New BlogReading Toxicity of Molecules with Neutral-Atom Quantum Processors](/blog/reading-toxicity-of-molecules-with-neutral-atom-quantum-processors)[Upcoming WebinarQuantum Computing for Finance · 28 July](/webinar-quantum-finance)[BlogClassical Surrogates for Quantum-Advantage Feature Extraction](/blog/classical-surrogates-for-quantum-feature-extraction)[ExploreThe Kipu Quantum Hub](/hub) ![Quantum Computing Background](/_next/static/media/2000H-Kipu-landingvisual-draft01_1.401f329c.jpg) ![](/_next/static/media/ChatLogo.34926ee9.png)Tinkuq · Quantum Matchmaker ### Build Your First Quantum Application Describe your problem step-by-step. Tinkuq, our matchmaking agent, will guide you from problem to quantum solution. Ask Tinkuq Popular use cases: Delivery RoutesPortfolio MixNetwork RoutingImage Classification # Unlock Quantum-centric Intelligence Build Enterprise-ready quantum solutions without any quantum computing knowledge. Easily transform complex challenges into competitive advantages. [Quantum Hub](https://hub.kipu-quantum.com)[See Pricing](/pricing) No credit card required Free tier included Cancel anytime ![](/_next/static/media/ChatLogo.34926ee9.png)Tinkuq · Quantum Matchmaker ### Build Your First Quantum Application Describe your problem step-by-step. Tinkuq, our matchmaking agent, will guide you from problem to quantum solution. Ask Tinkuq Popular use cases: Delivery RoutesPortfolio MixNetwork RoutingImage Classification Trusted by global quantum leaders and deep-tech investors ![IBM Quantum](/500H-IBM_Quantum_logotype_pos_RGB.svg)![QuEra](/500H-QuEra_logo.svg)![Pasqal](/500H-Pasqal_logo.svg)![IonQ](/500H-ionq-logo.svg)![NVIDIA](/500H-NVIDIA_logo.svg)![HV Capital](/500H-hv_capital_logo.svg)![QTN](/500H-logo-qtn.svg)![Verve Capital](/500H-logo-verve-vc.png)![AQAL Capital](/500H-logo-AQAL-web.png) 405 Organizations 1,843 Users 20+ Backends 26 Countries ## Why Choose Kipu Quantum Hub? A complete platform designed for researchers, enterprises, and universities to harness quantum-centric AI computing power with unprecedented ease. ### Leading Algorithms Access cutting-edge quantum algorithms optimized for real-world industrial applications with proven results. ### Enterprise Security Bank-grade encryption and compliance with industry standards to protect your most sensitive data. ### Scalable Solutions From proof-of-concept to production, scale seamlessly with our flexible cloud infrastructure. ### Expert Support Get guidance from quantum computing experts to maximize your ROI and accelerate implementation. ### Fast Integration RESTful APIs and SDKs make it easy to integrate quantum computing into your existing workflows. ### Digital Sovereignty Deploy and run solutions within fully governed environments tailored to your compliance and security needs. ## Industrial Applications Discover how leading companies are leveraging quantum computing to solve their most complex challenges. [ ![Telecommunication Routing](/_next/static/media/photo-1558494949-ef010cbdcc31.8295e319.jpg) \>5% Efficiency ### Telecommunication Routing Optimize optical network routing for maximum efficiency with quantum algorithms ](/examples#example-1) [ ![Capital Efficiency](/_next/static/media/photo-1579621970563-ebec7560ff3e.2d897d61.jpg) \>10% Capital Saved ### Capital Efficiency 10% Less Capital Locked with quantum-enabled portfolio optimization ](/examples#example-2) [ ![Logistics Optimization](/_next/static/media/photo-1701313056413-0915e1adf204.c0689c1b.jpg) \>12% Cost Reduction ### Logistics Optimization Quantum optimization for fleet logistics and scheduling with VRP solutions ](/examples#example-3) [View All Applications](/examples) ## Start Your Quantum Journey [Get Started Free](/pricing)[View Pricing](/pricing) Join hundreds of organizations already leveraging quantum computing to gain a competitive edge in their industries. --- # Quantum Computing Made Simple URL: https://kipu-quantum.com/product Platform Overview # Quantum Computing Made Simple Build enterprise-grade quantum applications without any quantum expertise. Our platform abstracts the complexity so you can focus on solving real business problems. [Start Today](https://login.hub.kipu-quantum.com/realms/planqk/protocol/openid-connect/registrations?client_id=planqk-login&redirect_uri=https%3A%2F%2Fhub.kipu-quantum.com%2Fmarketplace%23error%3Dlogin_required%26state%3Dd2fa07d2-c739-4635-9513-936a749c3e3b%26iss%3Dhttps%3A%2F%2Flogin.hub.kipu-quantum.com%2Frealms%2Fplanqk&state=f3f1e7bd-f713-4e07-a96a-474a377090e6&response_mode=fragment&response_type=code&scope=openid&nonce=1e76f0cc-eabb-41a1-bb9a-40298ce4f38e&code_challenge=muWbAdYk7A7HyGM1_PUt7yvnk9ENcdHbVtxzgCuZrks&code_challenge_method=S256)[View Pricing](/pricing) ## Platform Features Everything you need to build, deploy, and scale quantum computing solutions for your organization. ### No-Code Interface Build quantum applications without writing complex quantum code. Our intuitive interface makes quantum computing accessible to everyone. ### Pre-built Algorithms Access a library of industry-tested quantum algorithms ready to solve your specific use cases across multiple industries. ### 20+ Quantum Backends Run your algorithms on leading quantum hardware from IBM, Rigetti, IonQ, and more. Choose the best backend for your needs. ### Instant Deployment Deploy your quantum solutions to production with a single click. Scale from prototype to enterprise seamlessly. ### Real-time Analytics Monitor performance, track resource usage, and optimize your quantum workflows with comprehensive analytics. ### Enterprise Security Bank-grade encryption, compliance certifications, and role-based access control to protect your sensitive data. ## How It Works Get from idea to production in four simple steps 01 ### Choose Your Use Case Select from our library of pre-built quantum algorithms designed for specific industries and applications. 02 ### Configure Parameters Customize the algorithm for your specific needs using our intuitive no-code interface. No quantum expertise required. 03 ### Run on Quantum Hardware Execute your quantum workflow on 20+ backends. We automatically select the optimal hardware for your task. 04 ### Analyze & Deploy Review results, optimize performance, and deploy to production with enterprise-grade security and scalability. ## Proven Results See how organizations are using our platform to drive real business value ### Drug Discovery Simulate molecular interactions at quantum scale 10x faster ### Financial Modeling Optimize portfolios across thousands of scenarios +12% returns ### Supply Chain Solve complex routing and logistics problems 20% cost reduction [View All Applications](/examples) ## Ready to Get Started? [Start Today](/pricing)[View Pricing](/pricing) Start building quantum applications today. No credit card required. --- # Iskay Quantum Optimizer URL: https://kipu-quantum.com/iskay # Iskay Quantum Optimizer A QUBO and HUBO solver by Kipu Quantum that can outperform classical solvers. It runs on IBM Quantum hardware and takes only your objective function as input. [I’m ready to build](https://2dqpz5.share-eu1.hsforms.com/22nIlsuWuTAi5q3fMEseAUw?utm_source=kipu-website&utm_medium=iskay-page) ## Drop it into your Qiskit workflow Iskay is a first-class Qiskit Function on IBM Quantum, catalogued as `kipu-quantum/iskay-quantum-optimizer`. Load it, pass your objective, read the solution. Pre- and post-processing are managed. [Visit the documentation](https://quantum.cloud.ibm.com/docs/en/guides/kipu-optimization)[See pricing](/pricing) Iskay · IBM QuantumMiray · Kipu Hub iskay\_quickstart.py ``` from qiskit_ibm_catalog import QiskitFunctionsCatalog # pip install qiskit-ibm-catalog catalog = QiskitFunctionsCatalog( token=IBM_TOKEN, channel="ibm_quantum_platform", instance=INSTANCE_CRN, ) iskay = catalog.load("kipu-quantum/iskay-quantum-optimizer") # Objective as a QUBO/HUBO. Higher-order terms are native. hubo = { "()": 0.0, # constant "(0,)": -1.0, # linear "(1,)": -1.0, "(0, 1)": 2.0, # quadratic (QUBO) "(0, 1, 2)": -1.5, # cubic (HUBO), no extra qubits } job = iskay.run( problem=hubo, problem_type="binary", instance=INSTANCE_CRN, backend_name="ibm_fez", options={"shots": 100, "num_iterations": 3}, ) result = job.result() print(result["solution_info"]["cost"], result["solution"]) ``` ## Join the Iskay Community Already running Iskay as a Qiskit Function? Connect directly with Kipu’s engineering team and fellow practitioners solving real problems on IBM quantum computers. [I’m ready to build](https://2dqpz5.share-eu1.hsforms.com/22nIlsuWuTAi5q3fMEseAUw?utm_source=kipu-website&utm_medium=iskay-page) Launching soon. Free for Iskay users; founding membership pending interest. Developer check-ins Dedicated time for problem encoding, shot budgets and tuning. Early access Preview features before they reach the Qiskit Functions Catalog. Best practices HUBO/QUBO formulation patterns and benchmarks that work at scale. Shape the roadmap A direct channel that puts your requests at the front of the queue. ## What users have to say At the IBM Quantum Developer Conference QDC25 · Challenge winner “Kipu's Qiskit Function radically shortened the path from QUBO/HUBO formulation to execution on real 156-qubit hardware, freeing me to focus on tuning the quantum algorithm itself.” KN Khanyisa Noganta Principal Data Scientist · Market Split winner IBM Quantum · Organizer “Khanyisa won by tuning the parameters. It's proof that Kipu's Iskay Qiskit function works in practice. The new features allowed participants and other users to cater the function to their needs.” IBM Junye Huang IBM Quantum · ran the QDC25 challenge In the field Financial services “The results are excellent: a perfect 222-edge cut at 100 nodes, and 318 of 336 at 150.” FS Quantum team Financial services · Max-Cut benchmark Global IT consultancy “The function has been working well. We're scaling from 20 to 150 qubits on S&P 500 data.” IT Data-science team Global IT consultancy · portfolio optimization University research “I tested a larger problem and it works. Now I'm pushing to even larger instances.” UNI Optimization researcher University research group · vehicle routing ## Tune it to your needs shotsSamples per iteration.num\_iterationsMore iterations for a better solution.Transpilation levelTranspiler passes to optimize circuit for QPU.Pre / post-processingSimplify up front and refine afterwards. options = { "shots": 5000,"num\_iterations": 7,"preprocessing\_level": 1,"transpilation\_level": 3,"postprocessing\_level": 2, } Tuning in practice “With the recommended settings, our circuit dropped from 1901 to 1041 layers. Very useful.” UNI Quantum researcher University research group · biomedical HUBO At the Berlin Quantum Hackathon Berlin Quantum Hackathon “We're probing quantum utility by extracting combinatorially hard scheduling subproblems and encoding them to fit NISQ-sized QPUs while keeping circuits as shallow as possible. With Kipu's proven Iskay Optimizer, we can study solution-quality distributions in a hardware-realistic setting.” DC The Depth Compressors P. Kulkarni & A. Atre · BVG Optimization Challenge Hackathon mentor “BVG's use case represents a highly complex combinatorial optimization challenge. It was inspiring to see the energy it generated across the teams, combining advanced classical and quantum approaches.” AG Alejandro Gomez Cadavid Quantum Optimization Lead, Kipu Quantum [I’m ready to build](https://2dqpz5.share-eu1.hsforms.com/22nIlsuWuTAi5q3fMEseAUw?utm_source=kipu-website&utm_medium=iskay-page) ## Performant now. Better later. Iskay matches the best classical solvers on real IBM hardware today, and its advantage compounds as problems scale beyond what classical and QUBO methods can reach. Qubits required to encode a drone vehicle-routing problem, log scale. Lower is better. Qubits required to encode a drone vehicle-routing problem: QUBO (QAOA, others) versus native HUBO (Kipu) Problem size (delivery sites) QUBO qubits (QAOA, others) HUBO qubits (native, Kipu) 10 sites, 2 drones 55 20 50 sites, 5 drones 77K 250 100 sites, 10 drones 5M 1K 500 sites, 20 drones 625M 5K ~300x fewer qubits at 50 sites 5 drones ~5,000x fewer qubits at 100 sites 10 drones ~125,000x fewer qubits at 500 sites 20 drones In the most comprehensive benchmark to date, a single IBM **Heron r3** QPU matched classical solvers running on **128 vCPUs or 8 NVIDIA A100 GPUs**, reaching ground-state solutions in **14 of 20** instances in under a second. A collaboration with **IBM** and the **Zuse Institute Berlin**. [arXiv 2603.13607](https://arxiv.org/abs/2603.13607) The runtime edge becomes more pronounced as system size grows (arXiv 2505.08663). This sparse cubic VRP is expected to surpass classical runtime near 275 HUBO qubits (roughly 50 delivery sites with a 5-drone fleet), denser problems near 85, and richer constraints such as time windows lower it to 50–60 (Kipu Complexity Index). [See the demo.](https://hub.kipu-quantum.com/marketplace/use-cases/ecea3775-e56f-49c0-9037-34f215c9e123/demo) ## The research behind it Peer-reviewed and preprint work laying the groundwork for Kipu’s quantum optimization. [Quantum Feature Selection with Higher-Order Binary Optimization on Trapped-Ion HardwareIonQ · 2026-04](https://arxiv.org/abs/2604.26834)[Protein folding on a 64-qubit trapped-ion hardware via counterdiabatic quantum optimizationIonQ · 2026-04](https://arxiv.org/abs/2604.26861)[The Quest for Quantum Advantage in Combinatorial Optimization: End-to-end Benchmarking of Quantum Solvers vs. Multi-core Classical SolversIBM + Zuse · 2026-03](https://arxiv.org/abs/2603.13607)[Large-scale portfolio optimization on a trapped-ion quantum computerIonQ · 2026-02](https://arxiv.org/abs/2602.23976)[Constant Depth Digital-Analog Counterdiabatic Quantum ComputingarXiv · 2026-01](https://arxiv.org/abs/2601.01154)[Scaling advantage with quantum-enhanced memetic tabu search for LABSNVIDIA · 2025-11](https://arxiv.org/abs/2511.04553)[Quantum Combinatorial Reasoning for Large Language ModelsarXiv · 2025-10](https://arxiv.org/abs/2510.24509)[Hybrid Sequential Quantum ComputingarXiv · 2025-10](https://arxiv.org/abs/2510.05851)[Sequential Quantum ComputingarXiv · 2025-06](https://arxiv.org/abs/2506.20655)[Protein folding with an all-to-all trapped-ion quantum computerIonQ · 2025-06](https://arxiv.org/abs/2506.07866)[Runtime Quantum Advantage with Digital Quantum OptimizationarXiv · 2025-05](https://arxiv.org/abs/2505.08663)[Branch-and-bound digitized counterdiabatic quantum optimizationarXiv · 2025-04](https://arxiv.org/abs/2504.15367)[Quantum Optimization Benchmark Library - The Intractable DecathlonNature Computational Science · 2025-04](https://doi.org/10.1038/s43588-026-00991-1)[Efficient DCQO Algorithm within the Impulse Regime for Portfolio OptimizationPhys. Rev. Applied · 2023-08](https://doi.org/10.1103/PhysRevApplied.22.054037)[Digitized-Counterdiabatic Quantum OptimizationPhys. Rev. Research · 2022-01](https://doi.org/10.1103/PhysRevResearch.4.L042030)[Digitized-counterdiabatic quantum approximate optimization algorithmPhys. Rev. Research · 2021-07](https://doi.org/10.1103/PhysRevResearch.4.013141) [I’m ready to build](https://2dqpz5.share-eu1.hsforms.com/22nIlsuWuTAi5q3fMEseAUw?utm_source=kipu-website&utm_medium=iskay-page) ## Questions, answered What algorithm powers Iskay? Bias-field digitized counterdiabatic quantum optimization (BF-DCQO). It is non-variational, so it runs as a purely iterative loop with no classical parameter training to get stuck in. Counterdiabatic protocols compress circuit depth to fit today's gate-based devices, and each round updates bias fields from the lowest-energy samples to steer the next evolution toward better solutions. What problems can Iskay solve? Any unconstrained binary optimization problem, both QUBO (quadratic) and HUBO (higher-order), with higher-order terms run natively. Demonstrated applications include portfolio selection in finance on a 250-asset S&P 500 universe, optical-fibre routing and wavelength assignment in telecommunications validated in a live operator pilot, supply chain, fleet routing and job-shop scheduling in logistics, and protein folding and dense spin-glass models in materials and life sciences. Why solve HUBO natively instead of converting to QUBO? Forcing a higher-order problem into a quadratic QUBO form requires auxiliary qubits, and the qubit count explodes as the problem grows. A 100-site routing problem needs roughly five million QUBO qubits but only about a thousand native HUBO qubits. Iskay encodes HUBO directly, so real problems stay within today's hardware budget and the advantage compounds with problem size. What hardware does Iskay run on? Iskay runs on IBM Quantum hardware through the Qiskit Functions Catalog, catalogued as kipu-quantum/iskay-quantum-optimizer. The same BF-DCQO engine is available as Miray on the Kipu Quantum Hub, where it also runs on IonQ, Rigetti, QuEra and more. How do I get started? Load Iskay from the IBM Qiskit Functions Catalog and pass your objective function, or run Miray on the Kipu Quantum Hub. Pre- and post-processing are managed, so you only provide the problem. See the documentation for setup and the Hub pricing for plans. ## Available now on the IBM Qiskit Functions Catalog and the Kipu Quantum Hub [Iskay on IBM Qiskit](https://quantum.cloud.ibm.com/docs/en/guides/kipu-optimization)[Miray on the Hub](https://hub.kipu-quantum.com/marketplace/services/4d055207-e40f-49d0-ad43-d27a44f4cbeb/) --- # Rimay Quantum Feature Extraction URL: https://kipu-quantum.com/rimay # Rimay Quantum Feature Extraction A quantum machine learning service by Kipu Quantum that enriches tabular data, lifting the accuracy of your existing models. [I’m ready to build](/academy)[Open Rimay in the marketplace](https://hub.kipu-quantum.com/marketplace/services/f7375dbc-41ff-448f-9960-1e5f899fcf16/) ## Quantum features, into your Python pipeline Upload a tabular dataset to a Hub data pool, run Rimay, and it writes back quantum features as NumPy arrays: a quantum-transformed value for every feature plus hardware-aware correlations between coupled features. Drop them straight into `scikit-learn`, `XGBoost` or `PyTorch`. The same workflow runs unchanged on the free IBM Aer simulator and on IBM Heron hardware. Switch by naming a backend. Rimay is a quantum feature extraction service for machine learning, it computes enriched quantum features from your tabular data and hands them back to your existing classical models. [Try Rimay Simulator](https://hub.kipu-quantum.com/marketplace/services/c486bb09-7827-4324-a655-6ddb135d0ed9/)[See pricing](/pricing) Rimay Simulator · FreeRimay · IBM Quantum rimay\_simulator.py ``` import json, numpy as np from qhub.api.platform.client import HubPlatformClient from qhub.service.client import HubServiceClient # 1. Upload your tabular data to a Hub data pool (the file must be data.json). pools = HubPlatformClient(api_key=QHUB_ACCESS_TOKEN, organization_id=ORG_ID).data_pools dataset = { "training_tabular_data": X_train.to_dict(), # <= 15 features, >= 20 rows "training_target_data": y_train.to_dict(), "test_tabular_data": X_test.to_dict(), "test_target_data": y_test.to_dict(), } src = pools.create_data_pool(name="Rimay input") pools.add_data_pool_file(id=src.id, file=("data.json", json.dumps(dataset).encode())) dst = pools.create_data_pool(name="Rimay output") # 2. Extract quantum features on the free IBM Aer simulator. client = HubServiceClient( access_key_id=ACCESS_KEY_ID, secret_access_key=SECRET_KEY, service_endpoint=SERVICE_ENDPOINT, ) client.run(request={ "input_data_pool": {"id": src.id, "ref": "DATAPOOL"}, "output_data_pool": {"id": dst.id, "ref": "DATAPOOL"}, "num_shots": 500, "num_runs": 1, }).result() # 3. Single-body expectations + two-body correlations, ready for any classifier. Xq_train = np.load("1_Xq_train_0.npy") model = XGBClassifier().fit(Xq_train, y_train) ``` ## Join the Kipu Academy New to quantum machine learning? Kipu Academy teaches you to apply Rimay and quantum feature extraction hands-on, from your first workflow to a certified application on real quantum hardware. [I’m ready to build](/academy) Business and Technical tracks. Cohorts start at ten learners. Hands-on Rimay lab Build a quantum feature extraction pipeline end to end and run it on real quantum hardware. Quantum-classical workflows Learn to fold quantum features into your existing scikit-learn, XGBoost and PyTorch stack. Certify your skills Ship your own quantum-centric application and earn a Kipu Academy certificate. Learn with a cohort Weekly sessions with Kipu engineers and fellow practitioners, across Business and Technical tracks. ## What leaders are saying IBM “Kipu Quantum's quantum feature extraction is a great example of a cost-effective way to run hybrid QML workflows \[…\] with our quantum hardware delivering accurate results across a wide range of applications.” SC Scott Crowder Vice President, IBM Quantum Adoption Global Quantum Intelligence “Kipu's off-line surrogate framework achieves economic quantum advantage, capturing the 2–3% accuracy gains of a quantum processor while running inference entirely on classical hardware \[…\] actively applied to high-volume enterprise problems.” AK André König CEO, Global Quantum Intelligence QPU during training only, classical deployment Off-line surrogate framework · [arXiv 2605.19801](https://arxiv.org/abs/2605.19801) On the QPU Quantum extracts A quantum processor encodes a representative subsample of your data into many-body spin dynamics and reads out single-body expectations and two-body correlations. Train once Surrogate learns A lightweight classical model learns the quantum-induced representation. Quantum feature mappings are stable across backends, so it generalises reliably. In production Deploy classical Every prediction runs on classical hardware: microsecond latency, no quantum queue, and the same MLOps and procurement as any classical model. NTT DATA “Kipu's quantum feature surrogate framework marries quantum-derived representations with the classical infrastructure enterprises already trust: measurable accuracy gains, zero quantum dependency at inference. We are ready.” RN Rika Nakazawa Chief Commercial Innovation, NTT DATA MOEVE “Through the Kipu Quantum Hub we are optimizing classical models in image classification for predictive maintenance \[…\] using thermographic drone imagery for early detection of issues in our energy parks.” EV Estela Vilches Head of Digital Innovation, MOEVE KPMG “The scope of this technology is intentionally broad and industry-agnostic \[…\] letting enterprises leverage the computational advantages of quantum systems across their entire portfolio of data-intensive challenges today.” AK Aaron Kemp Senior Director Quantum Research & Enterprise Innovation, KPMG US [I’m ready to build](/academy) ## The research behind it Peer-reviewed and preprint work on quantum feature extraction and quantum-enhanced machine learning from Kipu Quantum. [Off-line quantum-advantage feature extraction for industrial productionarXiv · 2026-05](https://arxiv.org/abs/2605.19801)[Hybrid Quantum-Classical Model That Combines Spatial-Temporal EEG and Digitized Counterdiabatic Quantum Features for Motor Imagery ClassificationMayo Clinic · 2026-05](https://www.mayoclinicproceedings.org/article/S0025-6196\(26\)18494-8/fulltext)[Quantum Feature Selection with Higher-Order Binary Optimization on Trapped-Ion HardwareIonQ · 2026-04](https://arxiv.org/abs/2604.26834)[Quantum-enhanced satellite image classificationKPMG · 2026-02](https://arxiv.org/abs/2602.18350)[Analog Quantum Feature Selection with Neutral-Atom Quantum ProcessorsarXiv · 2025-10](https://arxiv.org/abs/2510.20798)[Digitized Counterdiabatic Quantum Feature ExtractionarXiv · 2025-10](https://arxiv.org/abs/2510.13807)[Quenched Quantum Feature MapsarXiv · 2025-08](https://arxiv.org/abs/2508.20975)[Digital-analog quantum convolutional neural networks for image classificationPhys. Rev. Research · 2024-12](https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.6.L042060) [I’m ready to build](/academy) ## Questions, answered What is Rimay? Rimay is Kipu Quantum's quantum feature extraction service. It transforms classical tabular data into richer quantum feature representations that boost the accuracy of standard machine learning models. Rimay runs as a managed service on the Kipu Quantum Hub, where it executes on IBM quantum hardware, and as a free simulator service for development and testing. What does quantum feature extraction actually produce? For each row of your dataset, Rimay returns two kinds of quantum-derived features: single-body expectation values, one quantum-transformed value per feature, and two-body correlations between pairs of features whose qubits are physically coupled in the backend's topology. These are concatenated into a new feature matrix you append to or swap in for your classical features, then train any classifier on top. How does Rimay extract features? Rimay encodes your classical features into the dynamics of many-body spin Hamiltonians on a quantum processor, then reads out expectation values of low- and higher-order observables. This captures statistical dependencies and higher-order correlations that classical preprocessing struggles to reach. Feature-to-qubit mapping is hardware-aware: features are assigned to qubits based on their correlation and the processor's coupling map. Do I need a quantum computer in production? No. With Kipu Quantum's off-line quantum feature surrogate framework, the quantum processor runs only during a targeted training stage on a small representative subsample, as little as 20 percent of the data. A lightweight classical surrogate then learns the quantum-induced representation and runs every prediction. Deployment is fully classical: microsecond inference latency, no quantum queue, and the same MLOps and procurement profile as any classical model. This delivers at least five times fewer quantum executions for the same accuracy. What hardware and limits does Rimay support? The free Rimay Simulator runs on the IBM Aer simulator with up to 15 features and 1,000 samples, ideal for prototyping. The managed Rimay service runs on the IBM Aer simulator up to 25 features or on IBM Heron quantum processors (ibm\_kingston, ibm\_torino, ibm\_pittsburgh, ibm\_fez, ibm\_marrakesh) up to 133 or 156 qubits, with up to 20,000 samples. You control the number of shots and runs per execution. How does Rimay fit into my existing ML pipeline? You upload your training and test data to a Hub data pool, run Rimay with a chosen backend, and the service writes the quantum features back as NumPy arrays. From there the features drop straight into your existing scikit-learn, XGBoost, or PyTorch workflow. An optional inference mode applies the same quantum transformation to new, unlabeled data. How is Rimay different from Iskay and Miray? Rimay, Iskay, and Miray are distinct Kipu Quantum services. Iskay and Miray are the same optimization engine, a QUBO and HUBO solver powered by bias-field digitized counterdiabatic optimization. Rimay is a different capability: it does not solve an optimization problem, it generates quantum features from your data to improve machine learning accuracy. The three are designed to be combined on the Kipu Quantum Hub. ## Live now on the Kipu Quantum Hub. Start free on the simulator. [Try the free simulator](https://hub.kipu-quantum.com/marketplace/services/c486bb09-7827-4324-a655-6ddb135d0ed9/)[Rimay on the Hub](https://hub.kipu-quantum.com/marketplace/services/f7375dbc-41ff-448f-9960-1e5f899fcf16/) --- # Kipu Quantum CLI (qhubctl) URL: https://kipu-quantum.com/cli # Quantum from your terminal qhubctl is the Kipu Quantum Hub command line. Run optimization jobs, deploy services as production REST APIs, and manage quantum endpoints. `npm i -g @quantum-hub/qhubctl` Installs in under a minute. Requires Node.js. [Full CLI reference](https://docs.hub.kipu-quantum.com/cli-reference) ## qhubctl cheat sheet ### Authenticate - `qhubctl login -t ` Sign in with an access token from the Hub. - `qhubctl logout` Clear stored credentials. - `qhubctl get-context` Show the active organisation and project. - `qhubctl set-context` Switch the active organisation or project. ### Build - `qhubctl init` Bootstrap a project to create a service. - `qhubctl serve` Run locally with the same HTTP endpoints. - `qhubctl openapi` Generate an OpenAPI description from your types. - `qhubctl compress` Package the current project into a ZIP. ### Deploy & run - `qhubctl up` Create or update a live service endpoint. - `qhubctl run ` Create a job execution against a service. - `qhubctl services list` List all services in the current context. - `qhubctl services build-status` Show a service build status. - `qhubctl services build-logs` Stream a service build's logs. - `qhubctl datapool upload` Upload files to a data pool. [Send me the PDF](https://2dqpz5.share-eu1.hsforms.com/21zGfIFSTQ-m0Uq-3P673Fg?utm_source=kipu-website&utm_medium=cli-cheatsheet) ## Questions, answered What is qhubctl? qhubctl is the command-line interface for the Kipu Quantum Hub. From your terminal you can authenticate, scaffold a service project, run it locally, deploy it as a live REST endpoint, and submit jobs to the Hub's pre-built quantum solvers. It is the scriptable, CI-friendly companion to the Hub web app and the Hub MCP server. How do I install the Kipu Quantum CLI? Install it globally from npm with: npm i -g @quantum-hub/qhubctl. It runs on any machine with Node.js, so the same workflow works on macOS, Linux and Windows, and in CI pipelines. How do I authenticate? Run qhubctl login -t followed by your access token. You generate the token after signing in at login.hub.kipu-quantum.com. Run qhubctl logout to clear your credentials. Organisation and project context is managed with qhubctl get-context and qhubctl set-context. Can I run a service locally before deploying? Yes. qhubctl serve runs your project locally via qhub-serve and exposes the same HTTP endpoints it will have in production, so you can test against the real interface before shipping. qhubctl up then creates or updates the live service. How do I run a quantum solver from the command line? qhubctl services list shows the solvers available in your context, including Kipu's own services such as Miray and Rimay alongside 20-plus pre-built solvers and industry baselines. qhubctl run with a service id and an input file creates a job execution and returns a result you can pipe straight into the rest of your stack. Do I need quantum computing knowledge to use it? No. The CLI returns production-ready results as JSON with business outcomes rather than raw circuits, so you submit a problem and read back an answer. Pre- and post-processing are managed by the Hub. Is the CLI suitable for automation and agents? Yes. Every command supports non-interactive use and JSON output, so qhubctl fits cleanly into CI pipelines and scripts. qhubctl openapi generates an OpenAPI description of your service, and the same endpoints are callable by AI agents through the Kipu Quantum Hub MCP server. ## Create an account, grab a token, and connect to quantum hardware [Create a free account](https://login.hub.kipu-quantum.com/realms/planqk/protocol/openid-connect/registrations?client_id=planqk-login&redirect_uri=https%3A%2F%2Fhub.kipu-quantum.com%2Fmarketplace%23error%3Dlogin_required%26state%3Dd2fa07d2-c739-4635-9513-936a749c3e3b%26iss%3Dhttps%3A%2F%2Flogin.hub.kipu-quantum.com%2Frealms%2Fplanqk&state=f3f1e7bd-f713-4e07-a96a-474a377090e6&response_mode=fragment&response_type=code&scope=openid&nonce=1e76f0cc-eabb-41a1-bb9a-40298ce4f38e&code_challenge=muWbAdYk7A7HyGM1_PUt7yvnk9ENcdHbVtxzgCuZrks&code_challenge_method=S256)[Read the documentation](https://docs.hub.kipu-quantum.com/cli-reference) Generate your access token after signing in at [login.hub.kipu-quantum.com](https://login.hub.kipu-quantum.com) --- # Quantum Computing in Action URL: https://kipu-quantum.com/examples Industrial Applications # Quantum Computing in Action Explore real-world applications where quantum computing delivers measurable business value. From pharmaceutical discovery to supply chain optimization, see how leading organizations are gaining competitive advantages with Kipu Quantum Hub. ![Telecommunication Routing](/_next/static/media/photo-1772862991841-f0e3e1502d7b.1ebf9439.jpg) Telecommunications ## Telecommunication Routing Optimize optical network routing for the biggest spanish telecommunication provider. Leveraged Kipu's quantum optimization solver to push the boundaries of performance, solving the biggest RWA problem tackled on a quantum computer using HUBO solver on IBM's 156-qubit quantum device. Assign light routes and wavelengths to optical connections while avoiding interference and optimizing resource usage Developed a quantum suitable encoding of the routing and wavelength assignment problem (RWA). Integrated with IBM's 156-qubit quantum device for scalable computation \>5% efficiency Higher Margin per Call Powered by[Miray Solver](https://hub.kipu-quantum.com/marketplace/services/4d055207-e40f-49d0-ad43-d27a44f4cbeb/) ![Capital Saving](/_next/static/media/photo-1579621970563-ebec7560ff3e.2d897d61.jpg) Financial Services ## Capital Saving 10% Less Capital Locked with quantum-enabled portfolio optimization. KIPU reduced regulatory capital consumption by >10% on real-sized bank portfolios through quantum solvers, achieving minimal portfolio rebalancing and faster computation fulfilling all regulatory requirements. Reformulated capital optimization as a HUBO problem and tackled with proprietary quantum solvers Reduced capital consumption with minimal portfolio rebalancing Seamless integration with existing risk infrastructure - no disruption to regulatory workflow \>10% capital Saved Fulfilled regulations Powered by[Miray Solver](https://hub.kipu-quantum.com/marketplace/services/4d055207-e40f-49d0-ad43-d27a44f4cbeb/) ![Logistics Optimization](/_next/static/media/photo-1701313056413-0915e1adf204.c0689c1b.jpg) Automotive & Logistics ## Logistics Optimization Quantum optimization for fleet logistics and scheduling. Tackled Vehicle Routing Problem (VRP) and Capacitated VRP using Kipu's flagship algorithm on IBM hardware. Delivered by our ready-to-use solution running on our Quantum Hub to ensure easy integration. Tailor quantum algorithms to customer specific optimization challenges Benchmark scalability of quantum vs. classical methods Ready to use integration via simple API call \>12% cost Reduction 10x higher Complexity Powered by[Miray Solver](https://hub.kipu-quantum.com/marketplace/services/4d055207-e40f-49d0-ad43-d27a44f4cbeb/) ## Ready to Transform Your Industry? [Start Free Trial](https://login.hub.kipu-quantum.com/realms/planqk/protocol/openid-connect/registrations?client_id=planqk-login&redirect_uri=https%3A%2F%2Fhub.kipu-quantum.com%2Fmarketplace%23error%3Dlogin_required%26state%3Dd2fa07d2-c739-4635-9513-936a749c3e3b%26iss%3Dhttps%3A%2F%2Flogin.hub.kipu-quantum.com%2Frealms%2Fplanqk&state=f3f1e7bd-f713-4e07-a96a-474a377090e6&response_mode=fragment&response_type=code&scope=openid&nonce=1e76f0cc-eabb-41a1-bb9a-40298ce4f38e&code_challenge=muWbAdYk7A7HyGM1_PUt7yvnk9ENcdHbVtxzgCuZrks&code_challenge_method=S256)[View Pricing](/pricing) Start with a free account and explore how quantum computing can solve your specific challenges. --- # Quantum Hardware. On Your Credit Card. URL: https://kipu-quantum.com/consumption # Quantum hardware. On your credit card. We just made it radically simpler to start running on real quantum systems. Buying time on a QPU is now as simple as a credit card payment. [Start in minutes](https://login.hub.kipu-quantum.com/realms/planqk/protocol/openid-connect/registrations?client_id=planqk-login&redirect_uri=https%3A%2F%2Fhub.kipu-quantum.com%2Fmarketplace%23error%3Dlogin_required%26state%3Dd2fa07d2-c739-4635-9513-936a749c3e3b%26iss%3Dhttps%3A%2F%2Flogin.hub.kipu-quantum.com%2Frealms%2Fplanqk&state=f3f1e7bd-f713-4e07-a96a-474a377090e6&response_mode=fragment&response_type=code&scope=openid&nonce=1e76f0cc-eabb-41a1-bb9a-40298ce4f38e&code_challenge=muWbAdYk7A7HyGM1_PUt7yvnk9ENcdHbVtxzgCuZrks&code_challenge_method=S256)[See pricing](/pricing) ## Getting on quantum hardware was a project. Procurement Weeks of paperwork before any access. Contracts Framework agreements before a single run. Budgets Six-figure commitments just to start. ## Card in. Compute out. No procurement loops Start in minutes, not months. Sign up, pay, run. No framework agreements Pay only for what you run. Stop whenever you want. No legal back-and-forth Self-serve, transparent, immediate. ## 20 quantum systems. One platform. Real QPUs from IBM, QuEra, Rigetti, IQM, IonQ and Quandela, plus high-performance simulators. Choose the backend that fits your problem. No separate contracts. ### Quantum processors IBM Quantum Superconducting · Heron-class Fez156qAachen156qKingston156qMarrakesh156qPittsburgh156qBoston156qMiami120qBerlin120q QuEra Neutral-atom Aquila256q Rigetti Superconducting Cepheus-1107q IQM Superconducting Emerald54qGarnet20q IonQ Trapped-ion Forte36q Quandela Photonic Belenossoon ### Simulators AWS Braket State-vector / density-matrix SV134qDM117q Qudora Trapped-ion emulator Qamelion32q Kipu Quantum State-vector QSim30q IonQ Ideal simulator Simulator29q Quandela Photonic simulator Altairsoon ## Not a beta. A live platform. Researchers, consultants and engineers are already running real workloads on the Kipu Quantum Hub. 405 Organizations 1,843 Users 20 Backends 26 Countries ## Teams that want to build, not negotiate. ### Researchers Run experiments without institutional procurement getting in the way. ### Consultants Test quantum for clients without committing to long programs. ### Engineers Bring quantum into existing workflows with the tools you already use. ## Three steps from zero to compute. 01 ### Sign up Create your account in seconds. No sales call required. 02 ### Add a card Top up your consumption balance with a card payment. 03 ### Run on a QPU Pick a backend, submit your job, get your results. ## Bring your whole team. One organisation. Credit-card access is per person. On a commercial Plus plan, your organisation shares backend credentials with role-based access, so the whole team runs on one set of keys. ### Shared provider credentials An owner configures provider access tokens once, in organisation settings. Every member then runs on those backends, with no per-person key juggling. ### Role-based access Viewer, Maintainer and Owner roles govern what each member can see, create, edit or delete. ### Personal and team, separate The account-context selector keeps personal work and organisation work cleanly apart. [Connect your AI agents to the Hub](/mcp)[Managing organisations](https://docs.hub.kipu-quantum.com/manage-organizations) ## Questions, answered Which quantum computers can I access? Twenty systems on one platform. Real QPUs from IBM Quantum (eight Heron-class processors up to 156 qubits), QuEra (Aquila, 256 neutral atoms), Rigetti (Cepheus-1, 107 qubits), IQM (Emerald and Garnet), IonQ (Forte), and Quandela (Belenos, coming soon), plus high-performance simulators from AWS Braket, Qudora, Kipu Quantum and IonQ. You pick the backend that fits your problem, with no separate contract per provider. How do I pay for quantum hardware? By card. You create a Kipu Quantum Hub account, top up a consumption balance with a credit-card payment, and pay only for the jobs you run. There is no framework agreement and no minimum commitment, and you can stop whenever you want. Do I need a contract or a procurement process? No. Access is self-serve. There is no procurement loop, no framework agreement and no legal back-and-forth: you sign up, add a card, pick a backend and submit your job. Most users go from sign-up to a running job in minutes. Can my whole team share access? Yes, on a commercial Plus plan. An organisation owner or maintainer configures provider access tokens once, and every member then runs jobs on those shared backend credentials. Role-based access for Viewer, Maintainer and Owner governs what each member can create, edit or delete, and personal and organisation work stay cleanly separated. What can I run on the hardware? Your own circuits, or Kipu Quantum's production solvers for combinatorial optimization, quantum feature extraction and sampling. The solvers run the same way across backends, so you can compare hardware without rewriting your problem. Is this a production platform or a beta? A live production platform. Researchers, consultants and engineers across more than twenty-five countries already run real workloads on the Kipu Quantum Hub. ## And there is more on the way. Easy hardware access is step one. In a few days, new packages will pair this credit-card access with our solvers, so you can go from a problem statement to a running quantum-classical solution without rewiring anything. Stay tuned for names, scope, and pricing. ## What is keeping your team from quantum? Budget, skills, access, trust: we genuinely want to hear it. [Sign up & top up](https://login.hub.kipu-quantum.com/realms/planqk/protocol/openid-connect/registrations?client_id=planqk-login&redirect_uri=https%3A%2F%2Fhub.kipu-quantum.com%2Fmarketplace%23error%3Dlogin_required%26state%3Dd2fa07d2-c739-4635-9513-936a749c3e3b%26iss%3Dhttps%3A%2F%2Flogin.hub.kipu-quantum.com%2Frealms%2Fplanqk&state=f3f1e7bd-f713-4e07-a96a-474a377090e6&response_mode=fragment&response_type=code&scope=openid&nonce=1e76f0cc-eabb-41a1-bb9a-40298ce4f38e&code_challenge=muWbAdYk7A7HyGM1_PUt7yvnk9ENcdHbVtxzgCuZrks&code_challenge_method=S256)Talk to us --- # Choose Your Quantum-centric AI Journey URL: https://kipu-quantum.com/pricing # Choose Your Quantum-centric Intelligence Journey ### Free €0 [Start Free](https://login.hub.kipu-quantum.com/realms/planqk/protocol/openid-connect/registrations?client_id=planqk-login&response_type=code&scope=openid&redirect_uri=https%3A%2F%2Fhub.kipu-quantum.com) Perfect for getting started and exploring quantum computing fundamentals. Runtime Environment Workflow Designer 5€ Total Consumption AI Matchmaker Community Forum Learning Material ### Plus €50 per month [Sign Up](https://hub.kipu-quantum.com/settings/billing/subscription) For professionals building quantum applications. Runtime Environment 5 Workflow Designers 20€/month Consumption 30q Simulator AI Matchmaker Community Forum Learning Material Most Popular ### Team Available Soon Early Access For teams building production quantum applications. Commercial Usage Runtime Environment 10 Workflow Designers 100€/month Consumption 30q Simulator AI Matchmaker Community Forum Learning Material Weekly Cohort Meeting Support Messenger ### Enterprise Custom Contact Sales Advanced features and dedicated support for large organizations. Commercial Usage Runtime Environments Unlimited Workflow Designers Custom Consumption Package 30q Simulator AI Matchmaker Community Forum Learning Material Weekly Cohort Meeting Support Messenger Custom Consulting We are dedicated to the community. Free plan stays free. Upgrades available and Pay-as-you-go included in all tiers. Yearly Research ## Compare All Features Enterprise solutions Research Feature Free Plus Team Enterprise Monthly Price Free €50 Coming Soon Custom Yearly Price Free €500 Coming Soon Custom Seats Single Single Coming Soon Unlimited API Access \- Custom Integrations \- \- \- Direct Support \- \- Hardware Access IBM Pay-as-you-go IonQ Pay-as-you-go IQM Pay-as-you-go QuEra Pay-as-you-go Rigetti Pay-as-you-go Hybrid Applications and Tools Workflow Designer [AI Matchmaker](/?matchmaker=1) Runtime Environment [Rimay Quantum](https://hub.kipu-quantum.com/marketplace/services/f7375dbc-41ff-448f-9960-1e5f899fcf16/) \- Trial [Rimay Simulator (15q)](https://hub.kipu-quantum.com/marketplace/services/c486bb09-7827-4324-a655-6ddb135d0ed9/) [Miray Quantum](https://hub.kipu-quantum.com/marketplace/services/4d055207-e40f-49d0-ad43-d27a44f4cbeb/) \- Trial [Miray Simulator (20q)](https://hub.kipu-quantum.com/marketplace/services/5d617061-92d5-443e-a58a-d41ce20c098b/) ## Frequently Asked Questions Get answers to common questions about our pricing ### What's the difference between commercial and non-commercial plans? Commercial plans are designed for businesses and enterprises using quantum computing for commercial purposes. Non-commercial plans are exclusively for academic institutions, research organizations, and educational purposes with special pricing. ### Can I switch between monthly and yearly billing? Yes! You can switch between monthly and yearly billing at any time. Yearly billing provides significant savings compared to monthly payments. Changing from monthly to yearly billing gives you access to the full yearly consumption package after payment. Monthly packages renew each end of billing cycle. ### What happens if I exceed my compute resources? Your jobs will be queued until resources become available or the next billing cycle begins. You can upgrade your plan anytime for increased resources and priority access. ### Do you offer discounts for yearly subscriptions? Yes, annual subscriptions provide approximately 8-10% savings compared to paying monthly. The exact discount is reflected in our yearly pricing. ### Can I upgrade or downgrade my plan? Absolutely! You can change your plan at any time. Upgrades take effect immediately, and downgrades apply at the start of your next billing cycle. ### Is there academic verification required for non-commercial plans? Yes, non-commercial plans require verification of your academic or research institution status. We'll guide you through this simple process during signup. ## Still Have Questions? Contact Sales[Start Free Trial](https://login.hub.kipu-quantum.com/realms/planqk/protocol/openid-connect/registrations?client_id=planqk-login&redirect_uri=https%3A%2F%2Fhub.kipu-quantum.com%2Fmarketplace%23error%3Dlogin_required%26state%3Dd2fa07d2-c739-4635-9513-936a749c3e3b%26iss%3Dhttps%3A%2F%2Flogin.hub.kipu-quantum.com%2Frealms%2Fplanqk&state=f3f1e7bd-f713-4e07-a96a-474a377090e6&response_mode=fragment&response_type=code&scope=openid&nonce=1e76f0cc-eabb-41a1-bb9a-40298ce4f38e&code_challenge=muWbAdYk7A7HyGM1_PUt7yvnk9ENcdHbVtxzgCuZrks&code_challenge_method=S256) Our team is here to help you find the right plan for your needs. --- # About Kipu Quantum URL: https://kipu-quantum.com/about # About Kipu Quantum We are pioneers in quantum-centric intelligence, making quantum computing frictionless to enterprises, researchers, and institutions worldwide. ## Our Mission Kipu Quantum Hub is dedicated to democratizing quantum computing by providing enterprise-ready solutions that require no prior quantum expertise. We bridge the gap between cutting-edge quantum research and real-world industrial applications. Founded by leading quantum computing researchers and industry experts, we've built a comprehensive platform that serves over 40,000 users across 50+ countries. Our team combines deep theoretical knowledge with practical engineering excellence to deliver solutions that solve today's most complex computational challenges. We believe quantum computing will revolutionize industries from pharmaceuticals to finance, and we're committed to making this transformation accessible to organizations of all sizes. Through our cloud platform, advanced algorithms, and expert support, we empower our clients to achieve quantum advantage today. ## Areas of Expertise Our multidisciplinary team excels across the full spectrum of quantum computing ### Quantum Algorithms Developing cutting-edge algorithms for optimization, simulation, and machine learning ### Quantum Hardware Integration with 20+ quantum computing backends and continuous hardware partnerships ### Enterprise Solutions Industry-specific applications in finance, pharmaceuticals, logistics, and manufacturing ### Research & Development Publishing breakthrough research and advancing the field of quantum computing ### Cloud Infrastructure Scalable, secure cloud platform serving 40,000+ users globally ### Education & Training Comprehensive learning resources and expert support for quantum practitioners ## Our Team World-class researchers, engineers, and innovators advancing quantum computing ![Raphael Neef](/_next/static/media/RaphaelNeef.bf50a622.jpg) View ![Dr. Murilo Oliveira](/_next/static/media/MuriloOliveira.19300261.jpg) View ![Dr. Tobias Grab](/_next/static/media/TobiasGrab.0d058d2e.jpg) View ![Sara Schöne](/_next/static/media/SaraSchoene.5270c1e0.jpg) View ![Antonio Ferrer Sánchez](/_next/static/media/image-7.690c24d3.png) View ![Tuan Fachinetti Meireles](/_next/static/media/TuanFachinettiMeireles.8662ebf3.jpg) View ![Michael Wurster](/_next/static/media/MichaelWurster.6380447a.jpg) View ![Dr. Florian Schöne](/_next/static/media/FlorianSchoene.e374b316.jpg) View ![Dr. Michael Falkenthal](/_next/static/media/MichaelFalkenthal.229fea64.jpg) View ![Dr. David Niehaus](/_next/static/media/DavidNiehaus.0ae65258.jpg) View ![Dr. Jan Trautmann](/_next/static/media/JanTrautmann.20a72620.jpg) View ![Xiaoxin Xao](/_next/static/media/XiaoxinXiao.df948033.jpg) View ![Dr. Sebastian Wagner](/_next/static/media/SebastianWagner.491f3aa0.jpg) View ![Jonathan Jones](/_next/static/media/JonathanJones.287fbf29.png) View ![Mathias Radtke](/_next/static/media/MathiasRadtke.0a89769a.png) View ![David Rodriguez](/_next/static/media/DavidRodriguez.d3432b36.jpg) View ![Dr. Qi Zhang](/_next/static/media/QiZhang.e7af651e.jpg) View ![Anton Simen Albino](/_next/static/media/image-6.7bd35086.png) View ![Dr. Eric Michon](/_next/static/media/EricMichon.e5743fdc.jpg) View ![Dr. Francisco Albarrán](/_next/static/media/FranciscoAlbarran.081553d5.jpg) View ![Carlos Flores](/_next/static/media/image-9.4413cb6e.png) View ![Tristan Steindor](/_next/static/media/TristanSteindor.012e0052.png) View ![Dr. Pavle Nikacevic](/_next/static/media/PavleNikacevic.a269cfee.jpg) View ![Dr. Mahul Pandey](/_next/static/media/MahulPandey.5396b23d.jpg) View ![Jane Leliveld](/_next/static/media/JaneLeliveld.db7d5f88.jpg) View ![Dr. Stefano Melchionna](/_next/static/media/StefanoMelchionna.d77a09d8.jpg) View ![Dr. Gabriel Dario Alvarado Barrios](/_next/static/media/GabrielDarioAlvaradoBarrios.41d74544.jpg) View ![Dr. Lukas Harzenetter](/_next/static/media/LukasHarzenetter.9df61dc8.jpg) View ![Pranav Chandarana](/_next/static/media/PranavChandarana.5348aefc.jpg) View ![Alejandro Gómez Cadavid](/_next/static/media/image-4.4deb7e83.png) View ![Prof. Dr. Enrique Solano](/_next/static/media/EnriqueSolano.4ecf856c.jpg) View ![Christoph Krieger](/_next/static/media/image-10.a12b9a00.png) View ![Robert Lahmann](/_next/static/media/RobertLahmann.30835849.jpg) View ![Dr. Gernot Füchsel](/_next/static/media/GernotFuechsel.b2299bbf.jpg) View ![Dr. Narendra Hegade](/_next/static/media/NarendraHegade.0cf8d9ee.jpg) View ![Ingo Uhlemann](/_next/static/media/IngoUhlemann.7787b26c.jpg) View View ## Join Our Team [Open Positions](https://kipu-quantum.jobs.personio.com/) We're always looking for talented individuals passionate about quantum computing. Help us shape the future of technology. --- # Contact URL: https://kipu-quantum.com/contact # Contact Your dedicated contacts at Kipu Quantum ![Jonathan Jones](/_next/static/media/JonathanJones.287fbf29.png) ## Jonathan Jones Head of Sales Region · UKI · NA · ROW Get in touch ![Tuan Fachinetti Meireles](/_next/static/media/TuanFachinettiMeireles.8662ebf3.jpg) ## Tuan Fachinetti Meireles Account Executive Region · LATAM Get in touch ![Robert Lahmann](/_next/static/media/RobertLahmann.30835849.jpg) ## Robert Lahmann Customer Success Manager Region · DACH Get in touch ## General contact Kipu Quantum GmbH Greifswalder Str. 212 10405 Berlin Germany Telephone: [+49 721 61902038](tel:+4972161902038) Email: [info@kipu-quantum.com](mailto:info@kipu-quantum.com) --- # Paper URL: https://kipu-quantum.com/paper # Paper Explore our latest research and publications in quantum computing Search papers by title, author, or abstract 20.05.2026 ### Off-line quantum-advantage feature extraction for industrial production Carlos Flores-Garrigós, Gabriel D. Alvarado Barrios, Qi Zhang, Anton Simen, Enrique Solano Quantum computing is no longer a lab curiosity for academic research. Industrial processors exceeding 100 qubits are commercially accessible and, for the first time, can extract information from data in ways that classical algorithms struggle to match. The most direct way to monetize this capability for industrial production today is quantum feature extraction: turning raw business data (images, customer records, molecules, or sensor readings) into richer representations that outperform standard machine learning models. There is one obstacle, however, that stands between today's demonstrations and tomorrow's production systems: every sample of data costs a quantum computing execution, making per-sample processing on quantum hardware unviable at enterprise scale. This work introduces quantum feature surrogates, a framework developed by Kipu Quantum that breaks this bottleneck. Instead of asking the quantum computer to look at every single sample, the framework lets it process a small, carefully chosen subsample whose distribution faithfully represents the full set. A simple classical surrogate model then learns the quantum-induced patterns and applies them to the rest of the dataset at near-zero cost. The quantum processor stops being a per-sample engine and becomes a teacher of representations, while production inference runs entirely on classical hardware. We demonstrate at least 5× fewer quantum executions for the same accuracy and substantially more as data volumes grow, classical inference at deployment with no quantum queue or per-prediction latency penalty, and accuracy matching the full quantum baseline on a real satellite-image benchmark (87% vs. an 84% ResNet-50 classical baseline, equalling the full quantum pipeline at one fifth of the quantum cost). The framework is industry-ready across satellite image classification, customer analytics, medical imaging, drug screening, churn prediction, and many more high-volume enterprise workloads. [Read Paper](https://arxiv.org/abs/2605.19801) 04.05.2026 ### Hybrid Quantum-Classical Model That Combines Spatial-Temporal EEG and Digitized Counterdiabatic Quantum Features for Motor Imagery Classification Carter RE, Wieczorek MA, Pacheco-Spann LM, Li F, Dougherty JM, Johnson PW, Wenzel B, Pandey M, Dalal A, Solano E, Yilmazer K, Soekadar SR, Thielen KR, Bruce CJ A hybrid quantum-classical model for motor imagery classification from electroencephalogram (EEG) waveforms, combining deep-learning spatial-temporal feature extraction with digitized counterdiabatic quantum features. Trained on 50 participants from a published, de-identified data set and evaluated on a held-out participant, the model reached 88.8% classification accuracy (AUROC 0.962) on motor-imagery EEG, demonstrating that quantum-enriched features can robustly classify brain signals and setting a foundation for quantum computing in healthcare. A Mayo Clinic and Kipu Quantum collaboration. [Read Paper](https://www.mayoclinicproceedings.org/article/S0025-6196\(26\)18494-8/fulltext) 29.04.2026 ### Quantum Feature Selection with Higher-Order Binary Optimization on Trapped-Ion Hardware Carlos Flores-Garrigós, Anton Simen, Qi Zhang, Enrique Solano, Narendra N. Hegade, Sayonee Ray, Claudio Girotto, Jason Iaconis, Martin Roetteler We present a quantum feature-selection framework based on a higher-order unconstrained binary optimization (HUBO) formulation that explicitly incorporates multivariate dependencies beyond standard quadratic encodings. In contrast to QUBO-based approaches, the proposed model includes one-, two-, and three-body interaction terms derived from mutual-information measures, enabling the objective function to capture feature relevance, pairwise redundancy, and higher-order statistical structure within a unified energy model. To suppress trivial all-selected solutions, we further include structured linear penalties that promote sparsity while preserving informative variables. The resulting HUBO instances are optimized with digitized counterdiabatic quantum optimization on IonQ Forte and compared against noiseless quantum simulation as well as two classical dimensionality-reduction baselines: SelectKBest based on mutual information and principal component analysis (PCA). We evaluate the proposed workflow on two benchmark classification datasets, namely the Gallstone dataset and the Spambase dataset, and analyze both predictive performance and selected-subset structure. The results show good qualitative agreement between hardware executions and noiseless simulations, supporting the feasibility of implementing higher-order feature-selection Hamiltonians on current trapped-ion processors. In addition, the quantum approach yields competitive classification performance while producing compact and informative feature subsets, highlighting the potential of higher-order quantum optimization for machine-learning preprocessing tasks. [Read Paper](https://arxiv.org/abs/2604.26834) 29.04.2026 ### Protein folding on a 64-qubit trapped-ion hardware via counterdiabatic quantum optimization Alejandro Gomez Cadavid, Pavle Nikačević, Pranav Chandarana, Sebastián V. Romero, Enrique Solano, Narendra N. Hegade, Miguel Angel Lopez-Ruiz, Claudio Girotto, Hanna Linn, Hakan Doga, Evgeny Epifanovsky, Panagiotis Kl. Barkoutsos, Ananth Kaushik, Martin Roetteler We report the largest trapped-ion hardware demonstration of lattice protein-folding optimization to date, using bias-field digitized counterdiabatic quantum optimization (BF-DCQO) on a fully connected 64-qubit Barium development system similar to the forthcoming IonQ Tempo line. Six peptide sequences with 14-16 amino-acid residues are encoded using a coarse-grained tetrahedral lattice model, yielding higher-order spin-glass Hamiltonians with long-range interactions involving up to five-body terms and mapped to 46-61 qubits. The resulting instances are demanding for near-term quantum hardware because low-energy configurations must satisfy backbone-geometry constraints while optimizing dense residue-contact interactions. BF-DCQO uses a non-variational bias-feedback mechanism, where low-energy samples from each round define longitudinal fields that guide subsequent quantum evolutions. Across the studied instances, BF-DCQO shifts raw sampled energy distributions toward lower energies than uniform random sampling, with the strongest improvements appearing in residue-contact variables. To preserve this signal, we introduce a consensus-based post-processing pipeline that combines quantum-learned contact information with feasible backbone geometries. The resulting hybrid workflow reaches the classical reference energy in multiple instances and improves over the corresponding random-seeded pipeline. These results show that BF-DCQO can generate structured samples for dense protein-folding Hamiltonians at previously unexplored trapped-ion scales. [Read Paper](https://arxiv.org/abs/2604.26861) 13.03.2026 ### The Quest for Quantum Advantage in Combinatorial Optimization: End-to-end Benchmarking of Quantum Solvers vs. Multi-core Classical Solvers Pranav Chandarana, Alejandro Gomez Cadavid, Enrique Solano, Thorsten Koch, Stefan Woerner, Narendra N. Hegade We perform an end-to-end benchmark of a hybrid sequential quantum computing (HSQC) solver for higher-order unconstrained binary optimization (HUBO), executed on IBM Heron r3 quantum processors to evaluate the potential of current quantum hardware for combinatorial optimization with sub-second end-to-end runtimes. All reported runtimes include the complete pipeline (from preprocessing to QPU execution and postprocessing) under strict wall-clock accounting. Across 20 benchmark instances, a single hybrid attempt produces high-quality solutions in less than one second, matching the ground-state energy in 14 cases. At the same runtime, CPU-based solvers, including simulated annealing, memetic tabu search, and EasySolve, do not reach the value obtained by HSQC, whereas an enhanced parallel tempering method and the GPU-accelerated solver ABS3 reach or surpass it. These results show that HSQC, executed on a single QPU, can achieve performance competitive with strong classical solvers running on 128 vCPUs or 8 NVIDIA A100 GPUs, while also providing a reproducible system-level benchmark for tracking progress as quantum hardware and hybrid sequential workflows improve. [Read Paper](https://arxiv.org/abs/2603.13607) 13.03.2026 ### Digitized counterdiabatic quantum critical dynamics Anne-Maria Visuri, Alejandro Gomez Cadavid, Balaganchi A. Bhargava, Sebastián V. Romero, András Grabarits, Pranav Chandarana, Enrique Solano, Adolfo del Campo, Narendra N. Hegade We experimentally demonstrate that a digitized counterdiabatic quantum protocol reduces the number of topological defects created during a fast quench across a quantum phase transition. To show this, we perform quantum simulations of one- and two-dimensional transverse-field Ising models driven from the paramagnetic to the ferromagnetic phase. We utilize superconducting cloud-based quantum processors with up to 156 qubits. Our data reveal that the digitized counterdiabatic protocol reduces defect formation by up to 48% in the fast-quench regime -- an improvement hard to achieve through digitized quantum annealing under current noise levels. The experimental results closely match theoretical and numerical predictions at short evolution times, before deviating at longer times due to hardware noise. In one dimension, we derive an analytic solution for the defect number distribution in the fast-quench limit. For two-dimensional geometries, where analytical solutions are unknown and numerical simulations are challenging, we use advanced matrix-product-state methods. Our findings indicate a practical way to control the topological defect formation during fast quenches and highlight the utility of counterdiabatic protocols for quantum optimization and quantum simulation in material design on current quantum processors. [Read Paper](https://doi.org/10.1038/s41534-026-01208-z) 02.03.2026 ### Analog Counterdiabatic Quantum Computing Qi Zhang, Narendra N. Hegade, Alejandro Gomez Cadavid, Lucas Lassabli\`ere, Jan Trautmann, S´ebastien Perseguers, Enrique Solano, Lo¨ıc Henriet, Eric Michon We propose analog counterdiabatic quantum computing (ACQC) to tackle combinatorial optimization problems on neutral-atom quantum processors. While these devices allow for the use of hundreds of qubits, adiabatic quan- tum computing struggles with non-adiabatic errors, which are inevitable due to the hardware’s restricted coherence time. We design counterdiabatic proto- cols to circumvent those limitations via ACQC on analog quantum devices with ground-Rydberg qubits. To demonstrate the effectiveness of our paradigm, we experimentally apply it to the maximum independent set (MIS) problem with up to 100 qubits and show an enhancement in the approximation ratio with a short evolution time. We believe ACQC establishes a path toward quantum advantage for a variety of industry use cases. [Read Paper](https://doi.org/10.1038/s44335-026-00056-6) 27.02.2026 ### Large-scale portfolio optimization on a trapped-ion quantum computer Alejandro Gomez Cadavid, Ananth Kaushik, Pranav Chandarana, Miguel Angel Lopez-Ruiz, Gaurav Dev, Willie Aboumrad, Qi Zhang, Claudio Girotto, Sebastián V. Romero, Martin Roetteler, Enrique Solano, Marco Pistoia, Narendra N. Hegade We present an end-to-end pipeline for large-scale portfolio selection with cardinality constraints and experimentally demonstrate it on trapped-ion quantum processors using hardware-aware decomposition. Building on RMT-based correlation-matrix denoising and community detection, we identify correlated asset groups and introduce a correlation-guided greedy splitting scheme that caps each cluster by the executable qubit budget. Each cluster defines a hardware-embeddable QUBO subproblem that we solve using bias-field digitized counterdiabatic quantum optimization (BF-DCQO), a non-variational method that avoids classical parameter-training loops. We recombine low-energy candidates into global portfolios and enforce feasibility with a two-stage post-processing routine: fast repair followed by a cardinality-preserving swap local search. We benchmark the workflow on a 250-asset universe taken from the S&P 500 and execute subproblems on a 64-qubit Barium development system similar to the forthcoming IonQ Tempo line. We observe that larger executable subproblem sizes reduce decomposition error and systematically improve final objective values and risk-return trade-offs relative to randomized baselines under identical post-processing. Overall, the results establish a hardware-tested route for scaling financial optimization problems, defined by a trade space in which executable problem size and circuit cost are balanced against the resulting solution quality. [Read Paper](https://arxiv.org/abs/2602.23976) 20.02.2026 ### Quantum-enhanced satellite image classification Qi Zhang, Anton Simen, Carlos Flores-Garrigós, Gabriel Alvarado Barrios, Paolo A. Erdman, Enrique Solano, Aaron C. Kemp, Vincent Beltrani, Vedangi Pathak, Hamed Mohammadbagherpoor We demonstrate the application of a quantum feature extraction method to enhance multi-class image classification for space applications. By harnessing the dynamics of many-body spin Hamiltonians, the method generates expressive quantum features that, when combined with classical processing, lead to quantum-enhanced classification accuracy. Using a strong and well-established ResNet50 baseline, we achieved a maximum classical accuracy of 83%, which can be improved to 84% with a transfer learning approach. In contrast, applying our quantum-classical method the performance is increased to 87% accuracy, demonstrating a clear and reproducible improvement over robust classical approaches. Implemented on several of IBM’s quantum processors, our hybrid quantum-classical approach delivers consistent gains of 2-3% in absolute accuracy. These results highlight the practical potential of current and near-term quantum processors in high-stakes, data-driven domains such as satellite imaging and remote sensing, while suggesting broader applicability in real-world machine learning tasks. [Read Paper](https://arxiv.org/abs/2602.18350) 03.01.2026 ### Constant Depth Digital-Analog Counterdiabatic Quantum Computing Balaganchi A. Bhargava, Shubham Kumar, Anne-Maria Visuri, Paolo A. Erdman, Enrique Solano, Narendra N. Hegade We introduce a digital-analog quantum computing framework that enables counterdiabatic protocols to be implemented at constant circuit depth, allowing fast and resource-efficient quantum state preparation on current quantum hardware. Counterdiabatic protocols suppress diabatic excitations in finite-time adiabatic evolution, but their practical application is limited by the non-local structure of the required Hamiltonians and the resource overhead of fully digital implementations. Counterdiabatic terms can be expressed as truncated expansions of nested commutators of the adiabatic Hamiltonian and its parametric derivative. Here, we show how this algebraic structure can be efficiently realized in a digital-analog setting using commutator product formulas. Using native multi-qubit analog interactions augmented by local single-qubit rotations, this approach enables higher-order counterdiabatic protocols whose implementation requires a constant number of analog blocks for any fixed truncation order, independent of system size. We demonstrate the method for two-dimensional spin models and analyze the associated approximation errors. These results show that digital-analog quantum computing enables a qualitatively new resource scaling for counterdiabatic protocols and related quantum control primitives, with direct implications for quantum simulation, optimization, and algorithmic state preparation on current quantum devices. [Read Paper](https://arxiv.org/abs/2601.01154) Previous 1234567 Next --- # Kipu Academy: Certify a Quantum-Centric Application URL: https://kipu-quantum.com/academy # Kipu Quantum Business and Technical Certifications Get your organization quantum-ready, trained by the team running industrial-scale workloads on today’s hardware. [Book a fit call](https://outlook.office.com/bookwithme/user/cb70977a93354b2c88fc6773304b2948@kipu-quantum.com/meetingtype/nmz50I8moE6h19JZtJH-9A2?anonymous&ismsaljsauthenabled&ep=mlink)[Try a tutorial](/academy/tutorials/first-entangled-circuit) ## Clients and board ask you about quantum And the questions are getting specific. Which of our problems does it fit? Can you show us how? What can we make of it beyond the hype, should we invest? You have an idea about the theory, but that is not the same as having a filter for where quantum applies. The academy is built to increase confidence by doing it yourself. ## Now imagine you could verify your instinct Currently, only a handful of people are proficient in practical quantum computing. Hands-on training can (in)form your judgement. Hardware roadmaps converge around 2029 for next-gen systems, where many current technologies merge. If you build the muscle memory now, you know what to look for in fault tolerance, too. ![Dr. Gabriel Dario Alvarado Barrios, Quantum Algorithm Engineer instructor at Kipu Academy](/_next/static/media/GabrielDarioAlvaradoBarrios.41d74544.jpg) ### Dr. Gabriel Dario Alvarado Barrios Quantum Algorithm Engineer ![Dr. Eric Michon, Lead Quantum Development instructor at Kipu Academy](/_next/static/media/EricMichon.e5743fdc.jpg) ### Dr. Eric Michon Lead Quantum Development ![Christoph Krieger, Fullstack Software Engineer instructor at Kipu Academy](/_next/static/media/image-10.a12b9a00.png) ### Christoph Krieger Fullstack Software Engineer ![Dr. Stefano Melchionna, Scientific Consultant instructor at Kipu Academy](/_next/static/media/StefanoMelchionna.d77a09d8.jpg) ### Dr. Stefano Melchionna Scientific Consultant ![Jonathan Jones, Head of Sales instructor at Kipu Academy](/_next/static/media/JonathanJones.287fbf29.png) ### Jonathan Jones Head of Sales Curriculum Business track (~10h) Technical track (~15h) 01Introduction to the Kipu Quantum Hub [01Kipu Product Ecosystem \[Hands-on Lab\]](/academy/tutorials/first-entangled-circuit) 02Optimization with Iskay and Miray 02Miray Quantum Optimizer \[Hands-on Lab\] 03Quantum Machine Learning with Rimay 03Rimay Quantum Feature Extraction \[Hands-on Lab\] 04Quantum for decision-makers, with Tinkuq and other business tools 04Quantum Hub Controls (SDK, CLI, MCP) \[Hands-on Lab\] Business track (~10h) 01Introduction to the Kipu Quantum Hub 02Optimization with Iskay and Miray 03Quantum Machine Learning with Rimay 04Quantum for decision-makers, with Tinkuq and other business tools Kipu Business Foundations Present your quantum-centric pitch. Technical track (~15h) [01Kipu Product Ecosystem \[Hands-on Lab\]](/academy/tutorials/first-entangled-circuit) 02Miray Quantum Optimizer \[Hands-on Lab\] 03Rimay Quantum Feature Extraction \[Hands-on Lab\] 04Quantum Hub Controls (SDK, CLI, MCP) \[Hands-on Lab\] Kipu Developer Foundations Ship your quantum-centric application. Kipu Business Foundations Present your quantum-centric pitch. Kipu Developer Foundations Ship your quantum-centric application. \+ Ongoing Workshops & Keynotes ## You work on the same Hub we do hub.kipu-quantum.com/marketplace ![The Kipu Quantum Hub marketplace: describe a problem to the Tinkuq quantum-centric agent, or pick a ready-to-use optimization or machine-learning service to run on real quantum hardware.](/academy-hub-preview.png) ## Quantum applications and why they are interesting to begin with Interactive portfolio optimizer. Move the risk-tolerance slider to select the best five-of-ten portfolio; the highlighted point walks the efficient frontier across every feasible portfolio. Chase return Minimize risk Implied risk-aversion λ ≈ 0.93 Expected return 11.8% Volatility 13.1% Implied λ 0.93 SoftwareSemisBankEnergyStaplesPharmaBeverageIndustrialAerospaceRetail Drag the slider: the optimizer re-picks the best five-asset portfolio for each risk appetite, tracing the efficient frontier. The tutorials below build and run this same optimization, from a few lines of code to the S&P 500. [ ### Your First Entangled Circuit Go from two independent random bits to one entangled pair on the free Kipu simulator, then map the stack it runs on. Beginner · ~75 minStart tutorial](/academy/tutorials/first-entangled-circuit)[ ### Quantum Portfolio Optimization Build a cardinality-constrained portfolio with a real three-body risk term, and run it. Part 1 of 2. Intermediate · ~20 minStart tutorial](/academy/tutorials/quantum-portfolio-optimization)[ ### Scaling to the S&P 500 Decompose the same kernel past the simulator's qubit limit, the pipeline Kipu and IonQ used for 250 names. Part 2 of 2. Advanced · ~25 minStart tutorial](/academy/tutorials/quantum-portfolio-optimization-part-2-scaling) ![IBM Quantum](/500H-IBM_Quantum_logotype_pos_RGB.svg)![IonQ](/500H-ionq-logo.svg)![QuEra](/500H-QuEra_logo.svg)![NVIDIA](/500H-NVIDIA_logo.svg) On the Hub: IBM Quantum, IonQ, QuEra, IQM, Pasqal, Rigetti, Quandela QPUs, plus NVIDIA-accelerated, AWS and Azure simulators. NTT DATAKPMGBASFMoeve > We are day-one, quantum power-users. Quantum is a topic close to our heart, and we want to show by example that industry users can derive value from quantum-centric applications. > > ![Robert Lahmann, Academy Coordinator at Kipu Quantum, host of the Kipu Academy](/_next/static/media/RobertLahmann.30835849.jpg) > > Robert Lahmann > > Academy Coordinator 34 commercial projects the playbook you learn from 67 published papers the science behind your training ¼M QPU dev budget algorithms that run on hardware today 6 QPU vendors 15 QPUs, one Hub you use [ IBM Think 2026, closing keynote “Our roadmap ahead is clear. I’m really, really excited and I really think you should be too.” Jay Gambetta, IBM. Kipu Quantum was highlighted running industrial-scale problems on IBM Quantum Heron. ](https://youtu.be/TJtUYtWU89Q?t=1988)[ IonQ Q1 2026 Earnings Call, 06 May 2026 World’s first large-scale portfolio optimization on real S&P 500 data, with Kipu Quantum. Cited by IonQ leadership as production-environment proof of systematic improvement in portfolio quality and execution time. ](https://investors.ionq.com/) Book a 15-minute call to see if it’s a fit. [Book a fit call](https://outlook.office.com/bookwithme/user/cb70977a93354b2c88fc6773304b2948@kipu-quantum.com/meetingtype/nmz50I8moE6h19JZtJH-9A2?anonymous&ismsaljsauthenabled&ep=mlink) ## Questions, answered Is the Academy self-paced? Yes. The course is online and free, and live sessions are recorded so you work through lectures and labs on your own schedule. The Business Track builds the foundation; the Technical Track puts it into practice with hands-on labs. Live or asynchronous? Lectures are live and recorded, so you can revisit them anytime. Labs are asynchronous Jupyter Notebook assignments, with a live check-in each cycle for questions and progress review. How much time does it take? None beyond the stated hours. Business Track is 10h of live sessions; Technical Track is 15h plus a final application project. Templates and a guided recipe mean no prior quantum background is needed. Sessions run 60 to 90 minutes each. Do I run on real quantum hardware? Labs run on simulators, sufficient for both tracks. Hardware credits can be purchased on demand through the Kipu Quantum Hub across 6 QPU vendors. How does certification work? The coursework is free. The certificate program is selective and graded: Business requires delivering a short quantum-centric pitch, Technical requires completing the lab assignments and presenting a working application. It is included for Team plan and higher on the Kipu Quantum Hub. It is permanent, and both tracks award Level 1 of 3 in the Kipu Academy pathway. When can I start? Anytime. The course is online and free to take at your own pace. Book a fit call and we will get you started. ## Materials available publicly. Managed cohorts to certify. [Book a fit call](https://outlook.office.com/bookwithme/user/cb70977a93354b2c88fc6773304b2948@kipu-quantum.com/meetingtype/nmz50I8moE6h19JZtJH-9A2?anonymous&ismsaljsauthenabled&ep=mlink) --- # Webinars URL: https://kipu-quantum.com/webinars # Webinars Join us live or catch up on recordings. Deep dives into quantum computing from the Kipu team and partners Upcoming Webinar ![Quantum Computing for Finance](/_next/static/media/photo-1550751827-4bd374c3f58b.20af9a91.jpg) Upcoming Webinar 28 July 2026 11:00 – 12:00 CET ## Quantum Computing for Finance A lightweight yet rigorous introduction to quantum computing and where it creates value in finance, including a hands-on session with Paqari, our quantum end-to-end deployment agent. No prior physics required. Speaker - ![Dr. Stefano Melchionna](/_next/static/media/StefanoMelchionna-webinar.c460d320.jpg) Dr. Stefano Melchionna Scientific Consultant [Register now](https://events.teams.microsoft.com/event/85affb3e-f485-4a92-a3b8-5b600fcc9205@bedf7ecf-b90d-4fda-a837-66edcb69e0d2)[View details](/webinar-quantum-finance) ## On-Demand Recordings Missed a session? Watch our previous webinars at your own pace. ![](/_next/static/media/KipuKnot.7abacc35.png) Click to play ### Experience Quantum-centric Intelligence for your Industrial Use-Case Dr. Jan Trautmann, Dr. Michael Falkenthal & Dr. Gernot Füchsel A live deep dive into how enterprises combine hybrid computing resources without any quantum computing knowledge. We built a hands-on, integration-ready service and shared insights from previous implementations. ![](/_next/static/media/KipuKnot.7abacc35.png) Click to play ### Quantum Computing for Optimization Problems Meets Flexibility Kipu Quantum & IBM Introducing Iskay Quantum Optimizer, a Qiskit function that enables developers and researchers to tackle complex optimization problems, alongside IBM’s Flex plan. ![](/_next/static/media/KipuKnot.7abacc35.png) Click to play ### Quantum Workflows with PLANQK ![](/_next/static/media/KipuKnot.7abacc35.png) Click to play ### Quantum Computing in Pharma: Research Use Cases and Tools ![](/_next/static/media/KipuKnot.7abacc35.png) Click to play ### Serverless Quantum Computing: What’s New? Serverless quantum computing with PLANQK simplifies access to quantum power, enabling innovation without operational overhead. ![](/_next/static/media/KipuKnot.7abacc35.png) Click to play ### Unlocking Quantum Potential: Making Quantum Computers Useful with New Algorithms Daniel Volz, CEO Kipu Quantum A look at advancements in quantum computing and real-world use cases, Kipu’s development roadmap, and the thresholds toward quantum advantage. ![](/_next/static/media/KipuKnot.7abacc35.png) Click to play ### Quantum Computing for Telecommunication Kipu Quantum, cinfo, MASORANGE and QuEra Computing Joint project results showing the potential of quantum computing for managing telecom networks, network resilience, and the effectiveness of different quantum hardware. --- # Blog URL: https://kipu-quantum.com/blog # Blog [ ![Reading Toxicity of Molecules with Neutral-Atom Quantum Processors](/_next/static/media/S-AIindrug.31c84e33.jpg) 10.07.2026 ### Reading Toxicity of Molecules with Neutral-Atom Quantum Processors A neutral-atom quantum processor generates quantum features that improve molecular toxicity prediction beyond classical methods: an early step toward accuracy quantum advantage for molecular toxicity classification. ](/blog/reading-toxicity-of-molecules-with-neutral-atom-quantum-processors) [ ![Classical Surrogates for Quantum-Advantage Feature Extraction: Bringing Quantum Computing to Production](/_next/static/media/S-classical-surrogate.78a4253e.jpg) 29.04.2026 ### Classical Surrogates for Quantum-Advantage Feature Extraction: Bringing Quantum Computing to Production Quantum feature extraction lifts ML accuracy on real industrial data, but requires the QPU at every inference. Classical surrogates trained on quantum data preserve the gains while making deployment fully classical. ](/blog/classical-surrogates-for-quantum-feature-extraction) [ ![Kipu Quantum Builds the Quantum One-Stop-Shop for Industrial Quantum Usefulness](/_next/static/media/Group_7.a8fd4f92.png) 2025 ### Kipu Quantum Builds the Quantum One-Stop-Shop for Industrial Quantum Usefulness Exploring the future of industrial quantum applications and how Kipu Quantum is building a comprehensive platform for quantum usefulness. ](/blog/industrial-quantum-usefulness) [ ![Scaling Advantage with Quantum-Enhanced Memetic Tabu Search](/_next/static/media/S-QE-MTS.b6c7877a.jpg) 2025 ### Scaling Advantage with Quantum-Enhanced Memetic Tabu Search Discover how quantum-enhanced algorithms are achieving scaling advantages in complex optimization problems. ](/blog/scaling-advantage-quantum-enhanced-memetic-tabu-search) [ ![Hybrid Sequential Quantum Computing](/_next/static/media/S-HSQC.1d7a13e4.jpg) 2025 ### Hybrid Sequential Quantum Computing Learn about hybrid quantum-classical workflows that achieve runtime quantum advantage through sequential processing. ](/blog/hybrid-sequential-quantum-computing) [ ![Digitized Counterdiabatic Quantum Sampling (DCQS)](/_next/static/media/S-DCQS.a645103d.jpg) 2025 ### Digitized Counterdiabatic Quantum Sampling (DCQS) An innovative approach to quantum sampling that leverages counterdiabatic protocols for improved performance. ](/blog/digitized-counterdiabatic-quantum-sampling) [ ![Analog Quantum Feature Selection with Neutral Atoms](/_next/static/media/S-featureselection.4e3a6624.jpg) 2025 ### Analog Quantum Feature Selection with Neutral Atoms Exploring how neutral atom systems enable analog quantum feature selection for machine learning applications. ](/blog/analog-quantum-feature-selection-with-neutral-atoms) [ ![Digitized Counterdiabatic Quantum Feature Extraction](/_next/static/media/S-featureextraction.2ed49982.jpg) 2025 ### Digitized Counterdiabatic Quantum Feature Extraction Advanced techniques for extracting features using digitized counterdiabatic quantum algorithms. ](/blog/digitized-counterdiabatic-quantum-feature-extraction) [ ![Quantum-Reasoning LLM (QR-LLM): Emergence of Quantum Intelligence](/_next/static/media/S-QR-LLM.9c6c4e83.jpg) 2025 ### Quantum-Reasoning LLM (QR-LLM): Emergence of Quantum Intelligence The convergence of quantum computing and large language models opens new frontiers in artificial intelligence. ](/blog/quantum-intelligence) [ ![Digital-Analog Quantum Error Correction](/_next/static/media/S-DAQEC.6d2bb57b.jpg) 2024 ### Digital-Analog Quantum Error Correction A breakthrough approach to quantum error correction using digital-analog techniques. ](/blog/digital-analog-quantum-error-correction) [ ![Runtime Quantum Advantage with BF-DCQO (II)](/_next/static/media/S-QvQ.47dde85c.jpg) 2024 ### Runtime Quantum Advantage with BF-DCQO (II) Demonstrating runtime quantum advantage through comparative analysis with existing quantum algorithms. ](/blog/runtime-quantum-advantage-with-bf-dcqo-ii) [ ![Sequential Quantum Computing](/_next/static/media/S-SQC.90257884.jpg) 2024 ### Sequential Quantum Computing How combining multiple quantum processors sequentially leads to superior computational results. ](/blog/sqc) [ ![Digital-Analog Quantum Computing for Higher-Order Problems](/_next/static/media/S-DAQC02.3b6117bf.jpg) 2024 ### Digital-Analog Quantum Computing for Higher-Order Problems Tackling complex higher-order optimization problems at the quantum advantage level. ](/blog/digital-analog-quantum-computing-for-higher-order-problems-at-the-quantum-advantage-level) [ ![Runtime Quantum Advantage with BF-DCQO (I)](/_next/static/media/S-BF-DCQO.23e72033.jpg) 2024 ### Runtime Quantum Advantage with BF-DCQO (I) First demonstration of runtime quantum advantage using branch-and-bound digitized counterdiabatic quantum optimization. ](/blog/runtime-quantum-advantage-with-bf-dcqo) [ ![Branch-and-bound Digitized Counterdiabatic Quantum Optimization](/_next/static/media/S-BBB-DCQO01.389232bf.jpg) 2024 ### Branch-and-bound Digitized Counterdiabatic Quantum Optimization A novel optimization technique combining classical branch-and-bound with quantum algorithms. ](/blog/branch-and-bound-digitized-counterdiabatic-quantum-optimization) [ ![Quantum Optimization Benchmark Library: "The Intractable Decathlon"](/_next/static/media/S-labs.c8defe5c.jpg) 2024 ### Quantum Optimization Benchmark Library: "The Intractable Decathlon" A comprehensive benchmark suite for evaluating quantum optimization algorithms on challenging problems. ](/blog/quantum-optimization-benchmark-library-the-intractable-decathlon) [ ![Unlocking Quantum Advantage with Digital-Analog Quantum Computing (DAQC)](/_next/static/media/S-DAQC01.a6a794af.jpg) 2024 ### Unlocking Quantum Advantage with Digital-Analog Quantum Computing (DAQC) The fundamentals of digital-analog quantum computing and its path to quantum advantage. ](/blog/unlocking-quantum-advantage-with-digital-analog-quantum-computing-daqc) [ ![Analog Quantum Convolutions for Advanced Image Classification](/_next/static/media/S-AQCNN01.c308f153.jpg) 2024 ### Analog Quantum Convolutions for Advanced Image Classification Leveraging analog quantum computing for state-of-the-art image classification tasks. ](/blog/analog-quantum-convolutions-for-advanced-image-classification) [ ![Feature Mapping and Industrial Machine Learning Applications](/_next/static/media/S-FeatureMapping03.91dc5549.jpg) 2024 ### Feature Mapping and Industrial Machine Learning Applications Real-world industrial machine learning applications powered by quantum feature mapping. ](/blog/feature-mapping-and-industrial-machine-learning-applications) [ ![Kipu Quantum at AI in Drug Discovery 2025](/_next/static/media/S-AIindrug.31c84e33.jpg) 2024 ### Kipu Quantum at AI in Drug Discovery 2025 How Kipu Quantum is advancing drug discovery through the integration of AI and quantum computing. ](/blog/kipu-quantum-at-ai-in-drug-discovery-2025) [ ![Unlocking the Power of Quantum Computing](/_next/static/media/S-blog-iskayxibm02.a16927a4.jpg) 2024 ### Unlocking the Power of Quantum Computing Introduction to the Iskay Quantum Optimizer and its capabilities for solving complex problems. ](/blog/iskay-quantum-optimizer-by-kipu-quantum) [ ![Pushing Boundaries in Material Design at the Quantum-Advantage Level](/_next/static/media/S-materialdesign02.04652863.jpg) 2024 ### Pushing Boundaries in Material Design at the Quantum-Advantage Level Quantum computing applications in advanced material design and discovery. ](/blog/pushing-boundaries-in-material-design-at-the-quantum-advantage-level) [ ![The Timeless Thread of Information](/_next/static/media/S-knot02.f3cdb0ab.jpg) 2024 ### The Timeless Thread of Information Our company's name, KIPU QUANTUM, is derived from the same Incan quipu - a sophisticated method of encoding information through intricate knots. ](/blog/the-timeless-thread-of-information) --- # Latest News URL: https://kipu-quantum.com/news # Latest News Stay updated with the latest developments, partnerships, and breakthroughs from Kipu Quantum Featured News [ ![Kipu Quantum Makes Quantum-Enhanced AI Deployable in Production](/_next/static/media/offlineDQFE.68eb3fb8.png) 20.05.2026 ## Kipu Quantum Makes Quantum-Enhanced AI Deployable in Production A new hybrid framework trains quantum-enhanced ML models on a quantum processor and deploys them entirely on classical hardware, preserving the accuracy gains of quantum feature extraction at classical cost, latency, and operational profile. Read Full Article ](/news/quantum-enhanced-ai-production) ## Recent Updates [ ![Kipu: Quantum-centric Intelligence](/_next/static/media/image-11.ce858265.png) 23.04.2026 ### Kipu: Quantum-centric Intelligence From intent to quantum solution in minutes. Our platform lets teams describe what they want to solve and get to a working quantum solution through unified access to quantum backends, proven solvers, and AI-powered orchestration. Read More ](/news/quantum-centric-intelligence) [ ![Kipu Quantum Teams With NVIDIA to Advance Hybrid Quantum Optimization Using CINECA's Leonardo Supercomputer](/_next/static/media/photo-1558494949-ef010cbdcc31.8295e319.jpg) 23.04.2025 ### Kipu Quantum Teams With NVIDIA to Advance Hybrid Quantum Optimization Using CINECA's Leonardo Supercomputer Building on recent work on quantum-enhanced memetic tabu search, numerical experiments have been extended to 43 qubits using CINECA's Leonardo supercomputer and NVIDIA CUDA-Q platform, exploring hybrid quantum-classical strategies for the challenging LABS optimization problem. Read More ](/news/nvidia-cineca-partnership) [ ![New Collaboration with Lufthansa Industry Solutions](/_next/static/media/photo-1436491865332-7a61a109cc05.3e1d4ee0.jpg) 21.01.2025 ### New Collaboration with Lufthansa Industry Solutions Kipu Quantum partners with Lufthansa Industry Solutions on the QCI QCMobility project to optimize strategic and tactical flight operations planning using quantum algorithms for over 100 aircraft across 13 locations. Read More ](/news/lufthansa-collaboration) [ ![EETimes: BASF and Kipu Focus on End-User Mastery of Quantum Computing](/_next/static/media/photo-1532634922-8fe0b757fb13.c3d1f1a4.jpg) 05.12.2024 ### EETimes: BASF and Kipu Focus on End-User Mastery of Quantum Computing BASF and Kipu Quantum collaborate to optimize complex logistics processes in chemical operations. CEO Daniel Volz emphasizes bringing hardware and algorithms together to reach the tipping point of quantum advantage. Read More ](/news/basf-partnership) [ ![Kipu Starts Commercial Quantum Advantage Era](/_next/static/media/photo-1635070041078-e363dbe005cb.c06dc1c4.jpg) 08.09.2024 ### Kipu Starts Commercial Quantum Advantage Era Solving optimization problems with industry relevance on IBM 156-qubit quantum processors using BF-DCQO algorithms, marking the start of the commercial quantum computing era where customers can reliably invest in quantum services for immediate business value. Read More ](/news/commercial-quantum-advantage-era) [ ![QInnovision Consortium Welcomes Kipu Quantum as First International Startup](/_next/static/media/photo-1552664730-d307ca884978.47d85c1e.jpg) 27.05.2024 ### QInnovision Consortium Welcomes Kipu Quantum as First International Startup Kipu Quantum joins QInnovision Consortium as first international startup member. Prof. Enrique Solano appointed as International Advisor to the steering committee, advancing quantum computing applications across pharmaceutical, chemical, logistics, and financial sectors. Read More ](/news/qinnovision-consortium) [ ![R, Cinfo, and Kipu Quantum Design Algorithm for Optimizing Telecommunication Networks](/_next/static/media/photo-1544197150-b99a580bb7a8.faa223bc.jpg) 23.01.2024 ### R, Cinfo, and Kipu Quantum Design Algorithm for Optimizing Telecommunication Networks Pioneering quantum solution for network resilience using D-Wave quantum annealers and QuEra neutral-atom processors to analyze R's optical fiber backbone network, identifying critical nodes to maximize service availability. Read More ](/news/r-cinfo-telecom-optimization) --- # Imprint URL: https://kipu-quantum.com/imprint # Imprint Information pursuant to Sect. 5 German Digital Services Act (DDG) Kipu Quantum GmbH Greifswalder Str. 212 10405 Berlin Germany ## Represented by its managing directors: Prof. Dr. Enrique Solano Dr. Tobias Grab Commercial Register: HRB 287200 Local court Charlottenburg ## Contact Telephone: [+49 721 61902038](tel:+4972161902038) Email: [info@kipu-quantum.com](mailto:info@kipu-quantum.com) ## VAT ID DE 346115126 ## Person responsible for editorial Prof. Dr. Enrique Solano ## Copyright Notice The content and works published on this website are protected by copyright and are subject to German copyright law. Any form of reproduction, modification, distribution, or use beyond the limits permitted by law is prohibited without the express written consent of the respective copyright holder. The information and content provided on this website are available exclusively for the purpose of evaluating and initiating business relationships. Downloads and copies of this website are, unless otherwise indicated, permitted only for personal and internal use within the scope of these purposes. Any use beyond this, particularly for independent commercial activities, is not permitted. Content provided by third parties is identified as such. The rights of third parties are respected. Should you nevertheless become aware of a possible copyright infringement, please notify us accordingly. Upon becoming aware of any legal violations, the relevant content will be removed immediately. ## Urheberrechtshinweise Die auf dieser Webseite veröffentlichten Inhalte und Werke sind urheberrechtlich geschützt und unterliegen dem deutschen Urheberrecht. Ohne ausdrückliche schriftliche Zustimmung des jeweiligen Rechteinhabers ist jede Form der Vervielfältigung, Bearbeitung, Verbreitung oder Verwertung außerhalb der gesetzlich zulässigen Grenzen untersagt. Die bereitgestellten Informationen und Inhalte dieser Webseite stehen ausschließlich zum Zweck der Evaluierung und Anbahnung von unternehmerischen Geschäftsbeziehungen zur Verfügung. Downloads und Kopien dieser Webseite sind, sofern nicht anders gekennzeichnet, nur für den eigenen und internen Gebrauch im Rahmen dieser Zwecke zulässig. Eine darüber hinausgehende Nutzung, insbesondere für eigenständige kommerzielle Aktivitäten, ist nicht gestattet. Inhalte, die von Dritten bereitgestellt wurden, sind entsprechend als solche gekennzeichnet. Die Rechte Dritter werden beachtet. Sollten Sie dennoch auf eine mögliche Verletzung von Urheberrechten aufmerksam werden, bitten wir um einen entsprechenden Hinweis. Bei Bekanntwerden etwaiger Rechtsverletzungen werden die betreffenden Inhalte umgehend entfernt. --- # Privacy Policy URL: https://kipu-quantum.com/privacy # Privacy How we handle your personal data in compliance with the GDPR ## General information The following information will provide you with an easy to navigate overview of what will happen with your personal data when you visit this website. The term “personal data” comprises all data that can be used to personally identify you. For detailed information about the subject matter of data protection, please consult our Data Protection Declaration, which we have included beneath this copy. The operators of this website and its pages take the protection of your personal data very seriously. Hence, we handle your personal data as confidential information and in compliance with the statutory data protection regulations and this Data Protection Declaration. ## Information about the responsible party and the data protection officer The responsible party (data controller) on this website is: Kipu Quantum GmbH Greifswalder Str. 212 10405 Berlin Telephone: [+49 721 61902038](tel:+4972161902038) Email: [info@kipu-quantum.com](mailto:info@kipu-quantum.com) The controller is the natural person or legal entity that single-handedly or jointly with others makes decisions as to the purposes of and resources for the processing of personal data (e.g., names, e-mail addresses, etc.). If you have any questions related to privacy at Kipu Quantum GmbH or if you would like to exercise your rights, you can send an e-mail to [privacy@kipu-quantum.com](mailto:privacy@kipu-quantum.com). If you would like to submit sensitive information, please send them via postal e-mail to: Kipu Quantum GmbH, Data Protection Officer, Greifswalder Str. 212, 10405 Berlin. The Kipu Quantum GmbH data protection officer will handle your request. Kipu Quantum GmbH has nominated an external data protection officer (Data Business Services GmbH & Co. KG, Severine Petersen, Nördliche Münchner Str. 47, 82031 Grünwald, Germany). ## Data collection and data processing ### Direct contact and contact form If you submit inquiries to us via our contact form, the information provided in the contact form (mandatory data: first and last name, business e-mail address, request; voluntary data: salutation, business phone number) will be stored by us in order to handle your inquiry and in the event that we have further questions. If you contact us by postal mail, e-mail, telephone or fax, your request, including all resulting personal data (name, business contact details, request) will be stored and processed by us for the purpose of processing your request. The processing of these data is based on Art. 6(1)(b) GDPR, if your request is related to the execution of a contract or if it is necessary to carry out pre-contractual measures. Without providing this data we cannot conclude a contract with you. In all other cases the processing is based on our legitimate interest in the effective processing of the requests addressed to us (Art. 6(1)(f) GDPR) or on your agreement (Art. 6(1)(a) GDPR) if this has been requested. Your personal data is managed in our CRM system HubSpot provided by HubSpot Ireland Limited who is acting as our data processor under Art. 28 GDPR. A Data Processing Agreement is in place. More information about data privacy at HubSpot can be found here: [https://legal.hubspot.com/privacy-policy](https://legal.hubspot.com/privacy-policy) The information you have entered into the contact form will be stored until your request is processed or if you revoke your consent if the data processing is based on consent. This shall be without prejudice to any mandatory legal provisions, in particular retention periods. **Form submission processor:** Submissions from the contact and “Get Notified” forms on this website are transmitted via FormSubmit (Mangle Ltd., United Kingdom) as a data processor under Art. 28 GDPR. FormSubmit forwards the submitted fields (name, email, optional company, optional message, consent record) by email to the responsible Kipu Quantum team. Privacy policy: [https://formsubmit.co/privacy](https://formsubmit.co/privacy). Because FormSubmit is based outside the EU, transfers rely on EU Standard Contractual Clauses. ### Webinar/event registration You can learn more about us if you register for a webinar or event. If we offer webinars or events, we will provide a registration form. We need to collect your personal data for administrative purposes and to carry out the webinar or event. The personal data we collect will be limited to the data necessary for the purposes. Usually your name, surname, business contact details and job information are collected. The data is processes based on Art. 6(1)(b) GDPR or Art. 6(1)(a) GDPR if we ask for your consent. ### Newsletter You will only receive our newsletter and marketing e-mails if you subscribe to it actively (Art. 6(1)(a) GDPR). We will process your name and business e-mail address, company name and if available job title in order to send you e-mails. You can withdraw your consent with future effect by clicking on the “unsubscribe” link in each newsletter or by contacting us directly. For newsletter dispatch we use our marketing automation tool HubSpot (HubSpot, Inc., 25 First Street, Cambridge, MA 02141 USA). HubSpot is acting as our data processor and a data processing agreement with Standard Contractual Clauses is in place. EU/German data centers are selected. ### Direct marketing KIPU collects information related to your person through publicly available sources or licenses data from B2B sales platforms. The information collected is limited to typical business card information, which may contain some or all of these categories of corporate organizational information: full name, company, office address, business phone number, business e-mail address, job title, job function, social media URL. The information collected is stored in our CRM system HubSpot and processed to get in contact with you via phone or e-mail to establish a business relationship or to inform you about our events. KIPU processes your information in accordance with regulations on data protection and electronic communications. KIPU processes your information based on the legitimate interest if consent is not collected. Please be informed that KIPU is a commercial enterprise and only addresses other commercial enterprises with regard to its products and services. Licensed data is only processed according to the license agreements in place with the vendors. The vendors are typically acting as independent data controllers and are subject to the privacy regulations once they collect your information. KIPU is mainly licensing data from LinkedIn Sales Navigator ([https://www.linkedin.com/legal/privacy-policy](https://www.linkedin.com/legal/privacy-policy)) and ZenLeads Inc. d/b/a Apollo.io ([https://www.apollo.io/privacy-policy](https://www.apollo.io/privacy-policy)). ### Matchmaking Agent We offer you the possibility to use a so-called “Matchmaking Agent” to describe your problem or use case in free-form text. The data you provide in this context will be transmitted to and used by us for the purpose of processing your request and improving our products and services. When you use the Matchmaking Agent, the following data may be processed: - the free-form text you submit describing your problem, including any information you voluntarily provide (e.g. problem class, problem size, current solution, quality of the solution and other requirements), - technical information about your usage of the Matchmaking Agent (e.g. date and time of the request, pages visited and clicks relating to the Matchmaking Agent feature, IP address and device information as recorded by Google Analytics, where applicable). For the processing of the free-form text within the Matchmaking Agent, we use the service “Claude” provided via the Anthropic API. Anthropic is a service provider based in the United States (Anthropic, PBC, [https://www.anthropic.com/legal/privacy](https://www.anthropic.com/legal/privacy)). We have concluded a data processing agreement with Anthropic to ensure that your personal data is processed strictly in accordance with our instructions and the requirements of the GDPR. Before we further analyze or store the submitted free-form text for statistical purposes, we use Claude to remove or pseudonymize personal data contained in your submission to the extent technically feasible. We instruct Anthropic to process the data only for this purpose and subject to appropriate contractual safeguards. In addition, we use Google Analytics on our website in order to record aggregate usage statistics of the Matchmaking Agent (e.g. number of clicks, page views and interaction events relating to the feature). For details on the use of Google Analytics, the categories of data processed, potential transfers to third countries and the applicable safeguards, please refer to the section on Google Analytics below. **Legal basis:** The legal basis for processing the data you submit via the Matchmaking Agent for the purpose of answering your request and operating the feature is Art. 6(1)(b) GDPR, where the processing is necessary for the performance of a contract with you or in order to take steps at your request prior to entering into a contract. To the extent that we further analyze the anonymized or pseudonymized content of your submissions in order to improve our Matchmaking Agent and other products and services, the legal basis is our legitimate interest pursuant to Art. 6(1)(f) GDPR. Our legitimate interest lies in continuously improving and optimizing our offerings based on aggregated and, where possible, anonymized usage data. Where required by law (in particular with regard to the use of Google Analytics and the placement of cookies or similar tracking technologies), the legal basis is your consent pursuant to Art. 6(1)(a) GDPR in conjunction with Art. 7 GDPR. In this case, you can withdraw your consent at any time with effect for the future as described in this Privacy Policy. **Purpose:** We process your data submitted via the Matchmaking Agent in order to receive and process your request and present you with suitable results or recommendations; to understand how users interact with the Matchmaking Agent and to improve its performance, relevance and usability; and to derive statistical information about typical problem classes, problem sizes, current solutions, quality of solutions and other requirements, in order to further develop and optimize our products and services. For these purposes, we analyze the content of your submissions only in anonymized or pseudonymized form to the extent technically feasible. **Storage period:** We store the original free-form text you submit via the Matchmaking Agent only for as long as necessary to fulfil the purposes described above. As a rule, the raw submissions are stored for a maximum of 30 days in order to allow for initial processing and anonymization or pseudonymization. After this period, we either delete the original submissions or transform them into anonymized datasets which no longer allow us to identify you. Anonymized datasets may be retained and used for statistical and analytical purposes without time limitation, as long as such data does not allow for any identification of you as an individual. Data that is processed by Google Analytics is stored in accordance with the retention periods set out in the corresponding section of this Privacy Policy. **Right to object (Art. 21 GDPR):** Where we process your personal data on the basis of our legitimate interests pursuant to Art. 6(1)(f) GDPR, you have the right to object to this processing at any time on grounds relating to your particular situation in accordance with Art. 21 GDPR. In such case, we will no longer process your personal data for these purposes unless we can demonstrate compelling legitimate grounds for the processing which override your interests, rights and freedoms or for the establishment, exercise or defense of legal claims. To exercise your right to object, please contact us at the e-mail address indicated above ([privacy@kipu-quantum.com](mailto:privacy@kipu-quantum.com)). Please note that, due to our anonymization and pseudonymization measures, we may no longer be able to attribute certain datasets to you personally; in such cases, we can no longer comply with a request relating to specific anonymized data. Where the processing is based on your consent pursuant to Art. 6(1)(a) GDPR, you may withdraw your consent at any time with effect for the future, without affecting the lawfulness of the processing carried out on the basis of your consent before its withdrawal. ### Storage duration Unless a more specific storage period has been specified in this privacy policy, your personal data will remain with us until the purpose for which it was collected no longer applies. If you assert a justified request for deletion or revoke your consent to data processing, your data will be deleted, unless we have other legally permissible reasons for storing your personal data (e.g., tax or commercial law retention periods); in the latter case, the deletion will take place after these reasons cease to apply. ### Data recipients When you visit our website, we use the third-party services as described below in this privacy policy. Additionally, we use a select number of trusted external service providers for certain technical data processing and service offerings. These service providers are carefully selected and meet high data protection and security standards. We only share information with them that is required for the services offered and we contractually bind them to treat any information we share with them as confidential and to process personal data only according to our instructions. Data Processing Agreements according to Art. 28 GDPR are concluded. ### Information on data transfer to the USA and other non-EU countries without adequacy decision We take care when selecting external service providers and make sure that your personal data stays within Europe whenever possible. Sometimes we need to commission service providers from third countries (e.g. USA) without an adequacy decision. In this case we make sure that we have appropriate safeguards (e.g. certification, EU Standard Contractual Clauses) in place before transferring your personal data. ### Technical and organizational security measures We are committed to safeguarding the personal data we process through a range of technical and organizational measures designed to ensure a high level of data protection and integrity. These measures include, but are not limited to: - **Access Controls:** Role-based access restrictions to ensure that only authorized personnel can access personal data on a need-to-know basis. - **Data Encryption:** Data is encrypted in transit using TLS (Transport Layer Security) and, where applicable, encrypted at rest to prevent unauthorized access. - **Secure Infrastructure:** Our systems are hosted in secure, ISO 27001-certified data centers with robust physical and network security protocols. - **Staff Training:** All employees undergo regular training on data protection principles, privacy laws, and secure handling of personal data and are obliged to confidentiality. - **Monitoring and Auditing:** Continuous monitoring of our systems and periodic audits help detect and respond to potential vulnerabilities or data breaches. - **Data Minimization:** We collect only the personal data that is necessary for specified purposes and retain it only for as long as needed. These measures are continuously reviewed and updated in accordance with industry best practices and legal requirements to ensure ongoing protection of personal data. ## Data Processing when using the Kipu Quantum Hub platform ### Registration In order to register at our platform and to use the platform you have to provide some data (name and surname, business contact details, job details) and assign a password. Please note that the platform is for business use only. This is why we classify all data collected as corporate organizational information. When you register at our platform, we will do a check whether you registered with a corporate e-mail address and whether you have the authorization to register. If this is approved, you will get access to the platform. The legal basis for data processing is Art. 6(1)(b) GDPR. If you are dismissed, your data is deleted. ### Platform usage If you log in to our platform and use the platform we collect log data. Collecting log data is necessary to guarantee the functionality and security of the platform. The information comprises: - The type and version of browser used - The used operating system - Referrer URL - The hostname of the accessing computer - The time of the server inquiry - The IP address - Date and time of login - Requests in the platform This data is not merged with other data sources. This data is recorded on the basis of our legitimate interests under Art. 6(1)(f) GDPR. Other personal data is not collected when using the platform. If you are part of an organisation your user data (name, surname, e-mail address) can be accessed by the administrator of your organisation and the users authorized by the administrator. Your organisation can set up collaborations with other organisations. In this case your user data might be visible to other organisations users. ### Storage period The data is processed until your account is closed. As soon as your account is closed your data will be deleted, unless we have other legally permissible reasons for storing your personal data (e.g., tax or commercial law retention periods). I this case the deletion will take place after the legal storage periods ended. ### Data recipients When you use our platform, we use data processors and service providers for the purposes as described below. These service providers are carefully selected and meet high data protection and security standards. We only share information with them that is required for the services offered and we contractually bind them to treat any information we share with them as confidential and to process personal data only according to our instructions. Data Processing Agreements according to Art. 28 GDPR are concluded. ### Information on data transfer to the USA and other non-EU countries without adequacy decision We take care when selecting external service providers and make sure that your personal data stays within Europe whenever possible. Sometimes we need to commission service providers from third countries (e.g. USA) without an adequacy decision. In this case we make sure that we have appropriate safeguards (e.g. certification, EU Standard Contractual Clauses) in place before transferring your personal data. ### Payment KIPU uses Stripe (Stripe Payments Europe, Limited (SPEL), 1 Grand Canal Street Lower, Grand Canal Dock, Dublin, D02 H210, Ireland, [https://stripe.com/privacy](https://stripe.com/privacy)) as a payment gateway. KIPU does not receive banking details or credit card details. ### Hosting Our platform is hosted in the Google Cloud (Google Cloud EMEA Limited, 70 Sir John Rogerson’s Quay, Dublin 2, Ireland, [https://policies.google.com/privacy](https://policies.google.com/privacy)) and in the Amazon Web Services Cloud (Amazon Web Services EMEA SARL, 38 Avenue John F. Kennedy, L-1855, Luxemburg, [https://aws.amazon.com/privacy/](https://aws.amazon.com/privacy/)). The data centers in the EU are selected. ### Logging The platform logging activities are carried out with Google Monitoring (Google Ireland Limited Gordon House, Barrow Street, Dublin 4, Ireland, [https://policies.google.com/privacy](https://policies.google.com/privacy)) and Datadog (Datadog, Inc., 620 8th Ave, 45th Floor, New York, NY 10018, USA, [https://www.datadoghq.com/legal/privacy/](https://www.datadoghq.com/legal/privacy/)). ## Your rights If you would like to exercise your rights under GDPR, please refer to the contact details indicated in this privacy policy. Whenever you submit a request, we will ask you to confirm your identity to ensure the protection of your personal data and to prevent unauthorized access. If conflicting legal regulations or other reasons prevent us from executing your request, we will provide you with the relevant information. ### Information and access You have the right to obtain the confirmation as to whether or not personal data concerning you are being processed, and, where that is the case, access to the personal data as of Art. 15(1) GDPR. ### Rectification If your personal data has changed, is incomplete or incorrect you can ask us to update your personal data or to delete your personal data. ### Restriction and erasure You have the right to obtain the deletion of all data related to your person without undue delay. If we cannot delete your data (e.g. because legal storage obligations apply) we will restrict the processing of your personal data. You can ask us to restrict the processing of your personal data instead of deleting it. ### Data portability You have the right to demand that we hand over any data we automatically process on the basis of your consent or in order to fulfil a contract be handed over to you or a third party in a commonly used, machine readable format. If you should demand the direct transfer of the data to another controller, this will be done only if it is technically feasible. ### Objection and withdrawal of consent If the data processing is based on your explicit consent, you can revoke your consent at any time with effect to the future. You have the right to object, on grounds relating to your particular situation, at any time to processing of personal data based on Art. 6(1)(e) or (f) GDPR, including profiling based on those provisions. ### Lodge a complaint You have the right to lodge a complaint about the processing of your personal data with our competent data protection authority. The responsible supervisory authority for KIPU is: Der Landesbeauftragte für den Datenschutz und die Informationsfreiheit Baden-Württemberg, Postfach 10 29 32, 70025 Stuttgart, Germany. A complaint can be lodged using their online form: [https://www.baden-wuerttemberg.datenschutz.de/beschwerde/](https://www.baden-wuerttemberg.datenschutz.de/beschwerde/) ### Automated decision making, including profiling pursuant to Art. 22 GDPR We can confirm that automated decision making, including profiling pursuant to Art. 22 GDPR does not take place. ### Rejection of unsolicited e-mails We herewith object to the use of contact information published in conjunction with the mandatory information to be provided in our Site Notice to send us promotional and information material that we have not expressly requested. The operators of this website and its pages reserve the express right to take legal action in the event of the unsolicited sending of promotional information, for instance via SPAM messages. ## Hosting and Content Delivery Networks (CDN) ### External Hosting This website is hosted by an external service provider (host). Personal data collected on this website are stored on the servers of the host. These may include, but are not limited to, IP addresses, contact requests, metadata and communications, contract information, contact information, names, web page access, and other data generated through a web site. The host is used for the purpose of fulfilling the contract with our potential and existing customers (Art. 6(1)(b) GDPR) and in the interest of secure, fast, and efficient provision of our online services by a professional provider (Art. 6(1)(f) GDPR). Our host will only process your data to the extent necessary to fulfil its performance obligations and to follow our instructions with respect to such data. We are using the following hosts: **Website hosting and delivery (this site):** Vercel Inc., 650 California Street, San Francisco, CA 94108, USA. Privacy policy: [https://vercel.com/legal/privacy-policy](https://vercel.com/legal/privacy-policy) Vercel delivers this website through a global edge network. Request data (including your IP address and User-Agent) is processed by Vercel for the purpose of serving the site. Because Vercel is based in the USA, personal data may be transferred outside the EU/EEA. We rely on the EU-U.S. Data Privacy Framework and EU Standard Contractual Clauses as transfer safeguards and have a Data Processing Addendum in place. **Backend infrastructure for services outside this website:** Hetzner Online GmbH, Industriestr. 25, 91710 Gunzenhausen, Germany We have concluded data processing agreements (DPAs) for the use of the above-mentioned services. ### Server log files The provider of this website and its pages automatically collects and stores information in so-called server log files, which your browser communicates to us automatically. The information comprises: - The type and version of browser used - The used operating system - Referrer URL - The hostname of the accessing computer - The time of the server inquiry - The IP address This data is not merged with other data sources. This data is recorded on the basis of Art. 6(1)(f) GDPR. The operator of the website has a legitimate interest in the technically error free depiction and the optimization of the operator’s website. In order to achieve this, server log files must be recorded. ### SSL and/or TLS encryption For security reasons and to protect the transmission of confidential content, such as purchase orders or inquiries you submit to us as the website operator, this website uses either an SSL or a TLS encryption program. You can recognize an encrypted connection by checking whether the address line of the browser switches from “http://” to “https://” and also by the appearance of the lock icon in the browser line. If the SSL or TLS encryption is activated, data you transmit to us cannot be read by third parties. ## Cookies Our websites and pages use what the industry refers to as “cookies.” Cookies are small text files that do not cause any damage to your device. They are either stored temporarily for the duration of a session (session cookies) or they are permanently archived on your device (permanent cookies). Session cookies are automatically deleted once you terminate your visit. Permanent cookies remain archived on your device until you actively delete them, or they are automatically eradicated by your web browser. In some cases, it is possible that third-party cookies are stored on your device once you enter our site (third-party cookies). These cookies enable you or us to take advantage of certain services offered by the third party (e.g., cookies for the processing of payment services). Cookies have a variety of functions. Many cookies are technically essential since certain website functions would not work in the absence of the cookies (e.g., the shopping cart function or the display of videos). The purpose of other cookies may be the analysis of user patterns or the display of promotional messages. Cookies, which are required for the performance of electronic communication transactions or for the provision of certain functions you want to use (category Essential, always active in the consent manager) or those that are necessary for the optimization of the website (e.g., cookies that provide measurable insights into the web audience), shall be stored on the basis of Art. 6(1)(f) GDPR, unless a different legal basis is cited. The operator of the website has a legitimate interest in the storage of cookies to ensure the technically error free and optimized provision of the operator’s services. If your consent to the storage of the cookies has been requested (category Analysis & Marketing), the respective cookies are stored exclusively on the basis of the consent obtained (Art. 6(1)(a) GDPR); this consent may be revoked at any time. You can access the consent manager to update your privacy settings by clicking on the fingerprint in the left corner at the bottom of the screen. You can adjust your consent preferences at any time via our Consent Manager, accessible by clicking the fingerprint icon located at the bottom left corner of the screen. This allows you to manage which types of data you agree to share, in line with your personal privacy preferences. You have the option to set up your browser in such a manner that you will be notified any time cookies are placed and to permit the acceptance of cookies only in specific cases. You may also exclude the acceptance of cookies in certain cases or in general or activate the delete function for the automatic eradication of cookies when the browser closes. If cookies are deactivated, the functions of this website may be limited. ## Third-party services ### Google Services We use the Google services on our website. The provider is Google Ireland Limited, Gordon House, Barrow Street, Dublin 4, Ireland. You can access the Google privacy policy here [https://policies.google.com/privacy](https://policies.google.com/privacy). We have executed a data processing agreement with Google and are implementing the stringent provisions of the German data protection agencies to the fullest when using Google services. The use of Google services on our website occurs on the basis of your consent pursuant to Art. 6(1)(a) GDPR and § 25(1) TTDSG. You may revoke your consent at any time by accessing the consent manager (category “Analysis”). ### Google Tag Manager The Google Tag Manager is a tool that allows us to integrate tracking or statistical tools and other technologies on our website. The Google Tag Manager itself does not create any user profiles, does not store cookies, and does not carry out any independent analyses. It only manages and runs the tools integrated via it. However, the Google Tag Manager does collect and process your IP address. ### reCAPTCHA reCAPTCHA is used based on our legitimate interests to protect our website against abuse, spam, and automated access. It is designed to determine whether actions performed on this website (e.g. form submissions or account registration) are carried out by a human user or by automated software. For this purpose, reCAPTCHA analyzes the behavior of website visitors based on various characteristics. The data processed by reCAPTCHA may include, in particular, IP addresses, mouse movements, time spent on the website, and other information required by the service to detect abusive or automated behavior and to ensure the security of the website. ### Google Analytics This website uses functions of the web analysis service Google Analytics. Google Analytics enables the website operator to analyze the behavior patterns of website visitors. To that end, the website operator receives a variety of user data, such as pages accessed, time spent on the page, the utilized operating system and the user’s origin. This data is summarized in a user-ID and assigned to the respective end device of the website visitor. Google Analytics uses technologies that make the recognition of the user for the purpose of analyzing the user behavior patterns (e.g., cookies or device fingerprinting). The website use information recorded by Google is, as a rule transferred to a Google server in the United States, where it is stored. ### IP anonymization On this website, we have activated the IP anonymization function. As a result, your IP address will be abbreviated by Google within the member states of the European Union or in other states that have ratified the Convention on the European Economic Area prior to its transmission to the United States. 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Status: June 2026 --- # Your First Entangled Circuit on the Kipu Quantum Hub URL: https://kipu-quantum.com/academy/tutorials/first-entangled-circuit - [0Set up the environment](#step-0) - [1Connect](#step-1) - [2The hardware layer](#step-2) - [3From coin flip to entanglement](#step-3) - [4Run the experiment](#step-4) - [5Fixing an error message](#step-5) - [6Find your job](#step-6) - [7Kipu's Quantum Hub four layers](#step-7) [Back to Academy](/academy) # Your First Entangled Circuit on the Kipu Quantum Hub Go from two independent random bits to one entangled pair on live Kipu Quantum Hub infrastructure, then use that one circuit to map the whole stack it runs on. Tutorial•Beginner•~75 min•[Companion primer](/academy/tutorials/first-entangled-circuit-primer) [Get in touch](/contact) > **Educational disclaimer.** This is a hands-on starter tutorial in quantum computing, meant for learning. The circuit is the smallest interesting one there is, and the platform tour around it is deliberately shallow. Backend counts, marketplace counts and measurement integers are snapshots from the day this was written, and they will drift. Treat the live pages and the API references as the single source of truth. ### 1. Build Turn two independent coin flips into one entangled pair. ### 2. Run it Transpile and submit to kipu.sim.qsim, the free Kipu simulator, to run the experiment. ### 3. Kipu stack Where this tutorial lives on the hardware layer, and how to find your job in the dashboard. Wondering what superposition and entanglement actually are, or why quantum is having its moment? Read the [primer](/academy/tutorials/first-entangled-circuit-primer) first, then come back. Every task below carries collapsed hints: Hint 1 tells you where you could look, Hint 2 gives additional pieces of the answer. Think first, and try before revealing the solution. * * * ## 0Step 0: Set up the environment To run your first quantum program, you need a Python project folder with the Hub SDK, and your personal access token. ### Build from scratch with uv, qhub-quantum and qhubctl We teach this approach with [uv](https://docs.astral.sh/uv/), use your favorite Python package manager at your own discretion. Either way, the code requires Python 3.11 or newer. shell ``` uv init kipu-hub-academy cd kipu-hub-academy uv venv uv add qhub-quantum ``` You will also want the CLI (optional, recommended), which is a robust authorization route for your code. It ships on npm and needs Node.js 20 or higher: shell ``` npm install -g @quantum-hub/qhubctl ``` ### After completion `qhub-quantum` brings Qiskit (the most popular and widely adopted programming SDK for quantum) with it, and does not require a separate install. To run your qhub python scripts you can now use: shell ``` uv run python example.py ``` * * * ## 1Step 1: Connect On Kipu's Quantum Hub, you authenticate with a personal access token. Think of them as unique identifiers to authorize actions inside your profile and organizations you are part of. Keep it safe like you would protect a password. Navigation: You can find it on the [home page](https://hub.kipu-quantum.com) to copy and regenerate if you suspect your secrets have been leaked. To generate and manage additional, context-specific and time-limited access tokens use the options in your profile settings. ![The Kipu Quantum Hub home page with the Personal Access Token panel, its value masked, next to reveal, copy and regenerate controls.](/academy/first-entangled-circuit/image-1a-token-home.png) Your personal access token lives on the Hub home page. ![The Hub Settings page open on Access Tokens, with the New personal access token dialog showing name and expiration controls.](/academy/first-entangled-circuit/image-1b-token-settings.png) Scoped, time-limited tokens are created under Settings, Access Tokens. Reference: [Manage access tokens](https://docs.hub.kipu-quantum.com/manage-access-tokens). ### How do I authenticate with my token? To authenticate, the qhub-SDK provides three options. 1. **CLI login (recommended).** Run `qhubctl login -t `. That writes `~/.config/qhubctl/config.json`, where the SDK reads it. 2. **Environment variable.** Export `KQH_PERSONAL_ACCESS_TOKEN=` in the environment you run the tasks from. Make sure to exclude it from uploading to git or docker containers (developer option). 3. **Plain text in code,** some objects allow you to pass your access\_token directly inline. This risks exposure and leaks to third parties. Be extra careful and rotate your token frequently. * * * ### 1Task 1. Write a Python script that connects to a Quantum Hub backend using your Personal Access Token. Hint 1, where to look The connect object lives in `qhub.quantum.sdk`. The [Quickstart](https://docs.hub.kipu-quantum.com/quickstart) shows exemplary implementations. For a detailed backend-specific description check [Quantum SDK reference](https://docs.hub.kipu-quantum.com/sdk-quantum) with further documentation-links. To prove everything works, ask the Hub for something. `kipu.sim.qsim` is a free Quantum simulator backend for testing the connection. Authenticate with your personal access token. Hint 2, what to test Reread [Quickstart (Coin Toss)](https://docs.hub.kipu-quantum.com/quickstart#example-coin-toss). You can omit circuit construction and running a simulation, declare `provider = …` and `backend = …` with the appropriate `qhub.quantum.sdk` import for this exercise. Solution python ``` # task1_connect.py from qhub.quantum.sdk import HubQiskitProvider try: provider = HubQiskitProvider() check = provider.get_backend('kipu.sim.qsim') print(f'Connected. You are connected to {check.name}.') except Exception as e: print(f'Connection failed: {e}\n') print('There are multiple options to complete this task:') print(' Route 1 (CLI, recommended): qhubctl login -t ') print(' Route 2 (ENV): export KQH_PERSONAL_ACCESS_TOKEN= and set HubQiskitProvider(access_token=os.getenv("KQH_PERSONAL_ACCESS_TOKEN"))') print(' Route 3 (CODE): declare HubQiskitProvider(access_token=) explicitly in the code. Take extra precautions and replace your token after exposing it.') ``` output ``` uv run python task1_connect.py # Connected. You are connected to kipu.sim.qsim. ``` * * * ## 2Step 2: The hardware layer The ground layer of the Hub is hardware: QPUs and simulators from several vendors, all reachable with your credentials. - `provider.backends()` returns the backend ids, as strings in a list. - `provider.backends(detailed=True)` returns backends with their specifications. Check the [Backend Documentation](https://docs.hub.kipu-quantum.com/sdk-api-quantum#backend) for a full reference. * * * ### 2Task 2. Write `task2_backends.py` to a. print the number of all available backends on the qhub-SDK. Then, b. from the detailed list, keep only the simulators, and print one line each with id, and qubit count. Hint 1, where to look `provider.backends()` gives you a list of all available backends. python ``` from qhub.quantum.sdk import HubQiskitProvider provider = HubQiskitProvider() print(provider.backends()) ``` For names, do not go by memory. The following code snippet prints all properties of a backend. Check the reference: [Backend Documentation](https://docs.hub.kipu-quantum.com/sdk-api-quantum#backend) for explanations, too. python ``` from qhub.quantum.sdk import HubQiskitProvider provider = HubQiskitProvider() detailed = provider.backends(detailed=True) print(sorted(t for t in dir(detailed[0]) if not t.startswith('_'))) print(sorted(c for c in dir(detailed[0].configuration) if not c.startswith('_'))) ``` Hint 2, which patterns to use You are interested in the `id`, `type`, and `configuration`. - `id` is the backend identifier (e.g. kipu.sim.qsim) - `type` indicates whether a backend is a `QPU`, `SIMULATOR`, `ANNEALER`, or `UNKNOWN`. - `configuration.qubit_count` holds the qubit count of the backend. `print(len(your_list))` prints the length of a list. `filtered_list = list(i for i in unfiltered_list if i.property == 'VALUE')` let's you filter a list based on a property value. Solution python ``` # task2_backends.py from qhub.quantum.sdk import HubQiskitProvider provider = HubQiskitProvider() detailed = provider.backends(detailed=True) print(f'Backends the qhub-SDK offers: {len(detailed)}') simulators = list(b for b in detailed if b.type == 'SIMULATOR') print(f'\nSimulators ({len(simulators)} of {len(detailed)}):') for b in simulators: print(f' {b.id:<24} {b.configuration.qubit_count} qubits') ``` output ``` Backends the qhub-SDK offers: 22 Simulators (6 of 22): aws.sim.dm1 17 qubits aws.sim.sv1 34 qubits azure.ionq.simulator 29 qubits kipu.sim.qsim 30 qubits quandela.sim.belenos 12 qubits qudora.sim.xg1 32 qubits # -> your count may differ: the catalogue grows, and access is per account. (Tutorial updated on Aug-04 2026) ``` The identifier is `b.id`. `b.display_name` holds the human label ("Kipu QSim Simulator") you might know from the backend page on Kipu's Quantum Hub. The specifications live under `b.configuration`, which also carries `connectivity`, `gates`, `shots_range` and `supported_input_formats`, all worth a look once you start choosing hardware for quantum-centric applications. [Hub / Quantum-Backends](https://hub.kipu-quantum.com/quantum-backends) shows all available backends and their IDs with surface-level info for you to browse on the Hub. Beware, the catalogue is growing: the numbers and availabilities for your account will change over time. Access to Kipu quantum simulator `kipu.sim.qsim` and Azure IonQ Simulator `azure.ionq.simulator` is free of charge. Other backends/devices require an account with active payment information. You can check for details under [Pricing](https://hub.kipu-quantum.com/pricing). For information about the full service offering and Enterprise accounts, contact [sales@kipu-quantum.com](mailto:sales@kipu-quantum.com). * * * ## 3Step 3: From coin flip to entanglement Think back to the [Quickstart](https://docs.hub.kipu-quantum.com/quickstart#example-coin-toss) coin toss circuit. A Hadamard operation on each qubit, then measure all. For two coins, both qubit measurements are independent of each other, because nothing in that circuit connects them. With 50-50 probability each for 0 (heads) and 1 (tails), there exist four outcomes, `00`, `01`, `10` and `11`, with equal probability of 25% each. > **You enter a bet with a rich consul, that you find to be a suspicious quantum wizard. He suggests both of you bet a gold coin on the outcome of a coin flip. If both coins land on the same symbol, you get to keep it, if they disagree, you concede your coin. A seemingly fair game. Would you take that bet?** Before you answer, you are presented with the ability to think and run quantum experiments. ### 3a. Build the circuit **Your task.** Write `task3_circuit.py`. Build a two-qubit circuit. Put qubit 0 in superposition with a Hadamard (`h`) gate. Then, apply a connecting controlled-X (`cx`) gate, that is controlled by qubit 0 and targets qubit 1. Add the `measure_all` operation, and print the circuit diagram with `print(circuit.draw())`. Hint 1, where to look Find the gate from the method list. - Qiskit's [QuantumCircuit API reference](https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit.QuantumCircuit) lists all methods on that page that you need for this exercise. Look among the controlled gates. - Or browse locally, without leaving your editor: `print([m for m in dir(qc) if not m.startswith('_')])`. `QuantumCircuit(2)` gives you a two qubit setup to build your circuit. Hint 2, the shape of the answer `circuit = QuantumCircuit(2)`: creates the two-qubit setup `circuit.h(0)`: The h-gate applies an equal superposition to qubit 0. A fair coin. `circuit.cx(0,1)`: The cx-gate takes two qubit arguments. The first is the **control** qubit, the second is the **target**. It flips the target (qubit 1) exactly when the control (qubit 0) is 1. On classical input it behaves like an ordinary if-statement. Here the control is in superposition, so the rule applies to all states at once: in the branch where qubit 0 is 0, the target stays 0 (`00`); in the branch where it is 1, the target flips (`11`). Neither qubit has a decided value yet; however, it is encoded in the state that they will match. `circuit.measure_all()`: Measurements read the qubits' states simultaneously. A circuit with no measurements transpiles and submits fine, then fails when running on a backend. Without measurements, no results to obtain. Solution python ``` # task3_circuit.py from qiskit import QuantumCircuit circuit = QuantumCircuit(2) circuit.h(0) circuit.cx(0,1) circuit.measure_all() print(circuit.draw()) ``` output ``` ┌───┐ ░ ┌─┐ q_0: ┤ H ├──■───░─┤M├─── └───┘┌─┴─┐ ░ └╥┘┌─┐ q_1: ─────┤ X ├─░──╫─┤M├ └───┘ ░ ║ └╥┘ meas: 2/══════════════╩══╩═ ``` You just applied a controlled-NOT! This maximally entangles the control qubit 0 and target qubit 1: measured simultaneously, the results always match. As the purest form of combining superposition and entanglement we call it the **Bell state**. A similar classical circuit must read the control bit before deciding to flip the target. The cx gate never reads anything; it acts on both branches of the superposition and eliminates some outcomes, very similar to destructive interference in waves. To investigate this state further you would need a Bell test; check [IBM's comprehensive tutorial](https://quantum.cloud.ibm.com/learning/en/modules/quantum-mechanics/bells-inequality-with-qiskit) for more. ### 3b. Stop and reflect, what do you expect to happen? What do you expect to measure when running the circuit? Your coin flip gave four outcomes at roughly a quarter each. With the circuit you just built, which states of `00`, `01`, `10` and `11` do you expect to survive, and with what probability? Write it down, or discuss with a partner. Check it after the experiment. * * * ## 4Step 4: Run the experiment `transpile(circuit, backend)` rewrites your circuit into instructions the target hardware chip can actually use. Each chip can use different gate sets and has a different qubit layout. This is an essential translation step. Pin the backend to `kipu.sim.qsim` as introduced in Step 2. It is one of the `free` simulators on Kipu's Quantum Hub. ![Two two-qubit circuit diagrams side by side. Both start with a Hadamard gate on the first wire. The left one repeats it on the second wire; the right one instead connects the wires with a single two-qubit cx gate, highlighted with a ring.](/academy/first-entangled-circuit/image-4-circuits.png) One gate, two qubits: the only difference between independent coins and an entangled pair. ### 4a. Transpile, submit, read the counts **Your task.** Write `task4_run.py`. Create and transpile the two-qubit bell circuit for `kipu.sim.qsim`, submit 1024 shots, print the job id, wait for the job to finish, and print the measurement counts. Hint 1, where to look The [Quickstart](https://docs.hub.kipu-quantum.com/quickstart) shows both the transpile and readout calls and [Job Documentation](https://docs.hub.kipu-quantum.com/sdk-api-quantum#job) lists all properties of the job object. python ``` results = job.result() print(type(results)) print([m for m in dir(results) if not m.startswith('_')]) ``` That two-line habit is the transferable skill in this step, and it is worth more than the answer it gives you here. Hint 2, the shape of the answer `job.id` holds the job ID; print it so you can find the job again later. `job.result()` hands you a **stock Qiskit result object**, that means you need to call `job.result().get_counts()` for the measurement results. Submitting is asynchronous. That means you can submit multiple jobs in parallel. At the same time, results take a while to compute on the cloud before the results are returned to your program. Solution python ``` # task4_run.py from qhub.quantum.sdk import HubQiskitProvider from qiskit import QuantumCircuit, transpile BACKEND_ID = 'kipu.sim.qsim' # free for testing SHOTS = 1024 circuit = QuantumCircuit(2) circuit.h(0) circuit.cx(0, 1) circuit.measure_all() # Guard, not a formality. Without measurements this transpiles and submits fine, then # fails on the backend, and the error surfaces at the readout where it looks unrelated. if 'measure' not in circuit.count_ops(): raise RuntimeError('This circuit has no measurements, so there is nothing to sample.') provider = HubQiskitProvider() backend = provider.get_backend(BACKEND_ID) transpiled = transpile(circuit, backend) job = backend.run(transpiled, shots=SHOTS) print(f'Submitted to {BACKEND_ID}, {SHOTS} shots.') print(f'Job id: {job.id}') print(f'Status: {job.status()}') job.wait_for_final_state() result = job.result() print(result.get_counts()) # -> {'00': 525, '11': 499} # Your specific counts will likely differ. Both states should be measured at roughly the same probability. ``` `result.get_counts()` returns the experiment results. Sometimes the transpiled and original circuits differ from each other. You can monitor them with `transpiled.draw()` and `circuit.draw()`. In this case, the circuit is already in its most efficient form. ### 4b. Did it work? **It worked** if only two outcomes appear, `00` and `11`, splitting the shots roughly evenly, with `01` and `10` absent or negligible. Every shot, both coins agree. That agreement is the thing two classical coins cannot do. ![Two bar charts over outcomes 00, 01, 10 and 11. The left chart has four bars near 25 percent each. The right chart has bars only on 00 and 11, near 50 percent each.](/academy/first-entangled-circuit/image-5-histograms.png) Left: illustrative independent coins. Right: the measured entangled run, 525 and 499 of 1024 shots on kipu.sim.qsim. Now go back to your Step 3b prediction and check it. If it matched, think about what you now think the cx gate does. Check your answer `00` and `11` survive, at roughly half each. `01` and `10` vanish. Half the shots the control reads 0, the target is left alone, and you get `00`. Half the shots the control reads 1, the target flips, and you get `11`. Neither qubit has a determined value before measurement; what is determined is that they will **match**. By measuring one qubit, you know the other. The randomness is still there, all of it, but it is now shared instead of independent. * * * ## 5Step 5: Fixing an error message Error messages are documentation, and the good ones are better than the docs. This step is designed to exercise a troubleshooting session, with a real error. ### 5a. Trigger it Connect to an IBM QPU through the provider you have been using all along. Save this as `task5_error.py` and run it. python ``` # task5_error.py, first version. Expected to raise an error. from qhub.quantum.sdk import HubQiskitProvider provider = HubQiskitProvider() provider.get_backend('ibm.qpu.fez') ``` Read the traceback. It does not merely tell you that you are wrong. It prints a labelled migration guide, with the replacement lines written out. ### 5b. Repair it **Your task.** Rewrite `task5_error.py` so it obtains a working handle on `ibm.qpu.fez`, using what the error message and documentation tells you. Prove the handle is live by printing the backend name. Do not submit to it yet. Hint 1, where to look Read the traceback. You can find the whole instruction there. Read the message **body**, not just its first line: the useful part is below the sentence that tells you what went wrong. Hint 2, the shape of the answer IBM's backends are not reachable through the provider you have been using, because they speak IBM's own runtime protocol rather than the Hub's native one. There is a second entry point for exactly that case, and it is a sibling in the same `qhub.quantum.sdk` module. You construct it the same way and authenticate with your same credential. `backend.name` holds the string you are looking for. Solution python ``` # task5_error.py, repaired. from qhub.quantum.sdk import HubQiskitRuntimeService service = HubQiskitRuntimeService() backend = service.backend('ibm.qpu.fez') print(backend.name) # -> ibm.qpu.fez # Nothing below this line. IBM hardware bills. ``` That is a live handle on a 156-qubit IBM machine, repaired by reading the error message. Resolving a handle costs nothing, because nothing was submitted. The exception you triggered was `BackendNotSupportedError`. It reveals both the class and the method scoped to your exact wrong call and gave you the replacement lines with a migration guide. The habit worth taking from this: read tracebacks to the last line before you open a browser tab. On a well-built SDK the answer is usually already in front of you. * * * ## 6Step 6: Find your job Jobs outlive your process. You can see all your submissions under Quantum Workloads on the Quantum Hub. To find a specific one, filter by Job ID. ### 6a. From the SDK **Your task.** Write `task6_jobs.py`. List your quantum jobs and print their id, the status, the backend and the shot count. Find the job id from Step 4 in the output. Use the `HubQiskitProvider` and `provider.jobs()` to list recent jobs. Hint 1, where to look The provider has one method for this, and it takes no arguments. The `dir()` pattern from Step 2's first hint surfaces it, and [Managing quantum jobs](https://docs.hub.kipu-quantum.com/manage-quantum-jobs) covers the surface. Print one listing entry's field list before you write the loop. The objects are not identical to the job you got back from `backend.run()`. Solution python ``` # task6_jobs.py from qhub.quantum.sdk import HubQiskitProvider provider = HubQiskitProvider() jobs = provider.jobs() # jobs() returns one unsorted page of up to 50 jobs; order it newest first jobs.sort(key=lambda j: j.created_at or '', reverse=True) print(f'Recent Jobs: {len(jobs)}.') for j in jobs[:5]: print(f' {j.id} {str(j.status):<12} {str(j.backend_id):<24} shots={j.shots}') ``` output ``` Getting your jobs from Kipu Quantum Hub, this may take a few seconds... Recent Jobs: 50. XXXXXXXX-XXXX-XXXX-XXXX-XXXXXXXXXXXX COMPLETED kipu.sim.qsim shots=1024 # -> your ids, count and history will differ. ``` ### 6b. From the dashboard Open the [quantum workloads](https://hub.kipu-quantum.com/quantum-workloads) and find the job id from Step 4. You can **Retrieve Inputs & Results** and even **Cancel Jobs** from the interface. ![The Kipu Quantum Hub quantum workloads list, showing a completed simulator job with its id, status, backend and creation time.](/academy/first-entangled-circuit/image-6a-workloads-list.png) Every submission appears under Quantum Workloads, newest first. ![The job detail page for a completed kipu.sim.qsim run: a two-bar measurement histogram and a summary panel showing backend, SDK and 1024 shots.](/academy/first-entangled-circuit/image-6b-job-detail.png) The same job id, status, backend and shot count the SDK printed, now in the dashboard. In addition to the Web-UI, you can retrieve results of previous jobs using the Job ID and the `HubQuantumClient` (constructed with an `api_key` argument): [Job Retrieval Reference](https://docs.hub.kipu-quantum.com/sdk-api-quantum#get-job). * * * ## 7Step 7: Kipu's Quantum Hub four layers So far, you have been working in the bottom two layers of the four-layer Quantum Hub. ![A four-layer diagram of the Kipu Quantum Hub: hardware at the bottom, orchestration above it, services above that, and customer applications at the top. A callout ringing the bottom two layers reads "you worked here".](/academy/first-entangled-circuit/image-7-stack.png) The four layers of the Kipu Quantum Hub. This tutorial lived in L0 and L1. Read bottom up. You have already worked in two of them. **L0 Hardware.** QPUs and simulators from several vendors. You worked with it in Step 2 and submitted to it in Step 4. **L1 Orchestration.** Everything that carries a workload down to L0 and results back up: the SDK, the MCP server, `qhubctl`, the REST API, data pools, classical compute, observability. `HubQiskitProvider` is L1. Steps 1, 4, 5 and 6 were all L1 work. **L2 Services.** Kipu's own algorithms, plus an open marketplace around them. **Miray** solves combinatorial optimization problems (a BF-DCQO solver), on simulator and hardware. **Rimay** does quantum machine learning (DQFE feature mapping), on simulator and hardware. - [Marketplace services](https://hub.kipu-quantum.com/marketplace/services) Each shows a price label of `Free`, `On Request` or `Commercial`. `Miray Advanced Quantum Optimizer - Simulator` is Free. `Rimay - Quantum Feature Extraction - Simulator` is Free. `Illay Base Quantum Optimizer` is Free. That means you can use them to test your quantum-centric workflows without being billed extra on top of your license. Later Tutorials will use them to teach how to use services. **L3 Applications.** Actual products and demos you would ship to a customer. Komatsu predictive maintenance, KPMG satellite image recognition, DB Systel anomaly detection in network traffic. Browse the [Marketplace use cases](https://hub.kipu-quantum.com/marketplace/use-cases) for more examples. * * * ## Optional, wire up the MCP server L1 also exposes the Hub to AI coding agents over MCP. It is a remote HTTP server, so there is nothing to install. Check the [MCP Server Reference](https://docs.hub.kipu-quantum.com/agentic/mcp-server) for more details. The server authenticates via OAuth. The first time your AI client connects, it opens a browser window where you log in to the Kipu Quantum Hub and authorize access. No tokens or credentials are stored in your config files. * * * ## Further exploration Think about one candidate application from your own work. A real problem, in one sentence. At which layer would you build it? - L3: there might be a L2 service you could build it on. - L2: or lower, think about what is missing from the marketplace today. - L1: you are building infrastructure, and we would like to offer you a job. - L0: you are building hardware, and we would like to partner with you. Business aside, we hope you enjoy building with the Kipu Hub. The team is super receptive to feedback. Please reach out and let us figure out a solution for your (quantum-centric) ideas. The map is only worth something if your own problem fits on it. * * * **Documentation:** [Kipu Quantum Hub](https://hub.kipu-quantum.com) | [Hub docs](https://docs.hub.kipu-quantum.com) | [Quickstart](https://docs.hub.kipu-quantum.com/quickstart) | [Quantum SDK reference](https://docs.hub.kipu-quantum.com/sdk-quantum) | [Access tokens](https://docs.hub.kipu-quantum.com/manage-access-tokens) | [Managing quantum jobs](https://docs.hub.kipu-quantum.com/manage-quantum-jobs) | [CLI reference](https://docs.hub.kipu-quantum.com/cli-reference) | [MCP server setup](https://docs.hub.kipu-quantum.com/agentic/mcp-server) | [Backends catalogue](https://hub.kipu-quantum.com/quantum-backends) | [Dashboard](https://dashboard.hub.kipu-quantum.com) Happy Optimizing 🚀 Last tested on the Kipu Quantum Hub · 4 August 2026 ## Ready to build? Run a finance or energy-trading book and want to assess practical fit on current hardware? Get in touch, or tell us if a step did not run for you. [Get in touch](/contact)[Report a bug or send feedback](/contact) --- # Superposition and Entanglement: Why Quantum, Why Now URL: https://kipu-quantum.com/academy/tutorials/first-entangled-circuit-primer [Back to Academy](/academy) # Superposition and Entanglement: Why Quantum, Why Now The probability you already know from coin flips, the connection between them you do not, and the fifty-year head start classical computing had. Tutorial•Beginner•~5 min•[Hands-on tutorial](/academy/tutorials/first-entangled-circuit) [Get in touch](/contact) ## Superposition and Entanglement Classical computers push bits around with and, or, not. Quantum computers add two more moves: superposition and entanglement. A quantum bit (qubit) can sit between 0 and 1. The Hadamard gate `H` parks it exactly in the middle, so a measurement comes out 0 half the time and 1 the other half. Try it on the Bloch sphere below. What happens if you press the `H` button? That is superposition, and you already know it. It is a coin flip. Measuring collapses the qubit to a plain 0 or 1, so a single run tells you almost nothing. You run the same circuit hundreds of times and read the statistics instead. Those runs are called shots. Entanglement is the part coin flips do not prepare you for. Two qubits can be wired so their results always agree. Both heads, or both tails. Neither outcome is decided in advance. They simply match. Each result is random. Which results can happen is not. Neither idea is exotic: both computing traditions grew out of the same nineteenth-century algebra. ![Two icon rails of computing milestones. The classical rail runs from Boolean algebra in 1847 to the microprocessor in 1971 and keeps scaling; the quantum rail repeats the same stages from matrix algebra in 1858 to the supremacy era in 2019 and on toward industrial use, about fifty years behind at each stage.](/academy/first-entangled-circuit/timeline-dual.png) Quantum computing is walking a path we have already walked, about half a century apart. Every quantum milestone lands roughly fifty years after its classical twin. Qubits are tiny and unstable, and that costs time. Closing the gap takes specialists from every profession, not only physicists. You, right now, working through the tutorial. From the Kipu team, a big ♥-thank you. * * * ## About our approach The [hands-on tutorial](/academy/tutorials/first-entangled-circuit) this primer belongs to runs seven steps. Six have you write a small Python file and run it from a terminal, so you finish with a project folder you can come back to. The seventh maps the Kipu Quantum Hub around your circuit. ### A note about hints in this course Tasks come with collapsed hints. Before opening one, guess. If a colleague or a chatbot you trust is nearby, argue it out first. Hints come in three tiers: - **Hint 1, where to look.** Points at the docs page or the command that surfaces the answer. No answers here. - **Hint 2, the shape of the answer.** Describes what you are reaching for without naming it. Enough to unstick you, not enough to skip the thinking. - **Solution.** Full working code, verified against the live Hub, with a copy button. Opening the Solution first is the one reliable way to get nothing out of this page. Finding the answer in the reference yourself is the skill that makes you independent of tutorials like this one. * * * Ready for the hands-on part? [Start the hands-on tutorial](/academy/tutorials/first-entangled-circuit). ## Ready to build? Run a finance or energy-trading book and want to assess practical fit on current hardware? Get in touch, or tell us if a step did not run for you. [Get in touch](/contact)[Report a bug or send feedback](/contact) --- # Quantum Optimization Quickstart URL: https://kipu-quantum.com/academy/tutorials/quantum-optimization-quickstart [Back to Academy](/academy) # Quantum Optimization Quickstart Run your first quantum optimization in a few lines of Python, on IBM Quantum with Iskay or on the Kipu Quantum Hub with Miray. Copy the code and follow along. Tutorial•Beginner•~15 min [I’m ready to build](https://2dqpz5.share-eu1.hsforms.com/2EAULWH4YQHqFoFFt_yxynw?utm_source=kipu-website&utm_medium=academy-quickstart)[Sign up on the Kipu Hub](https://login.hub.kipu-quantum.com/realms/planqk/protocol/openid-connect/registrations?client_id=planqk-login&response_type=code&scope=openid&redirect_uri=https%3A%2F%2Fhub.kipu-quantum.com) Combinatorial optimization is where quantum hardware is useful today. Kipu Quantum’s BF-DCQO engine encodes your objective directly as a higher-order binary problem (HUBO), so you spend qubits on variables, not on reducing higher-order terms to pairwise ones. The same engine ships two ways: as **Iskay**, a first-class Qiskit Function on the IBM Quantum Platform, and as **Miray** on the Kipu Quantum Hub, which also targets IonQ, Rigetti, and QuEra. This is the first tutorial on Kipu Academy. More are on the way, each pairing a hands-on walkthrough with code you can copy and a notebook you can run. ### 1. Connect Load Iskay as a Qiskit Function, or point the Hub client at the Miray service endpoint. ### 2. Define a HUBO Express your objective as binary variables with linear, quadratic, and higher-order terms. ### 3. Run and read the solution Submit, let Kipu manage encoding and post-processing, and read back the optimal bitstring. ## The code Same objective, two entry points. Switch tabs to compare the Iskay and Miray calls. Iskay · IBM QuantumMiray · Kipu Hub iskay\_quickstart.py ``` from qiskit_ibm_catalog import QiskitFunctionsCatalog # pip install qiskit-ibm-catalog catalog = QiskitFunctionsCatalog( token=IBM_TOKEN, channel="ibm_quantum_platform", instance=INSTANCE_CRN, ) iskay = catalog.load("kipu-quantum/iskay-quantum-optimizer") # Objective as a QUBO/HUBO. Higher-order terms are native. hubo = { "()": 0.0, # constant "(0,)": -1.0, # linear "(1,)": -1.0, "(0, 1)": 2.0, # quadratic (QUBO) "(0, 1, 2)": -1.5, # cubic (HUBO), no extra qubits } job = iskay.run( problem=hubo, problem_type="binary", instance=INSTANCE_CRN, backend_name="ibm_fez", options={"shots": 100, "num_iterations": 3}, ) result = job.result() print(result["solution_info"]["cost"], result["solution"]) ``` ``` from qhub.service.client import HubServiceClient # pip install qhub-service client = HubServiceClient( service_endpoint=SERVICE_ENDPOINT, access_key_id=ACCESS_KEY_ID, secret_access_key=SECRET_ACCESS_KEY, ) # Same objective, same engine — also runs on IonQ, Rigetti, QuEra. hubo = { "()": 0.0, "(0,)": -1.0, "(1,)": -1.0, "(0, 1)": 2.0, "(0, 1, 2)": -1.5, } execution = client.run(request={ "problem": hubo, "problem_type": "binary", "shots": 100, "num_iterations": 3, }) execution.wait_for_final_state() response = execution.result() print(response.result["cost"], response.result["mapped_solution"]) ``` The solver needs credentials before it runs. For **Miray** on the Hub, the [Quickstart](https://docs.hub.kipu-quantum.com/quickstart) walks you through account setup, the [Service SDK](https://docs.hub.kipu-quantum.com/sdk-service) documents `HubServiceClient`, and [access tokens](https://docs.hub.kipu-quantum.com/manage-access-tokens) issues your `access_key_id` and `secret_access_key`. For **Iskay**, load it as a Qiskit Function with your IBM Quantum Platform token and instance CRN. ## Run it on the Kipu Hub The Miray path runs on the Kipu Quantum Hub: create a free account, grab your service keys, and submit the same HUBO in minutes. [I’m ready to build](https://2dqpz5.share-eu1.hsforms.com/2EAULWH4YQHqFoFFt_yxynw?utm_source=kipu-website&utm_medium=academy-quickstart)[Sign up on the Kipu Hub](https://login.hub.kipu-quantum.com/realms/planqk/protocol/openid-connect/registrations?client_id=planqk-login&response_type=code&scope=openid&redirect_uri=https%3A%2F%2Fhub.kipu-quantum.com) --- # How Quantum Portfolio Optimization Helps Finance URL: https://kipu-quantum.com/academy/tutorials/quantum-portfolio-optimization - [1Formulate for Kipu's Quantum Optimizer](#step-1) - [2Run it on Kipu's Quantum Hub or IBM Qiskit Functions](#step-2) - [3Read & verify](#step-3) [Back to Academy](/academy) # How Quantum Portfolio Optimization Helps Finance Build a cardinality-constrained portfolio selector with a real three-body risk term and run it on Kipu's quantum optimizer. Part 1 of two. Tutorial•Intermediate•~20 min•[Part 1 of 2](/academy/tutorials/quantum-portfolio-optimization-part-2-scaling) [Get in touch](/contact) > **Educational disclaimer.** This is a hands-on starter tutorial in the beautiful field of quantum computing applications for finance, meant for learning. The numbers are illustrative and the models deliberately simplified; nothing here is complete or constitutes financial advice. * * * ## The rise of Quantum Computing in Finance Picking a portfolio is a simple selection problem. You want high expected return, but that comes at the cost of higher risk. The goal is to balance risk-reward and diversify enough to balance out worst-case scenarios. Buying everything is not always an option: mandates, transaction costs, and tracking budgets force you to hold *exactly k* of *n* candidates. That last constraint, called a **cardinality constraint**, is what turns a textbook optimization into a hard combinatorial problem. The number of ways to choose 125 items out of 250 is larger than the number of atoms in the observable universe. Classical solvers handle this with clever heuristics and branch-and-bound, and they do well up to a point. But the moment the objective stops being a clean convex function (real correlation structure, integer lot sizes, sector caps, higher-order interactions between holdings), the search space gets rugged and the heuristics stop working. Aside: why model assumptions matter (the 2008 Gaussian-copula story) The 2008 financial crisis was, in part, initiated by a mathematical model. Much of the credit-derivatives market priced correlated default risk with the **Gaussian copula**, a formula that compressed the joint behaviour of thousands of loans into a single pairwise correlation number. It was elegant, fast, and catastrophically wrong when the market panicked. Years before the crash even its inventor warned of its shortcomings. By 2009 Felix Salmon called it "The Formula That Killed Wall Street." In a nutshell, a Gaussian model is pinned down entirely by means and pairwise covariances. So *by construction* it encodes no higher-order co-movement at all. Three or more assets moving together could convey a much stronger market signal than any combination of pairs. Correlations that appeared small and were treated as independent in calm markets snapped toward 1, diversification assumptions failed, and everything came crashing down together in September 2008: a so-called **tail dependence** failure mode. Classical optimization has long been pushed toward pairwise-only models because higher-order terms are expensive to add computationally. However, real markets are full of precisely that higher-order interlinked structure. The regulatory aftermath of 2008 still shapes finance today. The **Basel III** reforms, and the Fundamental Review of the Trading Book (FRTB) within them, force banks to hold capital against exactly this kind of correlated market risk. Assembling a book that meets those capital rules at minimum cost is itself a constrained optimization, an adjacent problem we return to in the applications below. ### Introduction to the quantum portfolio optimization problem Let's be precise about what gap quantum closes. It does **not** make a risk model correct (garbage in, garbage out still holds). What it changes is **tractability**: a HUBO, the higher-order generalization of a QUBO, lets you write three-body and higher interactions directly, one variable per asset, and hand them to the optimizer as-is. The model structure can respect interdependence instead of the pairwise approximation. Now, quantum computers are limited in size and error budget. That means we are bound to smaller, representative instances of many problems. Over the course of the decade this will change dramatically, with many problems becoming viable around 2030, when many currently separate technologies merge into a fault-tolerant quantum computer. This and many other reasons motivate the exploration of QPUs in the financial context. Not because quantum computers try every combination at once (they don't), but because a quantum optimizer is very good at exploring interlinked data structures. These usually produce rugged energy landscapes where classical solvers, like greedy and local-search methods, miss good low-cost configurations. Kipu and IonQ ran a first hardware demonstration of exactly this, a 20-asset portfolio on a trapped-ion device, back in 2023 ([arXiv:2308.15475](https://arxiv.org/abs/2308.15475)). A follow-up study in 2026 ([arXiv:2602.23976](https://arxiv.org/abs/2602.23976)) scaled the problem to 250 assets. ### You may recognize the method if you work on… - **Portfolio and index construction.** Build a book under sector caps, lot sizes, and tracking-error limits. - **Energy trading and dispatch.** Select a constrained set of contracts whose payoffs co-move through fuel prices, weather, and load. - **Risk-budgeted hedging.** Cover exposure without doubling up on the same underlying factor. - **Feature selection** for factor models and ML trading signals. Kipu and IonQ ran exactly this higher-order problem on trapped-ion hardware ([arXiv:2604.26834](https://arxiv.org/abs/2604.26834)). - **Regulatory capital optimization (Basel III / FRTB-SA).** Assemble a book that meets capital rules at minimum cost. Kipu cut regulatory capital consumption by more than 10% on real bank portfolios ([Capital Saving case study](https://kipu-quantum.com/examples)). In this lab we will build the smallest version of this problem, run it on Kipu's quantum optimizer, and put it to the test with a three-body term below. [Part 2](/academy/tutorials/quantum-portfolio-optimization-part-2-scaling) then scales the very same kernel to a 100-asset universe. * * * ## 1Step 1: Formulate for Kipu's Quantum Optimizer Formulation is one of the most important steps in solving an optimization problem with a quantum computer. Its size (number of variables), density (non-zero terms), and order (linear, quadratic, cubic, ...) drive the circuit depth: the amount of sequential operations, or "length", of a quantum program. Current Quantum Processing Units are constrained in size (number of qubits) and error budget (hardware layout / qubit connectivity and 2-qubit-gate errors). Circuit depth is a decisive factor in whether a program can run within a given QPU's error budget. ### 1. Formulate Encode an 8-asset portfolio as a HUBO, with a real three-body risk term a QUBO cannot express. ### 2. Run on a quantum optimizer Submit it to Iskay on IBM Quantum, or Miray on the Kipu Quantum Hub. Same engine, your choice. ### 3. Read & verify Decode the pick, brute-force check the optimum, and see the value on the risk/return frontier. Changing the formulation to a problem- and hardware-specific one can lead to much better results. Many industry quantum teams engage in this exercise, often collaboratively, to achieve "Quantum Readiness". Even assuming perfect quantum computers, two questions remain: do you have suitable problems in your organisation, and can you formulate them so they are solvable? Sometimes useful problems are not runnable on current hardware, so it is worth checking regularly for upgrades. ### 1a. State the problem in numbers We will pick **4 assets out of 8** S&P 500 stocks, trading expected return against the risk of holding correlated pairs. This problem is small enough to check by brute force, but structured enough to show the behaviour and understand how to scale it. python ``` tickers = ["AAPL", "MSFT", "JPM", "XOM", "JNJ", "PG", "NVDA", "CVX"] sector = ["Tech", "Tech", "Financials", "Energy", "Health", "Staples", "Tech", "Energy"] # Expected annual return, in percent (illustrative) returns = [18.0, 16.0, 12.0, 11.0, 8.0, 7.0, 22.0, 10.0] # High pairwise correlations: holding both concentrates risk correlation = { (0, 1): 0.70, # AAPL - MSFT (mega-cap tech) (0, 6): 0.65, # AAPL - NVDA (1, 6): 0.68, # MSFT - NVDA (3, 7): 0.88, # XOM - CVX (energy) (4, 5): 0.55, # JNJ - PG (defensives) } k = 4 # hold exactly four names ``` ### 1b. Encode it as a HUBO Kipu's optimizer minimizes an objective written as a dictionary of variable interactions (a HUBO, the higher-order generalization of a QUBO). Each binary variable `x_i` is 1 if asset *i* is held, 0 if not. Four relationships influence the objective function: 1. **Reward return.** A negative linear term `-return_i` for each asset, so the minimizer prefers holding high-return assets. 2. **Penalize correlated pairs.** A positive quadratic term on each correlated pair. Prefer not to hold both. 3. **Model higher-order risk.** A positive *three-body* term on the mega-cap tech triple (AAPL, MSFT, NVDA), so holding all three together costs more than the three pairwise penalties alone. This tries to model the joint-sector-crash co-movement from the opening section, and it is the term a QUBO cannot express efficiently. BF-DCQO handles these higher-order terms natively, with no quadratization and no auxiliary qubits, which is the subject of its own paper ([arXiv:2409.04477](https://arxiv.org/abs/2409.04477)). 4. **Enforce the count.** A cardinality penalty `(Σ x_i − k)²` that is zero only when exactly *k* names are held, scaled large enough to dominate the return and risk terms. The full objective, and how it becomes one HUBO dictionary **1\. Add the four terms.** Summed together, the four relationships above are a single objective the optimizer minimizes over the held/not-held vector **x** (each `x_i ∈ {0, 1}`): `H(x) = − Σ_i r_i x_i + λ Σ_{i **Encoding rule.** Keep the cardinality penalty roughly 10× larger than the return-plus-risk range. Too small and the optimizer "cheats" by holding three or five names to dodge a correlation penalty; too large and the correlation-risk signal is drowned out. The constraint and the objective have to stay in balance. ### 1c. A trap a naive strategy might fall into Before running quantum workflows, we compare to a naive and greedy baseline. python ``` greedy = sorted(range(n), key=lambda i: -returns[i])[:k] print([tickers[i] for i in sorted(greedy)]) # -> ['AAPL', 'MSFT', 'JPM', 'NVDA'] ``` Three of those four (AAPL, MSFT, NVDA) are *exactly* the correlated tech triple we penalized. The naive pick maximizes headline return and walks straight into both the pairwise penalties and the three-body term. It concentrates risk in a single sector. A good portfolio optimizer refuses to do that. Optional: formulate with the Qiskit optimization mapper Hand-building the dictionary is the best way to *understand* the encoding. On a large instance with many constraints (sector caps, lot sizes, turnover limits) you do not want to hand-expand `(Σ x − k)²` and rebalance penalty weights each time. Qiskit ships a modeling addon, [`qiskit-addon-opt-mapper`](https://qiskit.github.io/qiskit-addon-opt-mapper/), that lets you state the problem declaratively (variables, objective, constraints) and emits the QUBO/HUBO for you. It also reads `docplex` and LP files, so an existing classical model comes across largely unchanged. For an example see Part 2. * * * ## 2Step 2: Run it on Kipu's Quantum Hub or IBM Qiskit Functions Both platforms feature the same Quantum Optimizer by Kipu Quantum. ### Option A: Iskay on IBM Quantum [Iskay](https://kipu-quantum.com/iskay) is Kipu's optimizer delivered as a Qiskit Function on the IBM Quantum Platform. If your stack is IBM, get in touch with your IBM Engagement Manager to get access. python ``` from qiskit_ibm_catalog import QiskitFunctionsCatalog # pip install qiskit-ibm-catalog catalog = QiskitFunctionsCatalog( token=IBM_TOKEN, channel="ibm_quantum_platform", instance=INSTANCE_CRN, ) iskay = catalog.load("kipu-quantum/iskay-quantum-optimizer") job = iskay.run( problem=hubo, problem_type="binary", backend_name="ibm_fez", options={"shots": 2000, "num_iterations": 4}, ) result = job.result() print(result["solution_info"]["cost"], result["solution"]) # Tip: increase shots and num_iterations for better results, or reduce for faster runtime. ``` ### Option B: Miray on the Kipu Quantum Hub [Miray](https://hub.kipu-quantum.com/) features the *same BF-DCQO engine* ([arXiv:2405.13898](https://arxiv.org/abs/2405.13898)) on the Kipu Quantum Hub, with a free simulator tier you can run with a one-line switch to hardware versions later. QHub account required. Related documentation pages: [Quickstart](https://docs.hub.kipu-quantum.com/quickstart) (account + first run), [Service SDK](https://docs.hub.kipu-quantum.com/sdk-service) (the `HubServiceClient` below), [access tokens](https://docs.hub.kipu-quantum.com/manage-access-tokens) (`access_key_id` / `secret_access_key`), and [using a service](https://docs.hub.kipu-quantum.com/services/using-a-service) (subscribe to the simulator). python ``` from qhub.service.client import HubServiceClient # pip install qhub-service client = HubServiceClient( service_endpoint=SERVICE_ENDPOINT, # Miray Advanced Quantum Optimizer - Simulator access_key_id=ACCESS_KEY_ID, secret_access_key=SECRET_ACCESS_KEY, ) execution = client.run(request={ "problem": hubo, "problem_type": "binary", "shots": 2000, "num_iterations": 6, "num_greedy_passes": 1, }) execution.wait_for_final_state() response = execution.result() print(response.result["cost"], response.result["mapped_solution"]) # Tip: increase shots and num_iterations for better results, or reduce for faster runtime. ``` * * * ## 3Step 3: Read & verify A Kipu Hub service returns a result object, not just a bitstring. You read it with `response.result["key"]`: `cost` is the objective value the optimizer reached, `mapped_solution` is the held/not-held assignment keyed by your original asset index, and `bitstring` is the same solution in post-transpilation qubit order. The next three steps decode that object, brute-force check it, and plot what it bought you. ### 3a. Read the result This is the actual output from running the Option B code above on the **Miray Advanced Quantum Optimizer (Simulator)** on the Kipu Quantum Hub, 2000 shots, 6 iterations, one greedy pass. Runtime: about 3 minutes. output ``` cost = -56.5 mapped_solution = {0:1, 1:0, 2:1, 3:1, 4:0, 5:0, 6:1, 7:0} ``` Decode the selected names (variables set to 1): python ``` sol = response.result["mapped_solution"] # keys are string asset indices selected = [tickers[int(i)] for i in sol if sol[i] == 1] print(selected) # -> ['AAPL', 'JPM', 'XOM', 'NVDA'] ``` Let's have a look at what the optimizer did (lower cost is better): Strategy Holdings Cost What happened Naive (top-4 by return) AAPL · MSFT · JPM · NVDA −27.7 holds the full tech triple **Quantum optimizer** AAPL · JPM · XOM · NVDA **−56.5** diversified across 4 sectors **Keeping the two highest-return tech bets** (NVDA at 22%, AAPL at 18%) but **dropping the redundant third** (MSFT, correlated 0.68 with NVDA and 0.70 with AAPL) in favor of JPM (financials) and XOM (energy) opens a 28.8-point gap. The optimizer preserved its return appetite while keeping modelled risk less concentrated. That is the value proposition of portfolio optimization. ### 3b. Verification. Never trust an optimizer you did not check For a problem this small you can confirm the global optimum by brute force, and you always should before trusting any solver, classical or quantum. The `energy` function below recomputes the same objective the optimizer minimized. Complexity grows quickly, though, and favors quantum computers long-term. python ``` from itertools import product def energy(x): e = card_penalty * k**2 for i in range(n): e += (-returns[i] + card_penalty * (1 - 2 * k)) * x[i] for i in range(n): for j in range(i + 1, n): rho = correlation.get((i, j), 0.0) e += (risk_penalty * rho + card_penalty * 2) * x[i] * x[j] e += 20.0 * x[0] * x[1] * x[6] # the three-body tech-triple term return e # 1. Cardinality holds assert sum(sol[str(i)] for i in range(n)) == k # 2. Reported cost matches a local recompute x = tuple(sol[str(i)] for i in range(n)) assert abs(energy(x) - response.result["cost"]) < 1e-3 # 3. It is the true global optimum best = min(product([0, 1], repeat=n), key=energy) assert energy(best) == energy(x) print("Verified: global optimum, exactly k held, energy consistent.") ``` All three checks pass on the verified run: exactly 4 names held, energy −56.5 matching the reported cost, and the selection equal to the brute-force optimum. ### 3c. Comparison. The risk/return frontier A single number ("cost −56.5") does not show *why* the pick is good. Plot every feasible portfolio in risk/return space and the answer is visual. There are only 70 ways to choose 4 of 8, so we can draw all of them: python ``` import itertools import matplotlib.pyplot as plt # Kipu brand colors (tokens.css) GOLD, AMARANTH, BG, FG = "#b38f12", "#a52469", "#EDECEC", "#0f1319" def port_return(bits): return sum(returns[i] for i in range(n) if bits[i]) def port_risk(bits): r = sum(rho for (i, j), rho in correlation.items() if bits[i] and bits[j]) if bits[0] and bits[1] and bits[6]: r += 20.0 / risk_penalty # three-body term, same risk scale return r pts = [] for combo in itertools.combinations(range(n), k): bits = [1 if i in combo else 0 for i in range(n)] pts.append((port_risk(bits), port_return(bits))) quantum = [1, 0, 1, 1, 0, 0, 1, 0] # the verified solution gcombo = sorted(range(n), key=lambda i: -returns[i])[:k] # the naive pick greedy = [1 if i in gcombo else 0 for i in range(n)] fig, ax = plt.subplots(figsize=(7, 5)) fig.patch.set_facecolor(BG); ax.set_facecolor(BG) ax.scatter([p[0] for p in pts], [p[1] for p in pts], c="#cfcdcd", s=30, label="all portfolios") ax.scatter(port_risk(quantum), port_return(quantum), c=GOLD, s=190, edgecolors="white", lw=1.5, zorder=3, label="Kipu quantum optimum") ax.scatter(port_risk(greedy), port_return(greedy), facecolors="none", edgecolors=GOLD, s=190, lw=2.4, zorder=2, label="naive (top-4 return)") ax.set_xlabel("Correlation risk score (lower is safer)", color=FG) ax.set_ylabel("Expected return (%)", color=FG) ax.set_title("4-of-8 portfolios: risk vs return", color=FG, fontweight="bold", loc="left") for s in ("top", "right"): ax.spines[s].set_visible(False) ax.legend(frameon=False) plt.show() ``` The Pareto-efficient portfolios (no other has more return at less risk) come out to just three points: Risk Return Portfolio Role 0.00 53 JPM / XOM / JNJ / NVDA minimum-risk efficient 0.65 63 AAPL / JPM / XOM / NVDA **quantum optimum (the knee)** 4.03 68 AAPL / MSFT / JPM / NVDA naive pick (max-return corner) A honest reading is more nuanced than "the optimizer wins." The naive pick is **not** irrational: it sits on the frontier, at the maximum-return corner. It takes on large risk for the last bit of return: going from the quantum optimum to the naive pick buys **+5 points of return for +3.4 points of risk**, while the step *into* the optimum bought +10 return for +0.65 risk. Up to that point each unit of risk is still buying a lot of return. The risk appetite we encoded (`risk_penalty = 10`) controls exactly where on that curve the optimizer lands. * * * ## Your move 1. **Run the lab.** Open the Kipu Quantum Hub, subscribe to the free Miray Advanced Quantum Optimizer (Simulator), and run the Option B code above. It is free and finishes in minutes. 2. **Swap in your universe.** Replace the 8 tickers with your candidate list, or real data with return and correlation estimates. The encoding does not change. 3. **Scale it past the simulator.** A single direct call tops out around 20 assets. [Part 2: scaling to the S&P 500](/academy/tutorials/quantum-portfolio-optimization-part-2-scaling) decomposes a 100-asset universe into hardware-sized clusters and stitches them back together, the pipeline Kipu and IonQ used to reach 250 names on trapped-ion hardware. 4. **Bring your problem.** If you run a finance or energy-trading book and want to assess practical fit on current hardware, the [Kipu Quantum Academy](https://kipu-quantum.com/academy) is built for you. **Documentation:** [Kipu Quantum Hub](https://hub.kipu-quantum.com/) | [Hub docs](https://docs.hub.kipu-quantum.com/) | [Iskay on IBM Quantum](https://kipu-quantum.com/iskay) | [Kipu Quantum Academy](https://kipu-quantum.com/academy) **Research:** [Large-scale portfolio optimization on a trapped-ion quantum computer (arXiv:2602.23976)](https://arxiv.org/abs/2602.23976) | [BF-DCQO, the optimizer's algorithm (arXiv:2405.13898)](https://arxiv.org/abs/2405.13898) | [BF-DCQO for higher-order (HUBO) optimization (arXiv:2409.04477)](https://arxiv.org/abs/2409.04477) | [DCQO portfolio optimization on IonQ, 20 assets (arXiv:2308.15475)](https://arxiv.org/abs/2308.15475) *Tested live on the Kipu Quantum Hub Miray simulator: the Step 3 run returned the verified global optimum (cost −56.5, AAPL/JPM/XOM/NVDA). The decomposition pipeline that scales this to 100 and 250 assets is built and verified in [Part 2](/academy/tutorials/quantum-portfolio-optimization-part-2-scaling).* Happy Optimizing 🚀 Last tested on the Kipu Quantum Hub · 25 June 2026 ## Ready to build? Run a finance or energy-trading book and want to assess practical fit on current hardware? Get in touch, or tell us if a step did not run for you. [Get in touch](/contact)[Report a bug or send feedback](/contact) --- # Scaling Quantum Portfolio Optimization to the S&P 500 URL: https://kipu-quantum.com/academy/tutorials/quantum-portfolio-optimization-part-2-scaling - [1Decompose and run the pipeline](#step-1) - [2Read & verify the results from Miray](#step-2) - [3Tune risk aversion with one variable](#step-3) [Back to Academy](/academy) # How to Scale Quantum Portfolio Optimization to the S&P 500 Scale the same kernel past the simulator's qubit limit by decomposition, the pipeline Kipu and IonQ used to reach 250 S&P 500 names on trapped-ion hardware. Part 2 of two. Tutorial•Advanced•~25 min•[Part 2 of 2](/academy/tutorials/quantum-portfolio-optimization) [Get in touch](/contact) > **Educational disclaimer.** This is a hands-on starter tutorial in the beautiful field of quantum computing applications for finance, meant for learning. The data is synthetic and the models deliberately simplified; nothing here is complete or constitutes financial advice. * * * ## The qubit wall, and how to get past it The free simulator tops out around 20 qubits, about 20 assets in one direct call. To handle 100 assets, or the paper's 250, you decompose. Meaning you split the universe into hardware-sized clusters, solve each on its own, and stitch the pieces back together. Following the pipeline of ["Large-scale portfolio optimization on a trapped-ion quantum computer"](https://arxiv.org/abs/2602.23976) (the Kipu/IonQ paper, summarized in *The research behind it* below) is part of the skillset that can make quantum optimization useful on near-term hardware at all. Now, let's run a genuine version of that pipeline on a **100-asset** universe (six sectors, hold exactly 50), a problem with 100-choose-50 ≈ 10²⁹ feasible portfolios, far beyond enumeration and far beyond one simulator call. The qubit budget is a hard limit: the free simulator sits at 20, and backends on Kipu's Quantum Hub and Qiskit Functions run larger (IBM Nighthawk: 120 qubits, Heron: 156). This influences the amount and size of clusters we need. > **A note on the model.** Unlike the paper, which is strictly quadratic (covariance is pairwise), we include the **three-body terms** from Part 1's encoding. A HUBO can express complex multi-variable interactions, and BF-DCQO solves them natively. ### 1. Decompose Split a 100-asset universe into hardware-sized clusters, solve each on Miray, then recombine and repair to a feasible book. ### 2. Read & verify Read the Miray results, brute-force check each cluster, and benchmark the portfolio against strong classical baselines. ### 3. Tune Sweep the risk-aversion dial λ and watch the portfolio trace the efficient frontier. ### Get up to speed Part 2 is self-contained, but it assumes Part 1's two essentials: a Miray client and a HUBO formulation. Drop these cells in first. (New here? [Part 1](/academy/tutorials/quantum-portfolio-optimization) builds both from scratch on an 8-asset book.) **1\. The Miray client** (same as Part 1, Step 2 Option B, Kipu Hub only). Hub docs: [Quickstart](https://docs.hub.kipu-quantum.com/quickstart), [Service SDK](https://docs.hub.kipu-quantum.com/sdk-service), [access tokens](https://docs.hub.kipu-quantum.com/manage-access-tokens), [using a service](https://docs.hub.kipu-quantum.com/services/using-a-service). python ``` from qhub.service.client import HubServiceClient # pip install qhub-service client = HubServiceClient( service_endpoint=SERVICE_ENDPOINT, # Miray Advanced Quantum Optimizer - Simulator access_key_id=ACCESS_KEY_ID, secret_access_key=SECRET_ACCESS_KEY, ) ``` **2\. The formulation, the advanced way.** Part 1 hand-builds the HUBO dictionary to *teach* the encoding. Since you are here to scale, take the declarative path instead: state the model with [`qiskit-addon-opt-mapper`](https://qiskit.github.io/qiskit-addon-opt-mapper/) (variables, objective, constraints) and let it expand the cardinality penalty for you. One small adapter folds the mapper's output into the plain dict Iskay and Miray expect, because binary `x² = x`, so each diagonal `(i, i)` term collapses into the linear one. This is the detailed version of the mapper that Part 1 only points to: python ``` from qiskit_addon_opt_mapper import OptimizationProblem # pip install qiskit-addon-opt-mapper from qiskit_addon_opt_mapper.converters import OptimizationProblemToHubo # A tiny 6-asset stand-in for Part 1's book, formulated declaratively. tickers = ["AAPL", "MSFT", "JPM", "XOM", "JNJ", "NVDA"] returns = [18.0, 16.0, 12.0, 11.0, 8.0, 22.0] correlation = {(0, 1): 0.70, (0, 5): 0.65, (1, 5): 0.68, (3, 4): 0.40} triple = (0, 1, 5, 20.0) # AAPL-MSFT-NVDA joint-crash penalty k, n = 3, 6 # hold exactly 3 of 6 risk_penalty, card_penalty = 8.0, 50.0 # Part 2's convention (Part 1's toy used 10.0) # 1. MODEL declaratively: one binary variable per asset, in asset order. op = OptimizationProblem("portfolio") for t in tickers: op.binary_var(name=t) # creation order == asset index # 2. OBJECTIVE: reward return (linear), penalize correlated pairs (quadratic), # add the tech-triple joint crash (higher_order). No cardinality term here. op.minimize( linear={tickers[i]: -returns[i] for i in range(n)}, quadratic={(tickers[i], tickers[j]): risk_penalty * rho for (i, j), rho in correlation.items()}, higher_order={3: {(tickers[triple[0]], tickers[triple[1]], tickers[triple[2]]): triple[3]}}, ) # 3. CONSTRAINT: "hold exactly k" as a real equality. The mapper expands it into # penalty terms, so you never hand-derive (Sum x - k)^2. op.linear_constraint(linear={t: 1 for t in tickers}, sense="EQ", rhs=k, name="cardinality") # 4. CONVERT to a HUBO with an explicit penalty (penalty=None auto-derives a # safe-but-large value that drowns the risk signal). obj = OptimizationProblemToHubo(penalty=card_penalty).convert(op).objective # 5. ADAPT to the plain Iskay/Miray dict: binary x^2 = x, so fold each diagonal # (i, i) quadratic term into the linear one. def to_kipu_hubo(obj, n): lin = {i: float(v) for i, v in obj.linear.to_dict().items()} h = {"()": float(obj.constant)} for (i, j), v in obj.quadratic.to_dict().items(): if i == j: lin[i] = lin.get(i, 0.0) + float(v) # x_i^2 -> x_i else: h[f"({min(i, j)}, {max(i, j)})"] = float(v) for i in range(n): h[f"({i},)"] = lin.get(i, 0.0) for order, expr in obj.higher_order.items(): # three-body and beyond for idx, c in expr.to_dict().items(): key = tuple(sorted(idx)) h["(" + ", ".join(map(str, key)) + ")"] = float(c) return h hubo = to_kipu_hubo(obj, n) print(len(hubo), "terms;", hubo["(0, 1, 5)"], "= the three-body penalty BF-DCQO takes natively") # -> 23 terms; 20.0 = the three-body penalty BF-DCQO takes natively ``` **3\. Confirm the setup** end to end on the free simulator (a 6-asset warm-up; the real 100-asset pipeline is Step 1): python ``` execution = client.run(request={ "problem": hubo, "problem_type": "binary", "shots": 2000, "num_iterations": 6, "num_greedy_passes": 1, }) execution.wait_for_final_state() print(execution.result().result["cost"], execution.result().result["mapped_solution"]) ``` That `to_kipu_hubo` adapter is the bridge you reuse below: Step 1's per-cluster builder emits the very same dictionary shape, just specialized to one hardware-sized cluster at a time. * * * ## 1Step 1: Decompose and run the pipeline Run this below the `client` you just set up. The universe is generated deterministically so the snippet is self-contained; in practice you load real returns and a denoised correlation matrix instead. For example from [yfinance](https://pypi.org/project/yfinance/). python ``` import itertools, random, math # --- Illustrative synthetic universe: 100 names across 6 sectors. --- def build_universe(seed=11): random.seed(seed) spec = [("TEC", 28, 20, 5, 0.72), ("FIN", 22, 13, 4, 0.55), ("ENE", 16, 11, 4, 0.68), ("HEA", 14, 9, 3, 0.50), ("IND", 12, 12, 4, 0.60), ("UTI", 8, 7, 2, 0.45)] names, sector, returns = [], [], [] for tag, n_s, mu, sd, _ in spec: for i in range(n_s): names.append(f"{tag}{i+1}"); sector.append(tag) returns.append(round(mu + random.uniform(-sd, sd), 1)) intra = {tag: rho for tag, _, _, _, rho in spec} correlation = {} for i in range(len(names)): for j in range(i + 1, len(names)): if sector[i] == sector[j]: rho = round(min(0.92, max(0.2, intra[sector[i]] + random.uniform(-0.12, 0.12))), 3) else: rho = round(max(0.0, random.uniform(0.0, 0.18)), 3) if rho: correlation[(i, j)] = rho return names, sector, returns, correlation names, sector, returns, correlation = build_universe() N, K, QMAX = len(names), 50, 20 # 100 assets, hold 50, 20-qubit budget risk_penalty = 8.0 # risk appetite (lambda); Part 1's toy used 10.0, swept in Step 3 # Three-body terms: joint co-movement a QUBO cannot express. Decomposition keeps # a triple only if all three members land in one cluster. triples = [(2, 13, 9, 18.0), (2, 14, 18, 14.4), (36, 37, 48, 12.6)] def abscorr(i, j): return 0.0 if i == j else correlation.get((min(i, j), max(i, j)), 0.0) def full_cost(bits): e = -sum(returns[i] for i in range(N) if bits[i]) for (i, j), rho in correlation.items(): if bits[i] and bits[j]: e += risk_penalty * rho for (i, j, k, p) in triples: if bits[i] and bits[j] and bits[k]: e += p return e # 1. COMMUNITY DETECTION: threshold the correlation graph, take connected # components (a stand-in for the paper's RMT denoise + Louvain). def connected_components(threshold=0.30): adj = {i: set() for i in range(N)} for (i, j), rho in correlation.items(): if rho >= threshold: adj[i].add(j); adj[j].add(i) seen, comps = set(), [] for s in range(N): if s in seen: continue stack, comp = [s], [] while stack: u = stack.pop() if u in seen: continue seen.add(u); comp.append(u); stack.extend(adj[u] - seen) comps.append(sorted(comp)) return comps # 2. GREEDY SPLIT (paper Algorithm 1): break any community larger than the qubit # budget by seeding on its highest-degree node and grabbing its strongest # neighbours, until every cluster fits QMAX. def greedy_split(community, qmax=QMAX): R, out = list(community), [] while R: if len(R) <= qmax: out.append(sorted(R)); break deg = {i: sum(abscorr(i, j) for j in R) for i in R} seed = max(R, key=lambda i: deg[i]) chosen = {seed} for j in sorted(R, key=lambda j: -abscorr(seed, j)): if len(chosen) >= qmax: break chosen.add(j) out.append(sorted(chosen)); R = [i for i in R if i not in chosen] return out # 3. PER-CLUSTER HUBO: returns + intra-cluster risk + intra-cluster 3-body terms # + a cardinality penalty (paper's adaptive Lambda = 2 * max influence). def build_cluster_hubo(cluster, budget): m = len(cluster) glob2loc = {g: l for l, g in enumerate(cluster)} lin = {l: -returns[cluster[l]] for l in range(m)} quad = {(a, c): risk_penalty * abscorr(cluster[a], cluster[c]) for a in range(m) for c in range(a + 1, m) if abscorr(cluster[a], cluster[c])} influence = [abs(lin[l]) + sum(abs(v) for (a, c), v in quad.items() if l in (a, c)) for l in range(m)] Lam = 2 * max(influence) hubo = {"()": Lam * budget ** 2} for l in range(m): hubo[f"({l},)"] = lin[l] + Lam * (1 - 2 * budget) for a in range(m): for c in range(a + 1, m): hubo[f"({a}, {c})"] = quad.get((a, c), 0.0) + 2 * Lam for (i, j, k, p) in triples: if i in glob2loc and j in glob2loc and k in glob2loc: key = tuple(sorted((glob2loc[i], glob2loc[j], glob2loc[k]))) hubo[f"({key[0]}, {key[1]}, {key[2]})"] = p return hubo, glob2loc # 4. SOLVE the clusters on Miray. The clusters are independent subproblems, so # SUBMIT them all first (non-blocking), then COLLECT once they finish. Total # wait is the slowest single cluster, not the sum of all eight. def submit_to_miray(cluster, budget, client): hubo, glob2loc = build_cluster_hubo(cluster, budget) execution = client.run(request={ "problem": hubo, "problem_type": "binary", "shots": 4000, "num_iterations": 10, "num_greedy_passes": 2, }) return execution, glob2loc # queued, not awaited def collect(execution, glob2loc): execution.wait_for_final_state() sol = execution.result().result["mapped_solution"] # local index -> 0/1 loc2glob = {l: g for g, l in glob2loc.items()} return [loc2glob[int(l)] for l in sol if sol[l] == 1] # 5. RECOMBINE the cluster picks, then REPAIR to exactly K with a # cardinality-preserving swap local search on the FULL objective. This is # what recovers the cross-cluster couplings the decomposition dropped. def recombine(cluster_solutions): bits = [0] * N for picks in cluster_solutions: for i in picks: bits[i] = 1 return bits def repair_swap(bits, K): bits = bits[:] flip = lambda b, i: b[:i] + [1 - b[i]] + b[i + 1:] while sum(bits) < K: outs = [i for i in range(N) if not bits[i]] bits[min(outs, key=lambda i: full_cost(flip(bits, i)))] = 1 while sum(bits) > K: ins = [i for i in range(N) if bits[i]] bits[max(ins, key=lambda i: full_cost(flip(bits, i)))] = 0 improved = True while improved: improved = False base = full_cost(bits) ins = [i for i in range(N) if bits[i]]; outs = [i for i in range(N) if not bits[i]] best_gain, best_swap = 0.0, None for a in ins: for b in outs: bits[a], bits[b] = 0, 1 gain = base - full_cost(bits) bits[a], bits[b] = 1, 0 if gain > best_gain + 1e-9: best_gain, best_swap = gain, (a, b) if best_swap: a, b = best_swap; bits[a], bits[b] = 0, 1; improved = True return bits # --- run it --- communities = connected_components(0.30) clusters = [] for c in communities: clusters += greedy_split(c) if len(c) > QMAX else [c] clusters.sort(key=lambda c: -len(c)) budgets = [round(len(c) / 2) for c in clusters] # K_sub = size / 2, sums to 50 jobs = [submit_to_miray(c, b, client) for c, b in zip(clusters, budgets)] # fan out solutions = [collect(ex, g2l) for ex, g2l in jobs] # gather portfolio = repair_swap(recombine(solutions), K) print(round(full_cost(portfolio), 2), "holding", sum(portfolio), "names") ``` The 100-asset universe decomposes into **8 clusters**, none larger than 20 qubits. output ``` cluster sector size budget carries 3-body terms 0 Tech 20 10 yes (two tech triples) 1 Financials 20 10 yes (one financials triple) 2 Energy 16 8 3 Health 14 7 4 Industrials 12 6 5 Tech (split) 8 4 6 Utilities 8 4 7 Financials (sp) 2 1 ``` The two oversized communities get split by the greedy rule: Tech (28 names) into 20 + 8, Financials (22) into 20 + 2. Let's visualize the results. python ``` import matplotlib.pyplot as plt from collections import Counter GOLD, BG, FG, CLOUD = "#b38f12", "#EDECEC", "#0f1319", "#cfcdcd" # Kipu brand colors (tokens.css) # Left: how the 100 assets split into clusters, each under the qubit budget, # with the share of names each cluster contributed to the final portfolio. labels = [f"{Counter(sector[i] for i in c).most_common(1)[0][0]} ({len(c)})" for c in clusters] held_per_cluster = [sum(portfolio[i] for i in c) for c in clusters] fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5)) fig.patch.set_facecolor(BG) for ax in (ax1, ax2): ax.set_facecolor(BG) for s in ("top", "right"): ax.spines[s].set_visible(False) ax.tick_params(colors=FG); ax.xaxis.label.set_color(FG); ax.yaxis.label.set_color(FG) y = range(len(clusters)) ax1.barh(y, [len(c) for c in clusters], color=CLOUD, label="cluster size (qubits)") ax1.barh(y, held_per_cluster, color=GOLD, label="names held") ax1.axvline(QMAX, color=FG, ls="--", lw=1.3, label=f"qubit budget = {QMAX}") ax1.set_yticks(list(y)); ax1.set_yticklabels(labels); ax1.invert_yaxis() ax1.set_xlabel("assets / qubits") ax1.set_title(f"100 assets decomposed into {len(clusters)} clusters", color=FG, fontweight="bold", loc="left") ax1.legend(fontsize=8, frameon=False) # Right: the 50-name portfolio stays diversified (Tech has 28 names available # but the optimizer refuses to over-concentrate in it). sectors = sorted(set(sector)) avail = [sum(1 for i in range(N) if sector[i] == s) for s in sectors] held = [sum(portfolio[i] for i in range(N) if sector[i] == s) for s in sectors] x = range(len(sectors)) ax2.bar([i - 0.2 for i in x], avail, 0.4, color=CLOUD, label="available") ax2.bar([i + 0.2 for i in x], held, 0.4, color=GOLD, label="held") ax2.set_xticks(list(x)); ax2.set_xticklabels(sectors); ax2.set_ylabel("names") ax2.set_title(f"{K}-name portfolio: balanced across sectors", color=FG, fontweight="bold", loc="left") ax2.legend(fontsize=8, frameon=False) plt.tight_layout(); plt.show() ``` * * * ## 2Step 2: Read & verify the results from Miray The script above submits all independent clusters to Miray in parallel. In practice you often reserve quantum solvers for the clusters that need it or combine them with classical ones. For example, running the two largest (the 20-qubit Tech and Financials subproblems with higher-order terms) on the Miray simulator at 4000 shots, 10 iterations, 2 greedy passes, and solving the remaining six exactly. This describes a quantum-classical hybrid workflow, which is precisely what brings quantum closer to industrial usefulness. output ``` Cluster 0 (Tech, 20 qubits, budget 10) Miray cost 50.548 = brute-force optimum (50.55) held -> TEC2 TEC5 TEC10 TEC12 TEC14 TEC15 TEC19 TEC20 TEC21 TEC28 Cluster 1 (Financials, 20 qubits, budget 10) Miray cost 39.472 = brute-force optimum (39.47) held -> FIN3 FIN4 FIN6 FIN9 FIN10 FIN11 FIN17 FIN18 FIN19 FIN22 ``` BF-DCQO solved both 20-qubit subproblems, higher-order terms included, with no QUBO reduction and no auxiliary qubits, the higher-order capability demonstrated on IBM hardware in [arXiv:2409.04477](https://arxiv.org/abs/2409.04477). Read them with `response.result["mapped_solution"]` (local index, not the transpiled `bitstring`). Then recombine all eight cluster solutions and repair to a feasible 50-name portfolio. Full comparison (lower is better): output ``` Greedy (top-50 by return) +2313.04 over-concentrated Quantum decomposition, recombined only +1066.87 eight cluster optima without repair Random (best of 30,000 draws) +994.36 Equal-per-sector (top return) +978.61 naive diversification: ~8 per sector Simulated annealing (60 restarts) +882.94 strong classical baseline Quantum decomposition + repair +882.50 balanced across all six sectors ``` Reading the table top to bottom: - **Greedy (top-50 by return)** ignores risk entirely: Part 1's concentration trap, at scale. - **Quantum decomposition, recombined only** glues the eight cluster optima together with no global fix-up. Each piece is solved well, but every cross-cluster coupling was dropped, hence the gap. - **Random** and **equal-per-sector** are naive diversification baselines. - **Simulated annealing (60 restarts)** is the strong classical reference. - **Quantum decomposition + repair** is the full pipeline, and the number to judge: solve each cluster on Miray, recombine the picks, then run a cardinality-preserving swap local search over the *full* objective to recover the cross-cluster couplings the split dropped. To *see* this rather than rank it: we cannot enumerate all 10²⁹ portfolios, so we sample a cloud of random feasible 50-name picks and drop the two real portfolios onto it. The objective splits cleanly into the two plotted axes: `cost = risk − return`. python ``` import matplotlib.pyplot as plt GOLD, BG, FG = "#b38f12", "#EDECEC", "#0f1319" # Kipu brand colors (tokens.css) def port_return(bits): return sum(returns[i] for i in range(N) if bits[i]) def port_risk(bits): # pairwise + 3-body penalties r = sum(risk_penalty * rho for (i, j), rho in correlation.items() if bits[i] and bits[j]) return r + sum(p for (i, j, k, p) in triples if bits[i] and bits[j] and bits[k]) def topk_by_return(K): # the naive baseline bits = [0] * N for i in sorted(range(N), key=lambda i: -returns[i])[:K]: bits[i] = 1 return bits greedy = topk_by_return(K) sampler = random.Random(7) cloud = [] for _ in range(3000): bits = [0] * N for i in sampler.sample(range(N), K): bits[i] = 1 cloud.append(bits) fig, ax = plt.subplots(figsize=(7, 5)) fig.patch.set_facecolor(BG); ax.set_facecolor(BG) ax.scatter([port_risk(b) for b in cloud], [port_return(b) for b in cloud], c="#cfcdcd", s=10, label="random feasible (sampled)") ax.scatter(port_risk(greedy), port_return(greedy), facecolors="none", edgecolors=GOLD, s=170, lw=2.4, zorder=3, label="naive (top-50 return)") ax.scatter(port_risk(portfolio), port_return(portfolio), c=GOLD, s=170, edgecolors="white", lw=1.5, zorder=4, label="quantum decomposition + repair") ax.set_xlabel("Correlation + 3-body risk score (lower is safer)", color=FG) ax.set_ylabel("Expected return", color=FG) ax.set_title("50-of-100 portfolios: risk vs return", color=FG, fontweight="bold", loc="left") for s in ("top", "right"): ax.spines[s].set_visible(False) ax.legend(fontsize=8, frameon=False) plt.tight_layout(); plt.show() ``` The naive portfolio sits alone in the high-risk corner: it wins on raw return but pays for it in risk, the concentration trap from Part 1. The quantum portfolio sits at the low-risk edge of the cloud, undominated: no sampled portfolio beats it on both axes at once. Three honest takeaways: - **The decomposition ties a strong classical baseline and demolishes the naive ones.** The repaired portfolio (+882.50) is level with 60-restart simulated annealing (+882.94) and less than half the cost of greedy (+2313), which takes all high-return assets and gets penalties from both correlations and three-body penalties. The model also beats *careful* diversification. The hand-built rule that holds roughly equal names per sector (+978.61) lands almost the same sector counts but still costs ~10% more, because the optimizer's real work is choosing *which* names within each sector to avoid the most mutually (pairs) and many-body-correlated ones (triplets). - **The repair step is not optional, and the pre-repair number is not a quantum failure.** Recombining the eight cluster optima scores +1066.87, a 21% gap above best-known. That gap is *not* a solver-quality problem (each cluster was solved well); it is the cost of dropping cross-cluster couplings and of the fixed per-cluster budget split. The simple global swap search (post-processing) closes it from +1066.87 to +882.50. Decomposition needs both halves: a good per-cluster solver and a global repair to stitch the clusters back together. - **The three-body terms changed the final portfolio.** In the Tech cluster the higher-order penalty pushed the optimizer to drop TEC3 (which sits in *both* tech triples) in favor of TEC12, avoiding exactly the joint co-movement a pairwise model does not include. BF-DCQO solved both higher-order subproblems natively, no QUBO reduction and no auxiliary qubits. > **Verification.** Each *cluster* is checked against its exact (brute-force) optimum, which is feasible because every cluster is ≤ 20 assets. The *full* 100-asset portfolio is not, at least on my Laptop in a reasonable amount of time (10²⁹ combinations). So we compare it against a high-quality feasible result from a strong classical heuristic without a proven global optimum. In practice, commercial and/or open-source solvers like CPLEX and Gurobi provide the reference the quantum-centric solution is measured against. Careful: not all commercial solver allow to be benchmarked, check your agreements. * * * ## 3Step 3: Tune risk aversion with one variable The portfolio above looks cautious because it uses `risk_penalty = 8.0`, the risk side is about 70% of the objective, so the optimizer spreads across sectors. `risk_penalty` is the **risk-aversion** λ: a single coefficient that says how many units of return you will give up to remove one unit of correlation risk. If you write the objective with λ pulled out as a variable, you can sweep it. λ scales the correlation penalty, wheras the higher-order three-body term stays a fixed structural penalty (a joint crash is a "no no" at any risk appetite, you might want to control that assumption independently): python ``` import matplotlib.pyplot as plt GOLD, BG, FG, MUTED = "#b38f12", "#EDECEC", "#0f1319", "#6b6b6b" # Kipu brand colors (tokens.css) def expected_return(bits): return sum(returns[i] for i in range(N) if bits[i]) def correlation_risk(bits): # pairwise risk the dial trades against return sum(rho for (i, j), rho in correlation.items() if bits[i] and bits[j]) def higher_order_risk(bits): # structural, NOT scaled by the dial return sum(s for (i, j, k, s) in triples if bits[i] and bits[j] and bits[k]) def objective(bits, risk_aversion): # risk_aversion = 8.0 reproduces full_cost return -expected_return(bits) + risk_aversion * correlation_risk(bits) + higher_order_risk(bits) # Trace the frontier classically (fast): from the all-return greedy seed, run a # swap local search at each risk_aversion. The quantum pipeline above solves at # whichever single value you pick; here we just want to see the whole dial. def seed(): bits = [0] * N for i in sorted(range(N), key=lambda i: -returns[i])[:K]: bits[i] = 1 return bits def solve_at(risk_aversion): bits = seed() improved = True while improved: improved = False base = objective(bits, risk_aversion) held = [i for i in range(N) if bits[i]] free = [i for i in range(N) if not bits[i]] best_gain, best_swap = 1e-9, None for a in held: for b in free: bits[a], bits[b] = 0, 1 gain = base - objective(bits, risk_aversion) bits[a], bits[b] = 1, 0 if gain > best_gain: best_gain, best_swap = gain, (a, b) if best_swap: a, b = best_swap; bits[a], bits[b] = 0, 1; improved = True return bits levels = [0, 1, 2, 4, 8, 16, 32] frontier = [solve_at(ra) for ra in levels] # The strategies from the comparison table, placed on the same axes so you can # see which land ON the frontier and which are dominated (above or below it). def equal_per_sector(): # naive diversification sectors = sorted(set(sector)) bysec = {s: [i for i in range(N) if sector[i] == s] for s in sectors} per, extra, held = K // len(sectors), K % len(sectors), [] for n, s in enumerate(sorted(sectors, key=lambda s: -len(bysec[s]))): take = min(per + (1 if n < extra else 0), len(bysec[s])) held += sorted(bysec[s], key=lambda i: -returns[i])[:take] bits = [0] * N for i in held[:K]: bits[i] = 1 return bits # (bits, color, marker, size, edge_lw) — quantum gets the heavy white ring. strategies = { "quantum decomp + repair": (portfolio, GOLD, "o", 340, 2.2), # the hero: gold circle, white edge "equal-per-sector": (equal_per_sector(), GOLD, "s", 120, 0.8), # distinct, sits off the frontier "greedy (top-50 return)": (seed(), MUTED, "X", 130, 0.8), } fig, ax = plt.subplots(figsize=(7.5, 5.5)) fig.patch.set_facecolor(BG); ax.set_facecolor(BG) xs = [correlation_risk(b) for b in frontier] ys = [expected_return(b) for b in frontier] ax.plot(xs, ys, "-o", color=FG, lw=1.3, ms=5, alpha=0.55, label="classical local search, swept risk_aversion") for ra, x, y in zip(levels, xs, ys): ax.annotate(f"λ={ra}", (x, y), textcoords="offset points", xytext=(6, 5), fontsize=8, color=MUTED) for name, (bits, color, marker, size, elw) in strategies.items(): ax.scatter(correlation_risk(bits), expected_return(bits), c=color, marker=marker, s=size, zorder=5, edgecolors="white", linewidths=elw, label=name) ax.set_xlabel("Correlation risk (lower is safer)", color=FG) ax.set_ylabel("Expected return", color=FG) ax.set_title("Strategies vs the efficient frontier", color=FG, fontweight="bold", loc="left") for s in ("top", "right"): ax.spines[s].set_visible(False) ax.legend(fontsize=8, frameon=False) plt.tight_layout(); plt.show() ``` output ``` λ = 0 return 862 risk 379 return-only: rebuilds the over-concentrated tech-heavy book λ = 1 return 803 risk 259 λ = 2 return 747 risk 220 λ = 4 return 682 risk 198 λ = 8 return 633 risk 189 <- the default used above λ = 16 return 608 risk 188 λ = 32 return 588 risk 187 diminishing safety, real return given up ``` The curve is the efficient frontier. At λ=0 the search maximizes raw return and rebuilds the over-concentrated greedy portfolio (the red marker in the high-risk corner). Crank λ up and it walks down the frontier, trading return for diversification, with sharply diminishing risk reduction past the default. Many naive strategies sit *below* the frontier: equal-per-sector offers similar return at higher risk, and the quantum decomposition + repair result lands right on the line near λ=8, which is the point of the whole exercise. I invite you to experiment with different values of λ. Quantum-Centric Optimization Pipeline Define assets with correlation matrix Random-matrix-theory denoising + community/sector detection Decompose to hardware budget (qubit count or error budget) Solve clusters, orchestrate quantum-classical workflow intelligently Recombine low-energy candidates, repair with swap-local-search Compare with a strong classical baseline This pipeline is **algorithmic, not hand-tuned**. In the paper every row is automated: random-matrix-theory denoising strips the noise eigenvalues (those inside the Marchenko-Pastur band) from the correlation matrix, then a correlation-guided greedy split keeps strongly-coupled names together so the couplings dropped across cluster cuts are the *weak* ones. That single design principle, strong correlations *inside* clusters and only weak coupling *across* the cuts, is what lets the global repair step recover what decomposition throws away. Step 1 above is a small, runnable version of exactly this. On real, densely cross-coupled S&P data, growing the qubit budget from 36 to 64 means fewer clusters, fewer dropped cross-cluster couplings, and a final portfolio that sits closer to the global optimum. Our universe is deliberately easier. Its sectors split cleanly, so the couplings across the cuts are weak and decomposition plus repair is simpler. The results start to get interesting when the correlation structure does *not* split neatly, and subject to further research. In the end, better hardware is better for harder, denser problems. And hardware gets better every year. * * * ## The research behind it This lab is a runnable miniature of Kipu Quantum and IonQ's February 2026 result, [*Large-scale portfolio optimization on a trapped-ion quantum computer*](https://arxiv.org/abs/2602.23976) ([IonQ write-up](https://www.ionq.com/blog/quantum-computing-meets-wall-street-running-real-portfolio-optimization-on-trapped-ion-hardware)): - **250 S&P 500 names**, selecting 125, decomposed onto a **64-qubit barium trapped-ion system**, with BF-DCQO solving inside each cluster. - **Larger executable subproblems reduced decomposition error and improved the final risk-return trade-off**, relative to randomized baselines under identical post-processing. The IonQ write-up additionally frames the work against the Gurobi classical solver. You build the kernel; the paper built the machine that tiles that kernel across an index. The same engine drives Kipu's real-world finance work, including the Basel III / FRTB [Capital Saving case](https://kipu-quantum.com/examples), which cut regulatory capital consumption by more than 10% on real bank portfolios. * * * ## Your move 1. **Run the pipeline.** It runs on the free Miray simulator: solve the two large clusters on the quantum optimizer, the rest exactly, then recombine and repair. 2. **Grow the qubit budget.** Trade the 20-qubit simulator cap for a larger backend (IBM Nighthawk 120, Heron 156): fewer clusters, fewer dropped couplings, a tighter final portfolio. 3. **New here? Start with Part 1.** [Part 1](/academy/tutorials/quantum-portfolio-optimization) builds and runs the optimizer on 8 assets before you scale it. 4. **Bring your problem.** If you run a finance or energy-trading book and want to assess practical fit on current hardware, the [Kipu Quantum Academy](https://kipu-quantum.com/academy) is built for you. **Documentation:** [Kipu Quantum Hub](https://hub.kipu-quantum.com/) | [Hub docs](https://docs.hub.kipu-quantum.com/) | [Iskay on IBM Quantum](https://kipu-quantum.com/iskay) | [Kipu Quantum Academy](https://kipu-quantum.com/academy) **Research:** [Large-scale portfolio optimization (arXiv:2602.23976)](https://arxiv.org/abs/2602.23976) | [BF-DCQO algorithm (arXiv:2405.13898)](https://arxiv.org/abs/2405.13898) | [BF-DCQO for higher-order HUBO (arXiv:2409.04477)](https://arxiv.org/abs/2409.04477) | [DCQO portfolio on IonQ, 20 assets (arXiv:2308.15475)](https://arxiv.org/abs/2308.15475) | [Feature selection HUBO on IonQ (arXiv:2604.26834)](https://arxiv.org/abs/2604.26834) *Tested live on the Kipu Quantum Hub Miray simulator: the two 20-qubit clusters each returned their brute-force-verified optimum (costs 50.548 and 39.472), and the recombined-and-repaired 100-asset portfolio (objective +882.50) ties a 60-restart simulated-annealing baseline (+882.94), while a naive top-50 pick scores +2313.04.* Happy Optimizing 🚀 * * * Last tested on the Kipu Quantum Hub · 25 June 2026 ## Ready to build? Run a finance or energy-trading book and want to assess practical fit on current hardware? Get in touch, or tell us if a step did not run for you. [Get in touch](/contact)[Report a bug or send feedback](/contact) --- # Run Long-Running Quantum Experiments on the Hub URL: https://kipu-quantum.com/events Kipu Quantum Hub # Long-running quantum experiments, off your laptop. Submit long-running jobs to the Hub. They run remotely, land in one consistent history, and are easy to share with your team. Free simulators and real quantum hardware from every major vendor, all driven from the CLI. [Sign up](https://hub.kipu-quantum.com/settings/billing/subscription)Talk to us Simulators & real hardware ## 20+ systems. One platform. Iterate on free simulators, then point the same code at real QPUs from different vendors, with no separate contracts. IBM Quantum IonQ IQM QuEra Rigetti Pasqal See the full, live list of available backends in the [Kipu Quantum Hub](https://hub.kipu-quantum.com/quantum-backends). [Sign up](https://hub.kipu-quantum.com/settings/billing/subscription) Built for real experiments ## Run it remotely. Keep every result. Long jobs that don't block your machine, a history that never gets lost, and results you can share, across simulators and real hardware. ### Long-running, remote Submit and walk away. Experiments run on the Hub, not your laptop. Close the lid and the job keeps running. ### One consistent history Every run, its parameters and its results live in one place. Nothing is lost between sessions or machines. ### Built to share Hand an experiment or its results to colleagues and fellow researchers with a link. Reproducible, not buried in a local notebook. ### Simulators + real hardware Free simulators to iterate, then direct access to QPUs from IBM, IonQ, IQM, QuEra, Rigetti and Pasqal, through the same API. ### Driven from the CLI Install qhubctl, log in, and go from a circuit to a real backend in a handful of commands. Scriptable end to end. ### Zero to quantum, today An account and a few lines of code. Free IonQ simulator access, no credit card to start. [Sign up](https://hub.kipu-quantum.com/settings/billing/subscription) Quickstart ## From install to a real backend in a handful of commands. Everything runs on the Hub. Build locally, run remotely, deploy as a service. 01Install ### Install the CLI Node.js 20+. One line installs qhubctl globally. terminal ``` # install the qhubctl CLI globally $ npm install -g @quantum-hub/qhubctl ``` 02Authenticate ### Log in with your token Copy your personal access token from the dashboard, then authenticate. terminal ``` # paste your personal access token $ qhubctl login -t ``` 03Set up ### Create an isolated project Python 3.11+. We recommend uv to keep dependencies isolated. terminal ``` $ mkdir ~/my-quantum-project $ cd ~/my-quantum-project # isolated env, Python 3.11+ $ uv venv && uv init $ source .venv/bin/activate ``` 04SDK ### Add the Quantum SDK A single command pulls in the SDK and everything it needs. terminal ``` # pulls in the Quantum SDK + dependencies $ uv add qhub-quantum ``` 05Build ### Write your first circuit A quantum coin toss: put qubits in superposition, then measure. coin\_toss.py ``` from qhub.quantum.sdk import HubQiskitProvider from qiskit import QuantumCircuit, transpile circuit = QuantumCircuit(2) for i in range(2): circuit.h(i) circuit.measure_all() ``` 06Run ### Run it on a quantum backend IonQ's simulator is free. Real QPUs just need active billing. coin\_toss.py ``` provider = HubQiskitProvider() backend = provider.get_backend("azure.ionq.simulator") circuit = transpile(circuit, backend) job = backend.run(circuit, shots=100) print(job.result().get_counts()) # {'00': 23, '01': 22, '10': 29, '11': 26} ``` 07Deploy ### Ship it as a service Scaffold a service, test locally, deploy, and execute on the Hub. terminal ``` $ qhubctl init # scaffold (Python Starter) $ qhubctl serve # test locally $ qhubctl up # deploy to the Hub $ qhubctl run # execute ``` Full walkthrough: [docs.hub.kipu-quantum.com/quickstart](https://docs.hub.kipu-quantum.com/quickstart). Free IonQ simulator access, no credit card to start. [Sign up](https://hub.kipu-quantum.com/settings/billing/subscription) Already in production ## Not a beta. A live platform. 405 Organizations 1,843 Users 20+ Backends 26 Countries ## Start your first experiment. Create your account, install the CLI, and run on a real backend today. [Sign up](https://hub.kipu-quantum.com/settings/billing/subscription)[See pricing](/pricing) --- # Quantum Optimization & Machine Learning in Action URL: https://kipu-quantum.com/flyer See it in action # Quantum advantage you can see. A quick look at how Kipu Quantum turns hard optimization and machine-learning problems into real results, on real hardware via the Kipu Quantum Hub. [Get started](https://login.hub.kipu-quantum.com/realms/planqk/protocol/openid-connect/registrations?client_id=planqk-login&redirect_uri=https%3A%2F%2Fhub.kipu-quantum.com%2Fmarketplace%23error%3Dlogin_required%26state%3Dd2fa07d2-c739-4635-9513-936a749c3e3b%26iss%3Dhttps%3A%2F%2Flogin.hub.kipu-quantum.com%2Frealms%2Fplanqk&state=f3f1e7bd-f713-4e07-a96a-474a377090e6&response_mode=fragment&response_type=code&scope=openid&nonce=1e76f0cc-eabb-41a1-bb9a-40298ce4f38e&code_challenge=muWbAdYk7A7HyGM1_PUt7yvnk9ENcdHbVtxzgCuZrks&code_challenge_method=S256)Talk to us Showcase video coming soon Quantum Optimization ## Solve the intractable. Hard combinatorial problems, solved faster than the best classical solvers. [ Up to 80× faster than CPLEX ### Runtime advantage on hard optimization BF-DCQO on IBM's 156-qubit Heron solves industry-relevant HUBO problems up to 80× faster than CPLEX and 12× faster than simulated annealing. Read the case ](/blog/runtime-quantum-advantage-with-bf-dcqo) [ With BASF ### Logistics & supply-chain optimization We bring hardware- and application-specific quantum optimization to real industrial logistics, in partnership with BASF. Read the case ](/news/basf-partnership) Quantum Machine Learning ## Better models, from quantum features. Quantum-generated features that lift the accuracy of classical machine learning. [ +5.5% AUC on tumor detection ### Quantum feature extraction for healthcare Digitized counterdiabatic quantum feature extraction lifts ML accuracy on medical data, with large precision gains on toxicity classification. Read the case ](/blog/digitized-counterdiabatic-quantum-feature-extraction) [ +2.72% AUC on images ### Quantum-enhanced image classification Analog quantum convolutions generate features that beat classical baselines on image classification, improving AUC by 2.72% and accuracy by 1.85%. Read the case ](/blog/analog-quantum-convolutions-for-advanced-image-classification) ## Bring your problem, see what quantum can do. Start on the Kipu Quantum Hub today, or talk to us about your use case. [Get started](https://login.hub.kipu-quantum.com/realms/planqk/protocol/openid-connect/registrations?client_id=planqk-login&redirect_uri=https%3A%2F%2Fhub.kipu-quantum.com%2Fmarketplace%23error%3Dlogin_required%26state%3Dd2fa07d2-c739-4635-9513-936a749c3e3b%26iss%3Dhttps%3A%2F%2Flogin.hub.kipu-quantum.com%2Frealms%2Fplanqk&state=f3f1e7bd-f713-4e07-a96a-474a377090e6&response_mode=fragment&response_type=code&scope=openid&nonce=1e76f0cc-eabb-41a1-bb9a-40298ce4f38e&code_challenge=muWbAdYk7A7HyGM1_PUt7yvnk9ENcdHbVtxzgCuZrks&code_challenge_method=S256)Talk to us --- # Connect AI Agents to Quantum Hardware via MCP URL: https://kipu-quantum.com/mcp # Connect your AI agent to quantum hardware `claude mcp add --transport http qhub-mcp https://api.hub.kipu-quantum.com/mcp` Claude Code. Connects over OAuth, no tokens in config. [Other clients](#connect) ## Connecting another client? CursorVS CodeClaude DesktopAntigravity ~/.cursor/mcp.json ``` { "mcpServers": { "qhub-mcp": { "url": "https://api.hub.kipu-quantum.com/mcp" } } } ``` ### MCP server connection settings Hosted at https://api.hub.kipu-quantum.com/mcp. Authentication is over OAuth in the browser on first connect; no credentials are stored in configuration files. Claude Code: run `claude mcp add --transport http qhub-mcp https://api.hub.kipu-quantum.com/mcp`. Headless agent runtimes without browser OAuth support (e.g. Antigravity) should instead authenticate with a static bearer token generated from [the Hub access tokens page](https://docs.hub.kipu-quantum.com/manage-access-tokens), passed via a `headers` field in their MCP client config. #### Cursor (~/.cursor/mcp.json) { "mcpServers": { "qhub-mcp": { "url": "https://api.hub.kipu-quantum.com/mcp" } } } #### VS Code (settings.json) { "mcp": { "servers": { "qhub-mcp": { "type": "http", "url": "https://api.hub.kipu-quantum.com/mcp" } } } } #### Claude Desktop (Settings → Connectors) Add custom connector URL: https://api.hub.kipu-quantum.com/mcp #### Antigravity (mcp\_config.json) { "mcpServers": { "qhub-mcp": { "url": "https://api.hub.kipu-quantum.com/mcp", "headers": { "Authorization": "Bearer " } } } } ## Organisation authentication for teams On a commercial Plus plan, your agent authenticates into your organisation’s context. The whole team runs on shared backend credentials, with role-based access. [See plans](/pricing) Organisation access on the commercial Plus plan and up. [How it works](https://docs.hub.kipu-quantum.com/manage-organizations) Shared credentials An owner sets provider tokens once. Every member's agent runs on those backends. Role-based access Viewer, Maintainer and Owner roles bound what each agent can see or change. Clean context The account-context selector keeps personal and organisation work separate. Shared billing Usage rolls up to one organisation balance, with per-member budgets. ## From a sentence to a solution You describe it plain language MCP routes it api.hub.kipu-quantum.com/mcp Runs on hardware IBM · IonQ · Rigetti You get the answer results + cost hub\_\* services, data pools, organisations, billing run\_solvercreateDataPoolcreateOrganizationgetMyBalance quantum\_\* jobs, sessions, backends getBackendscreateJobgetJobResultgetLeastBusyBackend With 200+ tools available, a recipe like the `new-notebook` skill expands a goal into the right sequence of tool calls. This and more skills are available from the `qhub-agent-toolkit` on the [Kipu Hub](https://hub.kipu-quantum.com). [Check the latest docs](https://docs.hub.kipu-quantum.com/agentic/mcp-server) ## Questions, answered What is the Kipu Quantum Hub MCP server? It is a Model Context Protocol server that connects your AI assistant to the Kipu Quantum Hub. Once added, your agent can list quantum backends, run production-grade solvers on real hardware, store inputs and results in data pools, and deploy a solver as a live REST API, all from plain-language instructions. Which AI assistants can connect? Any MCP-capable client. Setup is documented for Claude Code, Claude Desktop, Cursor and VS Code, and the same hosted endpoint works with any assistant that speaks the Model Context Protocol. How does authentication work? Over OAuth, with no credentials stored in configuration files. The first time your client connects, it opens a browser window where you sign in to the Kipu Quantum Hub and authorize access. The endpoint is https://api.hub.kipu-quantum.com/mcp. What does organisation authentication add on the Plus plan? On a commercial Plus plan your agent operates inside your organisation's context rather than a personal account. An organisation owner or maintainer configures provider access tokens once, and every member's agent runs jobs on those shared backend credentials. Role-based access (Viewer, Maintainer, Owner) governs what each member can create, edit or delete, and the account-context selector keeps personal and organisation work separate. What can my agent actually run? Kipu Quantum's production solvers across all major backends, including IBM, IonQ, Rigetti and IQM, plus simulators. Typical tasks are combinatorial optimization, quantum feature extraction for machine learning, and sampling. The agent matches your problem to a service, executes it on hardware, and returns an answer rather than a circuit. Do I need to know quantum computing? No. You describe the problem in plain language and the agent handles service matching, encoding, hardware selection and post-processing. Pre- and post-processing are managed by the Hub, so you provide the problem and read the result. ## Let your agent access quantum-centric intelligence [Sign up to the Hub](https://hub.kipu-quantum.com)[MCP setup guide](https://docs.hub.kipu-quantum.com/agentic/mcp-server) --- # Paqari: The Quantum-centric AI Agent URL: https://kipu-quantum.com/paqari # Describe your problem. Paqari builds the rest. Paqari, the executor, is our quantum-centric AI agent that turns a plain-language use case into a working quantum solution. Most people will struggle to operate a quantum computer. With Paqari, they don't have to. Sign up for a Plus Membership to explore the power of Paqari. [Sign Up](https://paqari.ai.kipu-quantum.com/)Talk to us ![The Paqari agent workspace on the Kipu Quantum Hub, ready to plan, write and run a quantum task.](/paqari-agent.png) ## Two agents. One path to a solution. If you are not sure if your use-case fits quantum talk to Tinkuq, the matchmaker, first. Tinkuq decides whether quantum is worth it. Paqari builds it. Together they take you from a sentence to a running service, with Paqari unleashing the full power of a quantum-centric intelligence. Tinkuq · matchmaker ### Tinkuq reads your use case Describe your optimization or machine-learning problem in plain language. Tinkuq tells you honestly whether quantum is worth it at today's system sizes, or on next-gen quantum computers. Paqari · executor ### Paqari builds the whole solution Paqari takes the matched problem and engineers the approach, writes the code and runs it, end to end. No quantum knowledge needed on your side. ## Plans it. Writes it. Runs it. Four steps from a plain-language problem to a service running on real quantum hardware. 01 ### Describe your problem Start with Tinkuq, the matchmaker. Explain your optimization or ML use case in plain language: no circuits, no framework. 02 ### Get an honest match Tinkuq evaluates whether a quantum computer is genuinely useful for your case at current system sizes, or on next-generation hardware. 03 ### Paqari takes over Forward the result to Paqari. Thanks to deep integration with the Kipu stack, it draws on our collective and individual knowledge from many projects to engineer, write and run a solution on its own. 04 ### Get a working service Paqari ships a service that runs in the Kipu Quantum Hub runtime, usable the moment it is built. Industrial-grade and scalable. ## It builds the solution on its own. Paqari takes the problem and develops its own solution, using Kipu's knowledge from many projects and connecting third-party services when needed. ### Deep Kipu integration Paqari lives inside our own system, so it can draw on Kipu's collective and individual knowledge accumulated across many industrial projects. ### Kipu services & external ones It builds on Kipu's own software services and hardware backends, and connects third-party services whenever a job needs them. ### Deployed on the Hub runtime The result is a real service deployed in the Kipu Quantum Hub runtime, ready to use immediately after it is created. ## A working service, ready to use. Weeks → a fraction of the time ### First working version, fast What used to take weeks of system-building now starts in a fraction of the time. The first version is up almost immediately. Fast & cost-efficient ### Built without the overhead Kipu creates the framework for solutions to be built quickly and cost-efficiently, so budget goes to solution quality, not plumbing. Focus on the result ### Concentrate on industrial value Hands-off from there. You focus entirely on the result and the industrial value behind it, not on operating a quantum computer. ## Pick your starting point. Describe your own task, or start from one of these. Paqari plans it, writes the code and runs it on Kipu Quantum Hub. [ ### Make a Bell state Create a maximally entangled two-qubit state and inspect the result. ](https://paqari.ai.kipu-quantum.com/) [ ### Explain superposition Get an intuitive explanation with a simple hands-on example. ](https://paqari.ai.kipu-quantum.com/) [ ### Try Grover search See Grover's algorithm search a small list with a quantum speedup. ](https://paqari.ai.kipu-quantum.com/) [ ### VQE on H₂ Run a variational quantum eigensolver on the hydrogen molecule. ](https://paqari.ai.kipu-quantum.com/) [ ### Visualize entanglement Plot the entanglement structure between two qubits. ](https://paqari.ai.kipu-quantum.com/) [ ### Quantum coin flip Build a true-random coin flip and view the result distribution. ](https://paqari.ai.kipu-quantum.com/) [Start with Tinkuq](https://tinkuq.ai.kipu-quantum.com) ## Bring your use case. Watch it get built. The era of industrial quantum usefulness is here, brought to you by Paqari, our quantum-centric executor agent. Start today, or talk to us about your use case. [Sign Up](https://paqari.ai.kipu-quantum.com/)Talk to us Free simulator access · No credit card · Cancel anytime --- # Analog Quantum Convolutions for Image Classification URL: https://kipu-quantum.com/blog/analog-quantum-convolutions-for-advanced-image-classification [Back to Blog](/blog) # Analog Quantum Convolutions for Advanced Image Classification Using D-Wave Advantage2 to reach quantum advantage By •04.04.2025 As quantum processors continue to expand their computational capabilities, they open new possibilities for tackling real-world problems involving complex, high-dimensional datasets such as those found in financial forecasting and healthcare diagnostics. Leveraging these systems to encode and process such data is especially promising when we make use of computationally hard regimes that are beyond the reach of classical methods. At Kipu Quantum, we are actively exploring how to apply advancements in commercially available quantum hardware, particularly the fast-annealing regime of D-Wave Advantage2, to industry-level use cases. By encoding image datasets into this architecture and generating quantum-convolved representations through quantum convolutions, we aim to boost the performance of classical machine learning models. In doing so, we extend demonstrations of [quantum supremacy in quantum simulations](https://www.science.org/doi/10.1126/science.ado6285) to quantum-advantage level applications in machine learning. #### Analog Quantum Convolutional Neural Networks (AQCNN) leveraging quantum quench dynamics In contrast to our previous work on [Digital-Analog Quantum Convolutional Neural Networks (DAQCNN)](https://arxiv.org/html/2405.00548v1), which was based on neutral atom hardware, we now develop a new approach to operate on analog superconducting quantum architectures. Specifically, we adapt our algorithm to leverage the fast-annealing regime in the D-Wave Advantage2 quantum processor using quantum quench dynamics. With access to over 1,200+ qubits on this system, we can encode and process large-scale datasets directly on the quantum hardware. ![AQCNN architecture diagram](/blog/analog-quantum-convolutions-for-advanced-image-classification/image01.jpg) Our current implementation applies quantum convolutions to classical image datasets by first encoding pixel information, like intensities, into spin-glass Hamiltonian and then evolving the system under quantum quench dynamics, a regime where quantum entanglement, a phenomenon difficult to simulate classically, is maximized. The result is a set of quantum-convolved image representations that, when used to train classical Convolutional Neural Networks (CNNs), leads to significantly improved model performance. ![Quantum convolution process visualization](/blog/analog-quantum-convolutions-for-advanced-image-classification/figure02.jpg) On benchmark datasets for breast cancer classification, our approach has demonstrated significant improvements over state-of-the-art techniques. Compared to leading classical algorithms, our method reduced training parameters by a factor of 1,000, improved the Area Under Curve (AUC) by 2.72%, and increased accuracy (ACC) by 1.85% when using analog quantum convolutions on D-Wave Advantage2. The reduction in the number of parameters is achieved by replacing parameterized convolutions with non-parameterized quantum convolutions. To this end, we implement parallel convolutions, each using 10s of qubits, on a 1200+ qubit chip. For higher-resolution images, we estimate to use convolutions requiring 100s of qubits, bringing us to the level of quantum advantage in this use case. To ensure the robustness of our results, we applied statistical evaluation techniques, including proportional representation of each class across multiple folds and repetitions. This careful validation helps guarantee an unbiased and reliable measure of the generalization capabilities of our model. #### Broad Applicability The application of our AQCNN technique is not limited to image datasets. Its flexibility allows it to be effectively applied across different industries. For example, our methods could capture correlations in time series datasets like stock market data, enhancing predictions by analyzing complex interactions among different variables and temporal points. One major benefit of AQCNN is its seamless integration with existing classical machine learning models. This compatibility ensures practical usability and immediate applicability, making superior quantum solutions available today across various domains, such as finance, science, and industrial settings. We encourage researchers and industry practitioners interested in exploring this innovative approach to collaborate with us, validate our findings, and further enhance these quantum-based methods. Looking ahead, Kipu Quantum is committed to continually demonstrating practical quantum advantages across various industries. Over the coming weeks and months, we anticipate sharing more results that highlight the effectiveness and broad applicability of our quantum computing solutions. ### Written by [Back to Blog Overview](/blog) --- # Analog Quantum Feature Selection with Neutral Atoms URL: https://kipu-quantum.com/blog/analog-quantum-feature-selection-with-neutral-atoms [Back to Blog](/blog) # Analog Quantum Feature Selection with Neutral Atoms ## From Classical Feature Selection to Analog Quantum Optimization By José J. Orquín Marqués, Carlos Flores & Anton Simen Albino In machine learning, feature selection searches for the smallest subset of variables that preserves predictive accuracy while avoiding redundancy. Since each feature can be included or excluded, the search space grows exponentially (2N) the problem into the NP-hard category. Classical heuristics such as greedy search or mutual-information ranking approximate this process but fail to scale efficiently or capture feature dependencies. The task can be formulated as a Quadratic Unconstrained Binary Optimization (QUBO) that balances relevance (information each feature shares with the target) and redundancy (information shared among features): ![QUBO Formula](/blog/analog-quantum-feature-selection-with-neutral-atoms/Screenshot2025-10-24at15.57.30.png) where 𝑧𝑖∈{0,1} indicates whether feature *i* is selected. Rather than solving this QUBO digitally, we implement it physically using arrays of neutral atoms in Rydberg states on Amazon Braket's Analog Hamiltonian Simulation (AHS) framework \[1\]. Feature relevance is encoded as local atomic detuning, while redundancy is mapped to Rydberg interactions that depend on interatomic distance. During adiabatic evolution, the system's natural dynamics guide it toward low-energy configurations that represent the optimal subsets, turning feature selection into a continuous analog quantum optimization process executed directly by the quantum hardware. ## Analog Quantum Computation as Natural Feature Selection: The Rydberg Blockade This same optimization balance appears naturally in the physics of neutral atoms excited to Rydberg states. When two atoms are closer than a critical distance known as the Rydberg blockade radius, they cannot be simultaneously excited because of strong dipole-dipole interactions. This blockade mechanism mirrors the principle of redundancy control in feature selection: if two variables carry overlapping information, they should not be selected together. In our analog quantum formulation, each atom represents a feature. Feature relevance is encoded as a local detuning bias that favors excitation, while redundancy is encoded through distance-dependent interactions: atoms representing correlated features are placed within blockade range, so the excitation of one suppresses the other. Independent features are separated beyond the blockade distance, allowing simultaneous excitation. Thus, the system's own physical dynamics perform feature selection: it evolves toward low-energy configurations that naturally minimize redundancy and favor relevant features. Rather than searching combinatorially, the array of Rydberg atoms self-organizes into the optimal subset through its intrinsic quantum behavior. To translate data correlations into spatial structure, we construct a redundancy matrix from pairwise mutual information and embed it into two dimensions via multidimensional scaling (MDS). The resulting atomic layout defines interaction strengths through the van der Waals potential Vij ∝ 1 / |𝑥⃗ᵢ − 𝑥⃗j|⁶. Local detunings encode feature relevance, while the distances implement redundancy constraints, creating a direct physical map from statistical dependencies to measurable atomic interactions. ![Mapping redundancy onto atom positions](/blog/analog-quantum-feature-selection-with-neutral-atoms/Picture_1.png) Figure 1. Mapping redundancy onto atom positions. Highly redundant features are placed within blockade range, while independent ones remain spatially separated. ## Results on Benchmark Datasets We evaluated our analog quantum feature selection (QFS) approach on three publicly available binary classification datasets with distinct redundancy profiles and variable types: **Adult Income \[2\]**: Contains 48,842 samples and 14 features, combining numerical and categorical variables related to demographics, education, and occupation. **Bank Marketing \[3\]**: Includes 45,211 samples and 16 input features describing client attributes and campaign interactions from a Portuguese bank. The goal is to predict whether a customer will subscribe to a term deposit. **Telco Churn \[4\]**: Comprises 7,043 samples and 19 features describing telecom service usage, contracts, and customer demographics. The target is to predict whether a customer will leave the company. The table below summarizes the main outcomes obtained using the XGBoost classifier on the three benchmark datasets. In all cases, the analog quantum feature selection (QFS) method achieves high AUC values while using a significantly smaller number of variables than the original datasets. This behavior highlights the ability of the proposed neutral-atom quantum-processor encoding to perform an efficient and physically grounded feature selection, easily scalable to beat classical solutions, where the system dynamics naturally isolate the most relevant and non-redundant features without compromising predictive performance. Table 1. Summary of feature selection results across the three benchmark datasets. Analog quantum feature selection (QFS) achieves comparable or superior AUC scores while reducing the number of features by up to 86% compared to classical baselines. Dataset Original Features QFS Features AUC (QFS) AUC (Baseline) Reduction (%) Adult Income 14 2 0.857 0.836 86% Bank Marketing 16 4 0.912 0.892 75% Telco Churn 19 3 0.815 0.809 84% These impressive results establish a path towards computational quantum advantage and early industrial quantum usefulness when running our quantum computing solutions on commercial quantum processors provided by [QuEra](https://www.linkedin.com/company/quera-computing-inc/posts/?feedView=all), [Pasqal](https://www.linkedin.com/company/pasqal/), [Planqc](https://www.linkedin.com/company/planqc/), [Atom Computing](https://www.linkedin.com/company/atom-computing/), and [Infleqtion](https://www.linkedin.com/company/infq/). ## References 1. Amazon Web Services, Inc. (n.d.). Analog Hamiltonian Simulation (AHS). In the Amazon Braket Developer Guide. Retrieved October 24, 2025, from [https://docs.aws.amazon.com/braket/latest/developerguide/braket-analog-hamiltonian-simulation.html](https://docs.aws.amazon.com/braket/latest/developerguide/braket-analog-hamiltonian-simulation.html) 2. Becker, B. & Kohavi, R. (1996). Adult \[Dataset\]. UCI Machine Learning Repository. [https://doi.org/10.24432/C5XW20](https://doi.org/10.24432/C5XW20). 3. Moro, S., Rita, P., & Cortez, P. (2014). Bank Marketing \[Dataset\]. UCI Machine Learning Repository. [https://doi.org/10.24432/C5K306](https://doi.org/10.24432/C5K306). 4. Kaggle. (n.d.). Telco Customer Churn \[Dataset\]. Kaggle. Retrieved October 24, 2025, from [https://www.kaggle.com/datasets/blastchar/telco-customer-churn/data](https://www.kaggle.com/datasets/blastchar/telco-customer-churn/data) ### Written by ![Carlos Flores](/_next/static/media/image-9.4413cb6e.png) Carlos Flores Quantum Machine Learning Engineer ![Anton Simen Albino](/_next/static/media/image-6.7bd35086.png) Anton Simen Albino Quantum Machine Learning Lead [Back to Blog Overview](/blog) --- # Branch-and-Bound Counterdiabatic Quantum Optimization URL: https://kipu-quantum.com/blog/branch-and-bound-digitized-counterdiabatic-quantum-optimization [Back to Blog](/blog) # Branch-and-bound Digitized Counterdiabatic Quantum Optimization By Anton Simen Albino, Alejandro Gómez Cadavid•23.04.2025 As quantum hardware becomes more accessible and stable, a critical question arises: can it solve real, hard optimization problems more efficiently than classical methods? In our [recent work](https://arxiv.org/abs/2504.15367) \[1\], we tested a new quantum algorithm, Branch-and-Bound Digitized Counterdiabatic Quantum Optimization (BBB-DCQO) on IBM's superconducting quantum processors to address this question directly. This new approach combines the benefits of classical well-established branch-and-bound algorithms with the efficacy and resource-efficiency of our most advanced optimization technologies: Bias-Field Digitized Counterdiabatic Quantum Optimization Algorithm (BF-DCQO) \[2, 3\]. The obtained results offer strong evidence that BBB-DCQO is not only practical on current quantum processors but can also outperform established classical and quantum approaches on challenging higher-order binary optimization tasks. The problems we considered fall under the category of dense 100-variable HUBO (Higher-Order Unconstrained Binary Optimization) problems. These are particularly difficult because they contain both two- and three-body interactions and lack the sparsity that often makes classical approximations more effective. Moreover, mapping such problems onto quantum annealers requires introducing auxiliary variables and penalty terms, increasing the resource requirements and introducing performance trade-offs. Contrary to the approximate solutions obtained with the best D-Wave devices, BBB-DCQO reaches exact solutions on IBM quantum computers with a reduction of up to 4.2x in the required number of qubits. We implemented BBB-DCQO on the IBM Marrakesh quantum processor using a maximum binary tree depth K=3 and executed two iterations of the BF-DCQO subroutine per branching node. Each circuit evaluation included 10,000 quantum shots, and branching was guided by expectation values to determine which spin variables were least biased. We also applied a lightweight greedy local search as post-processing to refine the low-energy samples. For a fair comparison, we benchmarked against two widely used methods: simulated annealing (SA) with a geometric cooling schedule, and quantum annealing (QA) implemented on a commercial D-Wave Advantage annealer, combined with a similar greedy post-processing step. ![Branch-and-bound algorithm animation](/blog/branch-and-bound-digitized-counterdiabatic-quantum-optimization/Branch-and-bound-algorithm.gif) Figure 1. Branch-and-bound algorithm that iteratively updates the bias fields. In both test instances, BBB-DCQO achieved the lowest-energy solutions with significantly fewer function evaluations. For the first problem, it matched the reference solution (obtained via long-run SA) using just 7 million function evaluations, compared to the 35 million used for SA. For the second problem, BBB-DCQO reached the optimal energy at the very first branching step, requiring only 5.1 million evaluations, whereas SA needed approximately 250 million evaluations to achieve the same result. This clearly indicates that optimal solutions were obtained using up to x50 less function evaluations on IBM quantum hardware. Function evaluations here include all quantum measurements, spin-flip operations in SA as warm-starting, and corrections applied during greedy local search. This metric is meaningful because it reflects the total computational effort, across both classical and quantum components, in the workflow. ![BBB-DCQO experimental results](/blog/branch-and-bound-digitized-counterdiabatic-quantum-optimization/bbb-dcqo.png) Figure 2. Experimental results for two 100-qubit HUBO instances. Plots (a) and (d) show the final energy distributions for BBB-DCQO, a greedy-optimized QA and a greedy local search algorithm for both problems. The reference value is obtained from a SA with 1e8 function evaluations. Figs (b) and (e) compare the solution quality obtained from BBB-DCQO and SA with respect to the number of function evaluations. Figs (c) and (f) illustrate the convergence of the algorithm across different layers of the binary tree. Beyond efficiency, the solution quality achieved by BBB-DCQO was consistently superior. Quantum annealing, even when enhanced with greedy correction, did not reach the same low-energy configurations. This is largely due to the difficulty of embedding dense HUBO problems into a QUBO form compatible with QA. The mapping process introduces additional variables and constraints, which distort the energy landscape and degrade performance. In contrast, BBB-DCQO operates directly on the original HUBO formulation and avoids this overhead entirely. These results prove that BBB-DCQO is practical and scalable for accurately solving higher-order, non-convex binary optimization problems, HUBO class, on current commercial quantum processors beyond classical methods. #### What's next? Rather than distant future, quantum computing is a present-day tool ready to tackle complex and large-scale optimization problems that are out of the reach of current classical solvers. Within a global context where industries must solve more intricate problems faster, quantum computing offers a transformative leap, unlocking novel pathways where traditional methods tend to fail. Moving from theory to actual solutions, Kipu's mission is to continue developing the most advanced quantum algorithms capable of addressing real-world use cases, showcasing tangible benefits with current and next-generation quantum hardware. With commercial quantum advantage as a main goal, Kipu keeps pushing on designing shorter-in-depth algorithms while guaranteeing faster convergence. **References** \[1\] [Simen, Anton, et al. Branch-and-bound digitized counterdiabatic quantum optimization](https://arxiv.org/abs/2504.15367) \[2\] [Cadavid, Alejandro Gomez, et al. Phys. Rev. Research 7, L022010 (2025)](https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.L022010) \[3\] [IBM Quantum, Iskay Quantum Optimizer - A Qiskit Function by Kipu Quantum](https://docs.quantum.ibm.com/guides/kipu-optimization) ### Written by ![Anton Simen Albino](/_next/static/media/image-6.7bd35086.png) Anton Simen Albino Quantum Machine Learning Lead ![Alejandro Gómez Cadavid](/_next/static/media/image-4.4deb7e83.png) Alejandro Gómez Cadavid Quantum Optimization Lead [Back to Blog Overview](/blog) --- # Classical Surrogates for Quantum Feature Extraction URL: https://kipu-quantum.com/blog/classical-surrogates-for-quantum-feature-extraction [Back to Blog](/blog) # Classical Surrogates for Quantum-Advantage Feature Extraction ## Bringing Quantum Computing to Production By Anton Simen, Carlos Flores-Garrigós, Qi Zhang & Gabriel Alvarado•29.04.2026 Quantum computers can extract features from data that make classical machine learning models more accurate. We have demonstrated this across various fields, including molecular toxicity prediction, medical image classification, and satellite remote sensing, utilizing IBM quantum processors with up to 156 qubits [\[1\]](https://arxiv.org/abs/2510.13807), [\[2\]](https://arxiv.org/abs/2602.18350). The gains are consistent and reproducible: 2-3% absolute accuracy improvements on satellite imagery, ~5% accuracy improvement on breast tumor detection, and ~10% accuracy improvement on molecular toxicity classification, all on top of strong classical baselines. But quantum feature extraction has a deployment problem: the quantum processor must process every sample, including at inference time, making it impractical for production systems. In this technical post, we introduce **classical surrogates**: classical models trained to replicate the quantum feature mapping. We show that it preserves the full quantum-enhanced performance while making the deployment pipeline entirely classical. The quantum computer running at quantum-advantage level is essential, but only for training, that is to generate the data that the surrogate learns from. **Our classical surrogate makes quantum enhancement scalable and efficient for industrial production.** ## Quantum Features Work. We Proved it Our Digitized Quantum Feature Extraction (DQFE) technology [\[1\]](https://arxiv.org/abs/2510.13807), [\[2\]](https://arxiv.org/abs/2602.18350) uses quantum processors to transform classical data into richer feature representations. By leveraging the physics of quantum systems, DQFE captures complex patterns and correlations in the data that standard classical methods miss. When these quantum-derived features are fed to standard classifiers, performance improves. DQFE is applicable to any tabular data classification problem. Whenever data can be represented as a feature vector, it can be encoded into a quantum circuit and processed through the DQFE pipeline. We have validated this on three real-world problems spanning different domains and data types: - **Molecular toxicity classification** [\[1\]](https://arxiv.org/abs/2510.13807): 156 molecular descriptors processed on IBM Kingston (156 qubits). Quantum features delivered a ~10% improvement in classification accuracy over the classical baseline. - **Breast tumor detection** [\[1\]](https://arxiv.org/abs/2510.13807): Ultrasound images from the MedMNIST benchmark, processed through classical feature extraction followed by DQFE. Quantum features delivered a ~5% improvement in classification accuracy over the classical baseline. - **Satellite image classification** [\[2\]](https://arxiv.org/abs/2602.18350): Multi-sensor remote-sensing data from the TreeSatAI benchmark, processed on IBM quantum backends. Quantum features delivered 2-3% absolute accuracy improvement. ## The problem: You can't deploy a Quantum Computer Here is the tension. If a classifier is trained on quantum features, then **every sample it will ever classify must also be quantum-processed**, not just during training, but at inference time. Every new molecule to screen, every medical image to diagnose, every satellite image to classify would need to be queued, encoded, executed, and measured on a quantum processor. For production systems, this is a showstopper. Industrial deployment demands millisecond latency, 24/7 availability, and scalability to millions of samples. Current quantum processors cannot meet any of these requirements and it may take a while to make it possible along next years. The result is a paradox: quantum feature extraction improves model performance at the quantum-advantage level, but it is difficult to deploy with current commercial quantum hardware capabilities. ## Our Solution: Classical Surrogates Trained on Quantum Data We resolve this conundrum by **training a classical model to replicate the quantum feature mapping**, then deploying the classical model in place of the quantum processor, bringing quantum enhancement into production level. The key insight is that the quantum mapping, despite relying on inherently noisy quantum measurements, produces features that are stable and consistent. This has been demonstrated by the reproducible accuracy gains across different hardware backends [\[1\]](https://arxiv.org/abs/2510.13807), [\[2\]](https://arxiv.org/abs/2602.18350). This means the mapping carries a learnable signal. We can run the quantum processor on a manageable dataset, collect the input-output pairs (classical features in, quantum features out), and train a classical surrogate to learn that relationship. The surrogate concept is model agnostic: any regression architecture can serve as the surrogate, chosen based on the complexity of the mapping and deployment needs. Once trained, the surrogate replaces the quantum processor entirely at inference time. ![The classical surrogate pipeline: train on input-output pairs from a quantum computer, then deploy the classical surrogate at inference.](/blog/classical-surrogates-for-quantum-feature-extraction/figure1.png) Fig. 1. The classical surrogate pipeline. Left: the surrogate model is trained on input-output pairs (xi, qi) produced by a quantum computer. Classical features go in, quantum features come out, and the surrogate learns this mapping. Right: the trained surrogate replaces the quantum computer at inference time, producing equivalent quantum-like features from classical inputs alone. ## Offline Quantum Advantage **The ultimate test:** does the surrogate preserve the quantum advantage? We applied it to the satellite image classification task, training a Ridge regressor surrogate on quantum features generated by DQFE on IBM hardware, then evaluating on the same test set. The result speaks for itself. Approach Features / Qubits Accuracy (%) Classical Baseline 120 84 Quantum (DQFE on IBM hardware) 120 86 to **87** Classical Surrogate of DQFE 120 87 The surrogate preserves the quantum-enhanced performance while transforming the operational picture: QPU at inference Surrogate at inference Latency Minutes (queue + execution) Microseconds Scalability Limited by hardware availability Millions of samples Availability Shared access, maintenance windows 24/7, any classical server Cost Per-shot, scales with data volume Near-zero marginal cost Explainability Irreversible mapping, opaque Depends on model choice (e.g. linear models are fully interpretable) The quantum computer's role shifts from a runtime dependency to a **data-generation step**. The quantum advantage is distilled into a classical model that inherits the performance while meeting industrial deployment requirements. ## Looking Ahead The surrogate concept is general. It does not depend on the current version of DQFE. Wherever a quantum processor produces features that enhance classical machine learning. The pattern is: 1. Use the quantum processor to generate quantum features for a manageable dataset. 2. Train a classical surrogate to replicate the mapping. 3. Deploy the surrogate at scale, retaining the performance gains. This redefines the role of quantum computers in the ML stack: not runtime components present at every inference, but **training-time oracles** that produce data too complex for classical methods to generate from scratch, yet structured enough for classical methods to learn from examples. As quantum hardware improves, the surrogate approach ensures each generation's gains translate directly into deployable, production-ready models. But a surrogate is only as good as what it learns from. A surrogate trained on mediocre quantum features will reproduce mediocre results. The value of the surrogate is entirely determined by the quality of the quantum feature extraction it replaces, and that is where Kipu Quantum leads. Our DQFE technology, built on proprietary quantum algorithms and validated across domains on real quantum hardware, produces the quantum features that are worth surrogating. Best classical surrogates start with best quantum features obtained at quantum-advantage level. ## Bibliography 1. Simen, Anton, et al. *Digitized Counterdiabatic Quantum Feature Extraction*. arXiv preprint [arXiv:2510.13807](https://arxiv.org/abs/2510.13807), 2025. 2. Zhang, Qi, et al. *Quantum-enhanced satellite image classification*. arXiv preprint [arXiv:2602.18350](https://arxiv.org/abs/2602.18350), 2026. 3. Simen, Anton, et al. *Quenched Quantum Feature Maps*. arXiv preprint [arXiv:2508.20975](https://arxiv.org/abs/2508.20975), 2025. 4. Frankle, Jonathan, et al. *The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks*. arXiv preprint [arXiv:1803.03635](https://arxiv.org/abs/1803.03635), 2018. Tinkuq · AI matchmaker ### Try it on your own use case Describe your problem in plain English. Tinkuq, our AI matchmaker, guides you from your industrial use case to the right quantum approach. Surrogates, DQFE and beyond. [Ask Tinkuq about your use case](/) Live webinar · 13.05.2026 ### See it running in production Join us for a hands-on session on integrating DQFE and surrogates into industrial pipelines. No quantum expertise required. [Register for the webinar](/webinars) ### Written by ![Anton Simen Albino](/_next/static/media/image-6.7bd35086.png) Anton Simen Albino Quantum Machine Learning Lead ![Carlos Flores](/_next/static/media/image-9.4413cb6e.png) Carlos Flores Quantum Machine Learning Engineer ![Dr. Qi Zhang](/_next/static/media/QiZhang.e7af651e.jpg) Dr. Qi Zhang Head of Technology ![Dr. Gabriel Dario Alvarado Barrios](/_next/static/media/GabrielDarioAlvaradoBarrios.41d74544.jpg) Dr. Gabriel Dario Alvarado Barrios Quantum Algorithm Engineer [Back to Blog Overview](/blog) --- # Digital-Analog Quantum Computing for HUBO Problems URL: https://kipu-quantum.com/blog/digital-analog-quantum-computing-for-higher-order-problems-at-the-quantum-advantage-level [Back to Blog](/blog) # Digital-Analog Quantum Computing for Higher-Order Problems at the Quantum Advantage Level By Dr. Narendra Hegade•13.05.2025 ### *Higher-Order Binary Optimization (HUBO), Quantum Simulation of materials, and enabling Early Quantum Error Correction* We extend digital-analog counterdiabatic quantum computing (DACQC), going beyond two-body Hamiltonians, targeting higher-order Hamiltonians, to lay the groundwork in achieving quantum advantage in Higher-Order Binary Optimization (HUBO), quantum simulations and realize early quantum error correction. #### The challenge of higher-order problems Higher-order Hamiltonian based problems naturally arise in applications from finance and logistics to machine learning and quantum chemistry. Unlike second-order problems, which involve only pairwise couplings, higher-order problems can include 3-, 4-, or even higher k-body terms: ![Higher-order Hamiltonian equation](/blog/digital-analog-quantum-computing-for-higher-order-problems-at-the-quantum-advantage-level/Screenshot2025-05-13at16.23.46.png) where σi = X, Y, Z Pauli matrices. Such Hamiltonians describe: - Higher‐order binary optimization problems in logistics, finance, and machine learning, where multi-bit couplings capture complex cost functions; - p-spin models in spin-glass theory and statistical physics, used to study glassy landscapes, mean-field phase transitions, and neural-networks; - Quantum chemistry problems from correlated electron dynamics and multi-reference correlation to vibronic coupling in molecular systems, where k-body terms arise naturally in electronic structure Hamiltonians; - Topological quantum error‐correcting codes such as the surface code and toric code are themselves defined by 4-body plaquette Hamiltonians on a 2D lattice, with each plaquette term enforcing local parity checks that detect and correct physical errors, laying the groundwork for fault-tolerant quantum computation. Encoding these multi-spin interactions digitally demands deep circuits and many two-qubit gates, which rapidly become prohibitive on NISQ devices. Furthermore, the scaling increases as the number and non-locality of the higher-order terms increase. #### The DACQC advantage for higher-order problems Digital-Analog Quantum Computing (DAQC) merges the control of gate-based circuits with the native, continuous multipartite dynamics of quantum processors. By splitting a HUBO Hamiltonian into: 1\. Continuous evolution under available multi-qubit interactions, and 2\. Digital pulses to re-program basis and tune required coefficients we can compress the most costly, higher-order terms into short depth sequences. The result is circuits with: \- Higher fidelity per Trotter step \- Shallower overall circuit depth These features lead to overall superior encodings suitable for NISQ processors and for early error-corrected architectures. The requirement from the quantum processor is programmable analog blocks to activate/deactivate desired couplings to realize the target Hamiltonian. This has been experimentally demonstrated by Google: [see Google's nature paper](https://www.nature.com/articles/s41586-024-08460-3). And is also available as [Programmable analog block in trapped ions](https://arxiv.org/abs/2502.13302) and in Neutral atom processors such as those demonstrated in [QuEra's Logical Qubits](https://www.nature.com/articles/s41586-023-06927-3). In our recent developments, we utilized superconducting processor's exchange interaction as native analog block and achieve an encoding that can surpass pure digital encodings by a factor of **10X** in the circuit depth. This is illustrated by evaluating the scaling of the encoding scheme on a 2-dimensional n×n superconducting processor to realize all-to-all 4-body couplings (Fig. 1). ![Grid-based superconducting processor](/blog/digital-analog-quantum-computing-for-higher-order-problems-at-the-quantum-advantage-level/Screenshot2025-05-13at15.25.561.png) Figure 1: Grid-based superconducting processors: Layout of the superconducting processor consisting of nearest neighbor qubits (red dots). Native exchange interactions of the processor can be used as analog blocks. #### Depth scaling: from N=6 to N=102 qubits, with maximum analog block size of N/2 Circuit Depth is often the limiting resource on NISQ machines. It is an estimate of how many parallel layers of entangling gates are needed in a quantum circuit. Moreover, the number of entangling gates needed in each layer contributes to propagation of experimental errors in the hardware. For higher-order problems, the scaling of pure digital methods start to scale abruptly, due to large number of non-local terms that require deep circuits. This is exactly where the real advantage of DAQC lies, as with the long-range analog blocks, supplemented with correct digital gate operations, the protocol can realize multiple higher-order terms. **For all-to-all 4-body HUBOs, DAQC delivers dramatic depth reductions:** Performing a scaling analysis for the digital-analog decompositions, for a single Trotter step, we find that DAQC maintains one order (10-times) less scaling in the required circuit depth compared to the pure digital (Fig. 2). When run on hardware, this depth compression will not only help mitigate numerical error accumulation but also the experimental, since the required circuit fidelity falls abruptly with the gate fidelity as *Fidelitym* where *m* is the number of gates. This brings larger, more complex problems within reach of today's quantum devices. ![Circuit depth scaling comparison](/blog/digital-analog-quantum-computing-for-higher-order-problems-at-the-quantum-advantage-level/Picture1.png) Figure 2: Circuit depth scaling of digital-analog and pure digital methods: For 4-body Hamiltonians such as those described by HUBO's and error correcting codes (Surface code, Toric code) DAQC achieves one order less scaling. #### Robustness towards errors for a fixed system size One issue that prohibits performing DAQC in the hardware is the sequential application of digital and analog pulses for a number of trotter steps, as this demands enhanced control of the analog block. Any imperfections in the analog block can propagate through the number of trotter steps required and can affect the simulation. To counteract this, we apply **digital-analog counterdiabatic (CD)** driving to facilitate rapid solutions, meaning to finish the algorithm in few trotter steps. ![Solution quality comparison](/blog/digital-analog-quantum-computing-for-higher-order-problems-at-the-quantum-advantage-level/Picture2.png) Figure 3: Comparing solution quality of DAQC and Digital methods with respect to the exact solution: Fidelity of obtaining a final ground state showcasing DAQC's robustness towards numerical errors, achieving a much higher solution quality. The trends of this plot (Fig. 3) from this 3×3 grid based superconducting processor for higher-order counterdiabatic drivings, performed with a native exchange interaction as the analog block highlight a broader point: digital-analog counterdiabatic decompositions are inherently robust in handling complex higher-order interactions. Intuitively, a method working well on 9 qubits with many k-local interactions for a single trotter step, one expects the advantage to grow with system size. Larger systems typically have even more terms in their Hamiltonians (more pairs, more possible multi-qubit interactions), so a fully digital approach would face an explosion of gates and Trotter steps to maintain accuracy. The DAQC approach, by harnessing the analog parallelism and with CD driving, can keep the simulation manageable. For example, imagine scaling from a 3×3 grid to a 5×5 grid of qubits. The number of possible 4-body terms (like plaquettes on a lattice) increases dramatically. A digital approach would need muliple layers (depth) of gate sequences for each of these terms, dropping the fidelity unless the number of steps is increased (which then makes the circuit longer and more prone to noise). DAQC would aim to cover many of those interactions in just a few analog block sequences, preserving fidelity without a combinatorial increase in circuit depth. This robustness is a hallmark of digital-analog methods: by using the hardware's natural interactions, they scale more gracefully than brute-force gate methods. It reflects a co-design philosophy. You design the algorithm with the hardware's strengths in mind. If your hardware can naturally do a certain two-body coupling (or a set of two-body couplings simultaneously), why not use it? The result is not only higher algorithmic fidelity but often a more scalable path to simulating bigger quantum systems. In fact, the fidelity advantage seen in the plot (DAQC vs. digital) at fixed size is likely even more pronounced if we consider increasing the number of qubits: prior studies have noted that DAQC's edge in fidelity grows as the processor size increases as in [Mitigating noise in digital and digital-analog quantum computation](https://www.nature.com/articles/s42005-024-01812-5#:~:text=that%20outperforms%20digital%20quantum%20computation,Moreover), and in [DAQC with trapped ions](https://iopscience.iop.org/article/10.1088/2058-9565/ad8b64). The digital approach tends to suffer as more qubits imply more 2-qubit gates, whereas DAQC can maintain a higher performance by using analog blocks as the quantum circuit building unit. From a hardware implementation perspective, demonstrating that DAQC maintains high fidelity for complex interactions is a proof-of-concept that future quantum computers could be built or tuned to favor such analog blocks. It hints that hybrid control - partly analog, partly digital might be the key to unlocking quantum advantage on intermediate-scale devices and enabling early quantum error correction. #### Towards practical quantum advantage and early quantum error correction Key takeaways for higher-order problems: - Digital-Analog evolution blocks natively synthesize k-body couplings and syndrome-extraction operators, bypassing deep gate decompositions. - Gate count and runtime drop by 10X in benchmark higher-order problems such as HUBOs and error correcting code, collapsing circuit-depth overhead from *O(N2k)* to *O(Nk+1)* - Depth compression not only mitigates Trotter error but also suppresses coherent and stochastic noise accumulation, enabling early demonstrations of quantum error correction (e.g. small-scale surface-code syndrome extraction) on NISQ hardware. This hybrid DAQC paradigm therefore unlocks both larger HUBO problem sizes and the building blocks of early quantum error correction. #### A call to hardware providers Despite these compelling results, DAQC remains under-leveraged by many quantum-hardware companies. Programmable platforms, from superconducting qubits (Google, Rigetti, IQM) to trapped ions (AQT, eleQtron), neutral atoms (QuEra, Pasqal), and photonics (Quandela), already possess analog resources for multi-spin evolution: - Superconducting resonator couplings can natively drive 4-body plaquette terms. - Global multimode ion drives can realize long-range k-spin interactions. - Rydberg blockade graphs support higher-order couplings in atom arrays. By integrating DAQC tools-compact analog pulses complimented with digital controls, hardware vendors can demonstrate near-term quantum advantage on quantum optimization and simulation. #### Looking ahead at Kipu Quantum At Kipu, we're pushing DAQC forward to solve problems in the following fields: - Material simulations (e.g., extended Hubbard and Holstein models); - Quantum chemistry of strongly correlated molecules; - Complex HUBO optimizations in logistics, finance, and ML; - Early quantum error correction Our benchmarks using existing Kipu quantum algorithms already outperform classical solvers (tensor networks, Gurobi, CPLEX) on mid-size instances Bias-field DCQO for HUBO's. We invite hardware partners to collaborate on DAQC-driven demonstrations of quantum advantage in the coming months. #### References & Further Reading 1. [DAQC for QUBO](/blog/unlocking-quantum-advantage-with-digital-analog-quantum-computing-daqc) 2. [DAQC of Fermion-Boson models with Superconductors](https://www.nature.com/articles/s41534-025-01001-4) 3. [Multi-Mode Global Driving of Trapped Ions](https://arxiv.org/abs/2502.13302) 4. [Google's Digital-Analog Quantum Processor](https://www.nature.com/articles/s41586-024-08460-3) 5. [QuEra's 100 Logical Qubits based on Digital-Analog](https://www.nature.com/articles/s41586-023-06927-3) ### Written by ![Dr. Narendra Hegade](/_next/static/media/NarendraHegade.0cf8d9ee.jpg) Dr. Narendra Hegade Fellow [Back to Blog Overview](/blog) --- # Digital-Analog Quantum Error Correction URL: https://kipu-quantum.com/blog/digital-analog-quantum-error-correction [Back to Blog](/blog) # Digital-Analog Quantum Error Correction ## Realizing early quantum error correction By Shubham Kumar & Bhargava Balaganchi•16.07.2025 Quantum Error Correction (QEC) has rapidly shifted from a theoretical necessity to a core part of experimental roadmaps. Companies like QuEra and Pasqal are already demonstrating QEC primitives with neutral atoms ([Nature, 2023](https://www.nature.com/articles/s41586-023-06927-3)), while Quantinuum has showcased logical qubit teleportation using trapped-ions ([arXiv preprint](https://arxiv.org/abs/2404.16728)). Google has demonstrated its Willow superconducting processor's surface-code memories up to distance-7 [Google Research](https://research.google/blog/making-quantum-error-correction-work/?utm_source=chatgpt.com). These advances are significant, but they underlie a critical limitation: the substantial overhead required to scale quantum error correction. The number of physical qubits per logical qubit grows quadratically often exceeding 100 qubits for a single logical qubit leaving current chips with capacity for only one or two logical qubits at best. At Kipu Quantum, we believe the time is right to bridge QEC protocols with the physical capabilities of today's quantum hardware. Through Digital-Analog Quantum Error Correction (DAQEC), we're pioneering a faster, and hardware-specific path to logical fidelity and we're inviting the hardware ecosystem to join us. We develop universal and scalable quantum computing solutions for industry use cases at quantum-advantage level with hardware- and application-specific adaptations to smoothly run along the roadmap of each quantum hardware provider. ## The Scalability Challenge in QEC Quantum Error Correction (QEC) is no longer theoretical but a practical necessity. But, as we push toward fault-tolerant quantum computing, one challenge persists: scalability. To reach logical error rates compatible with large-scale algorithms, we need: - **Thousand(s) of physical qubits** per logical qubit - **Deep circuit layers** that stretch coherence times and exceed control budgets - **QEC cycles** that become slower and more error prone as code distance increases These requirements quickly outpace what near-term hardware can support. Take the well-known example from [Google's 2023 experiments](https://www.nature.com/articles/s41586-022-05434-1): their Sycamore processor successfully demonstrated a **distance-5 surface code** with a **logical error rate below threshold**, marking a key milestone. However, each QEC cycle took nearly **one microsecond**, already approaching the limits of qubit coherence and control latency. Scaling to larger code distances without a new architectural strategy, one that reduces depth or qubit overhead becomes increasingly impractical. ## DAQEC: A path to scalable quantum error correction DAQEC extends the principles of digital-analog quantum computing (see [Physical Review A](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.101.022305)) to the domain of fault-tolerant quantum error correction. In such protocols, circuit decompositions with layers of two-qubit and single-qubit gates are replaced with a compact sequence of global or multi-qubit analog entangling blocks interleaved with single-qubit or two-qubit digital gates. This leads to shallow circuits in simulation tasks, as shown for example by using global Mølmer-Sørensen, XX or ZZ type gates, as shown in [Quantum Science and Technology](https://iopscience.iop.org/article/10.1088/2058-9565/ad8b64). Within this paradigm, we obtained that the rotated surface code (Fig.1) Hamiltonian along with its counterdiabatic (CD) correction can be encoded using digital-analog schemes natively in grid-based superconducting circuits (see [our blog post on higher-order CD driving](/blog/digital-analog-quantum-computing-for-higher-order-problems-at-the-quantum-advantage-level)) ![Rotated Surface Code](/blog/digital-analog-quantum-error-correction/figure1.png) Fig.1. A rotated surface code patch with d = 5. Z and X denote the star and Plaquette operators. In our latest benchmarking study, with a hardware specific scheme, we tested DAQEC using the native exchange interactions (as available in superconducting processor like [Google's digital-analog quantum simulator](https://www.nature.com/articles/s41586-024-08460-3)) as the analog blocks and iSWAP digital gates, obtaining that DAQEC enables: - **4× reduction** in circuit depth (Fig. 2). - Up to **2× reduction in physical qubits per logical qubit** for the same target error rate when using **Kipu's DAQEC scheme**. - Improved logical error suppression at higher code distances. - Compatibility with grid-based superconducting circuits, neutral atoms and trapped-ion devices. ![Circuit Depth Scaling](/blog/digital-analog-quantum-error-correction/figure2.png) Fig. 2. Circuit depth scaling for the rotated surface code using pure digital and digital-analog encodings. **As shown in Fig. 3, DAQEC achieves an exponential suppression of logical error rates with increasing code distance**. For example, at distance d=5, DAQEC yields a logical error rate approximately **32× lower** than its digital counterpart, demonstrating a dramatic reduction in Logical error rate. This gap **widens with code distance**, meaning that for any given target logical error rate, **DAQEC enables the use of smaller code distances**, fewer physical qubits, and shallower circuits. ![Logical Error Rate Comparison](/blog/digital-analog-quantum-error-correction/figure3.png) Fig. 3. Circuit depth scaling for the rotated surface code using pure digital and digital- analog encodings. For example, with **Kipu's DAQEC** one can achieve using a rotated surface code, a logical error rate of 10\-3 with d=7 (49 physical qubits per logical qubit), whereas a Digital QEC scheme would require roughly d=10 (100 physical qubits per logical qubit). This leads to an observed **roughly 2× (50 % less) fewer physical qubits per logical qubit**. With the best encodings proposed (using 3-qubit CCZ gates), the maximum improvement achievable is 27% less physical qubits (see [Hartmann et. al.](https://arxiv.org/pdf/2506.09028)). This positions DAQEC as a hardware-specific QEC strategy that reduces both qubit and time budgets. ## Why This Matters for Quantum Hardware Providers A hardware-software co-design strategy is essential to unlocking the full potential of today's quantum devices. With DAQEC, we offer a practical and hardware-native framework that significantly improves logical-qubit capacity per chip.In our benchmarking, we demonstrated that DAQEC can deliver the same logical error rate using only half the number of physical qubits compared to fully digital QEC meaning that on a fixed-size chip, twice as many logical qubits can be realized. This directly translates into 2× higher logical qubit density, which is critical for scaling in the NISQ-to-early-QEC transition. DAQEC naturally aligns with the strengths of several quantum hardware platforms: - Neutral-atom platforms: Can benefit from analog multi-qubit interactions (e.g., Rydberg-based entanglement) in DAQEC stabilizer preparation. QuEra has already demonstrated the applicability of analog multi-qubit interactions and digital gates for scalable error correction (see [QuEra’s Nature demonstration](https://www.nature.com/articles/s41586-023-06927-3)) - Superconducting qubits: Can use XY exchange interactions as entangling primitives for depth-efficient encoding. - Trapped-ion systems: Can implement global multi-qubit gates such as Mølmer-Sørensen gate among other multi-qubit gates such as the XX or ZZ type to reduce the number of decomposed two-qubit gates (see [DAQC in trapped-ions](https://iopscience.iop.org/article/10.1088/2058-9565/ad8b64)). - Digital-analog native systems (e.g., [D-Wave's roadmap](https://www.linkedin.com/news/story/d-wave-quantum-soars-on-new-tech-6408452/)): Already structured to benefit from DAQC protocols for early surface-code deployment. By integrating DA-QEC principles, hardware teams can demonstrate early-QEC with reduced system demands, within current hardware specs. ## Hardware Momentum You Can Leverage Today At Kipu Quantum, we are developing simulation frameworks tailored to DAQC compatible architectures such as superconducting circuits, neutral atoms and trapped-ions. These are not abstract models, they are optimized for the hardware constraints that today's platforms face. We are currently partnering with hardware providers to: - Validate logical qubit preparation speeds using DAQC encodings - Optimize stabilizer measurement cycles for minimal decoherence - Quantify error suppression scaling with reduced-depth protocols - Co-develop hardware-native error correction stacks If you're building the next generation of quantum processors, we'd invite to collaborate on deploying DAQEC on your platform. Reach out to us. Let's accelerate early quantum error correction together. ### Written by [Back to Blog Overview](/blog) --- # Digitized Counterdiabatic Quantum Feature Extraction URL: https://kipu-quantum.com/blog/digitized-counterdiabatic-quantum-feature-extraction [Back to Blog](/blog) # Digitized Counterdiabatic Quantum Feature Extraction By Anton Simen Albino & Carlos Flores In machine learning, we often need to turn raw data into meaningful features. This step, called feature extraction, helps models learn patterns and make better predictions. In our recent work, we explore how to use complex quantum dynamics to do that and significantly enhance machine learning tasks \[1\]. We apply our methods to realistic use cases, including breast tumor detection \[2\] and molecular toxicity prediction \[3\]. We use many-body spin Hamiltonians to generate complex and informative features from the provided data. These features arise from the dynamics of quantum spins, which evolve under an accelerated process called counterdiabatic quantum dynamics. After digitizing the final result, we obtained a quantum algorithm that can run on advanced IBM quantum processors. Therefore, the name of our method is "Digitized Counterdiabatic Quantum Feature Extraction". ## How it works Each data sample, which can be a molecule, an image, or similar, is encoded into a spin-glass Hamiltonian. We do that by mapping both individual values and their statistical correlations onto the coupling strengths among quantum spins. After that, we let the system evolve using a counterdiabatic quantum dynamics in the impulse regime, implemented digitally on **IBM's Heron r2 156-qubit processor** (***ibm\_kingston***). Finally, we perform suitable measurements to get local magnetizations and higher-order correlations, which become our quantum-extracted features. ![Quantum Feature Extraction Process](/blog/digitized-counterdiabatic-quantum-feature-extraction/schem_tox.jpg) Figure 1: Each data sample (a molecule, an image, etc.) is encoded into a spin-glass Hamiltonian. (a) Tabular dataset X, from which samples and classical correlations are selected. (b) The extracted information from X is encoded into the local fields and higher-order coefficients of spin Hamiltonians differing in the order of interaction terms. (c) Local magnetizations and quantum correlations are measured from the two circuits and concatenated, yielding the quantum-extracted features. ## Testing with two realistic use cases We tested the approach on two different problems: 1\. **Molecular toxicity classification \[2\]** Predicting whether a molecule is toxic or not. 2\. **Breast tumor detection \[3\]** Classification from 224x224 ultrasound images. For the molecules, we used circuits with both two-body and three-body interaction terms. For the images, we combined classical features (from FFT, Gabor filters, etc.) with quantum ones. Both cases used Gradient Boosting models for classification. ![Image Classification Protocol](/blog/digitized-counterdiabatic-quantum-feature-extraction/schem_breast.jpg) Figure 2: Protocol for the image classification case, combining classical and quantum feature extraction methods. (a) Image-based dataset, where conventional feature extraction techniques are used to construct a tabular dataset X, from which samples and classical correlations are selected. (b) The extracted information from X is encoded into the local fields and two-body coefficients of a spin Hamiltonian. (c) Local magnetizations and quantum correlations are measured and concatenated, forming the quantum-extracted features. ## What we found Quantum features clearly contributed to getting better results. When we combined them with classical ones, the accuracy neatly improved. As shown in Fig. 3, in the toxicity task, precision jumped by 121%, and most of the model's essential features (based on SHAP analysis) come from quantum correlations. For breast tumor detection, the mean cross-validated AUC increased by 5.5% and beat well-established deep learning baselines, even though we only used 156 features. Table 1 shows that the best performance on the test dataset (Breast MNIST) is achieved using the SHAP-selected features. Specifically, the SVC (SHAP-selected) model attains an AUC of 0.937 and an accuracy of 0.876, improving Google AutoML Vision by approximately 2% in AUC and 1.7% in accuracy. This demonstrates the effectiveness of SHAP-based feature selection in enhancing the performance of traditional machine learning models. Table 1: Test performance on the Breast MedMNIST dataset. Comparison between traditional machine learning models (SVC, GB) trained with SHAP-based feature selection and the state-of-the-art deep learning methods. Method AUC Accuracy SVC (SHAP-selected) **0.937** **0.876** SVC (Original features) 0.887 0.830 GB (SHAP-selected) 0.919 0.827 GB (Original features) 0.882 0.830 ResNet-18 0.891 0.833 ResNet-50 0.866 0.842 Auto-sklearn 0.836 0.803 AutoKeras 0.871 0.831 Google AutoML Vision 0.919 0.861 ![Performance and Feature Importance](/blog/digitized-counterdiabatic-quantum-feature-extraction/results_shap_metrics.png) Figure 3: Performance and feature importance for the two tasks. (a) Molecular toxicity classification and (b) breast tumor detection. Left: model performance using classical and quantum features. Right: SHAP analysis showing which features contribute most to the predictions. ## Why it matters These results show that quantum computers can already produce results at the level of quantum advantage applied to industrial and medical machine learning problems, without the necessity of waiting for fault-tolerant quantum computers. By encoding correlations directly into local qubit terms and qubit interactions, we can extract richer, more structured features that classical preprocessing may easily miss. We have shown that today's quantum processors, combined with codesigned quantum solutions provided by IBM and Kipu Quantum, respectively, can produce an early but real sign of quantum usefulness in data-driven applications. ## References 1. Simen, Anton, et al. Digitized Counterdiabatic Quantum Feature Extraction, 2025, [https://arxiv.org/abs/2510.13807](https://arxiv.org/abs/2510.13807) 2. YANG, Jiancheng, et al. Medmnist v2-a large-scale lightweight benchmark for 2d and 3d biomedical image classification. Scientific Data, 2023, vol. 10, no 1, p. 41. 3. Gül, Ş. & RAHIM, F. (2021). Toxicity \[Dataset\]. UCI Machine Learning Repository, [https://doi.org/10.24432/C59313](https://doi.org/10.24432/C59313). ### Written by ![Anton Simen Albino](/_next/static/media/image-6.7bd35086.png) Anton Simen Albino Quantum Machine Learning Lead ![Carlos Flores](/_next/static/media/image-9.4413cb6e.png) Carlos Flores Quantum Machine Learning Engineer [Back to Blog Overview](/blog) --- # Digitized Counterdiabatic Quantum Sampling (DCQS) URL: https://kipu-quantum.com/blog/digitized-counterdiabatic-quantum-sampling [Back to Blog](/blog) # Digitized Counterdiabatic Quantum Sampling (DCQS) By Paolo Andrea Erdman, Pranav Chandarana, Anne-Maria Visuri & Narendra Hegade Boltzmann sampling lies at the heart of numerous industrial problems, from molecular simulation and drug discovery to financial risk analysis and energy grid optimization. Classical algorithms such as Metropolis-Hastings and parallel tempering have been refined over decades and are among the most powerful tools for sampling complex energy landscapes \[1\]. However, even these mature techniques encounter severe slowdowns in a particularly important regime: low temperatures, where energy barriers grow steep and relevant configurations become exponentially hard to access. Kipu Quantum introduces a new paradigm: Digitized Counterdiabatic Quantum Sampling (DCQS) \[2\]. A hybrid classical-quantum algorithm that leverages quantum dynamics to overcome this bottleneck and achieve quantum-advantage level runtime and sampling efficiency for low-temperature Boltzmann sampling on current quantum hardware. ## What is Digitized Counterdiabatic Quantum Sampling? At low temperatures, Boltzmann distributions are dominated by low-energy configurations. Classical samplers rely on thermal fluctuations to explore this landscape but become inefficient at low temperatures, making important configurations increasingly hard to discover. DCQS addresses this limitation by using **quantum fluctuations** instead, which can overcome high energy barriers by quantum tunneling to access low-energy regions more efficiently. Counterdiabatic protocols, combined with an iteratively refined bias field, are employed to steer the system toward these relevant configurations, suppressing unwanted excitations. DCQS then reconstructs accurate low-temperature Boltzmann distributions using classical reweighting techniques, achieving efficient, low-depth sampling on today's quantum computers. ![DCQS Conceptual Illustration](/blog/digitized-counterdiabatic-quantum-sampling/fig_11.png) Figure 1: Conceptual illustration comparing classical samplers (Metropolis-Hastings and parallel tempering) with DCQS. While classical samplers rely on thermal fluctuations to traverse the energy landscape, which can lead to poor sampling in the low-temperature regime, DCQS employs quantum fluctuations guided by counterdiabatic protocols, enabling more efficient access to low-energy configurations. ## Validated at Scale on Quantum Hardware The algorithm was validated experimentally on IBM's Marrakesh and Fez quantum processors, scaling up to 156 qubits. Across benchmarks including disordered Ising and spin-glass Hamiltonians, we found cases where DCQS outperforms state-of-the-art classical sampler parallel tempering in the low-temperature regime. Parallel tempering required three orders of magnitude more samples to match the accuracy of DCQS, establishing an approximate 2× runtime quantum-advantage \[2\]. ![DCQS Performance Comparison](/blog/digitized-counterdiabatic-quantum-sampling/fig_2.png) Figure 2: Comparison of DCQS and parallel tempering performance. (a) Energy distributions of DCQS and (b) energy distribution of parallel tempering for a challenging 156 qubit problem with three-body interactions. (c) Runtime necessary to accurately reproduce the low-temperature Boltzmann distribution. DCQS achieves a runtime advantage reaching the target accuracy in 5 seconds. Meanwhile, a high-performance parallel tempering implementation generating 8.7 million samples per second requires at least 8 seconds across 5 different runs. This demonstrates a tangible quantum acceleration for sampling on current quantum hardware. ## Industrial Relevance and Applications Efficient Boltzmann sampling is at the heart of numerous industrially relevant use cases. - **Pharmaceuticals**: Boltzmann sampling governs how molecular systems occupy conformations at equilibrium. Accurate sampling of protein-ligand configurations determines binding affinities, drug efficacy, and pathway kinetics \[3,4\]. DCQS accelerates access to these rare low-energy states, potentially reducing the computational cost of molecular dynamics and docking pipelines. - **Finance**: Many financial models depend on exploring distributions of portfolio states or stochastic processes under uncertainty. Boltzmann sampling enables efficient estimation of rare but impactful events in risk and derivative pricing models \[5\]. By improving sampling efficiency, DCQS can accelerate stress testing (the evaluation of portfolio resilience under extreme market conditions) and enhance portfolio optimization in Monte Carlo simulations. - **Energy and Logistics**: Optimization problems such as grid scheduling or logistics routing can be formulated as minimizing energy-like cost functions. Sampling from Boltzmann distributions over possible configurations enables probabilistic search for near-optimal solutions \[6\]. Quantum sampling enhances exploration of rugged cost landscapes, offering speedups in optimization pipelines for energy dispatch and industrial planning. - **Materials Science**: The low-temperature phases of materials are determined by rare low-energy configurations in complex atomic or spin systems. Boltzmann sampling provides access to equilibrium distributions that describe stability, defect formation, or phase transitions \[7\]. Efficient Boltzmann sampling can aid the design of new materials and magnetic systems. - **Machine Learning**: Many generative and probabilistic models, such as Boltzmann machines or diffusion-based samplers, rely on efficient exploration of energy landscapes to learn equilibrium-like distributions \[8\]. DCQS can serve as a quantum-accelerated sampler, improving convergence in energy-based models and offering a foundation for quantum-enhanced learning architectures. ## Outlook DCQS demonstrates that hybrid classical-quantum strategies can already deliver practical value. Its robustness to noise, low circuit depth, and iterative bias-field scheme make it ideal for near-term deployment. Looking forward, integration with machine-learning-based Boltzmann generators or hybrid Markov chain Mote Carlo pipelines could enable broader quantum-enhanced modeling in chemistry, finance, and materials engineering, paving the way towards industrial quantum advantage. ## References 1. D. J. Earland and M. W. Deem, "Parallel tempering: Theory, applications, and new perspectives", [Phys. Chem. Chem. Phys. 7, 3910 (2005)](https://doi.org/10.1039/B509983H). 2. N. N. Hegade, N. L. Kortikar, B. A. Bhargava, J. F. R. Hernandez, A. G. Cadavid, P. Chandarana, S. V. Romero, S. Kumar, A. Simen, A.-M Visuri, E. Solano, and P. A. Erdman, "Digitized Counterdiabatic Quantum Sampling", [arXiv:2510.26735 (2025)](https://arxiv.org/abs/2510.26735). 3. D. Frenkel and B. Smit, "Understanding Molecular Simulation", [Academic Press (2002)](https://doi.org/10.1016/B978-0-12-267351-1.X5000-7). 4. F. Noé, S. Olsson, J. Köhler, and H. Wu "Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning", [Science 365, eaaw1147 (2019)](https://doi.org/10.1126/science.aaw1147). 5. P. Glasserman,"Monte Carlo Methods in Financial Engineering", [Springer New York (2013)](https://doi.org/10.1007/978-0-387-21617-1). 6. D. Sahu, N., R. Chaturvedi, S. Prakash, T. Yang, R. S. Rathore, and I. Alsolbi, "Optimizing energy and latency in edge computing through a Boltzmann driven Bayesian framework for adaptive resource scheduling", [Sci. Rep. 15, 30452 (2025)](https://doi.org/10.1038/s41598-025-16317-6). 7. J.M. Yeomans, "Statistical Mechanics of Phase Transitions", Oxford University Press (1993). 8. J. Ngiam, Z. Chen, P. W. Koh, and A. Y. Ng, "Learning deep energy models", [Proc. Int. Conf. Mach. Learn. (2011)](https://icml.cc/2011/papers/557_icmlpaper.pdf). ### Written by ![Pranav Chandarana](/_next/static/media/PranavChandarana.5348aefc.jpg) Pranav Chandarana Quantum Optimization Engineer ![Dr. Narendra Hegade](/_next/static/media/NarendraHegade.0cf8d9ee.jpg) Dr. Narendra Hegade Fellow [Back to Blog Overview](/blog) --- # Feature Mapping for Industrial Machine Learning URL: https://kipu-quantum.com/blog/feature-mapping-and-industrial-machine-learning-applications [Back to Blog](/blog) # Feature Mapping and Industrial Machine Learning Applications At quantum-advantage level on D-Wave's fast annealing regimes By Anton Simen Albino•25.03.2025 As advances of quantum processors start to display quantum-supremacy capacities, there is huge potential in the smart encoding of computational tasks where complex quantum dynamics can offer practical advantages over classical methods. In particular, real-world applications involving high-dimensional, complex data, such as those encountered in drug discovery and medical diagnostics, present promising opportunities for exploring the capabilities of near-term quantum systems. Among the various paradigms we are considering, the use of complex quantum dynamics of commercial quantum hardware for data representation is a compelling direction, especially when grounded in computationally hard regimes that are difficult to simulate classically. Inspired by this idea, at Kipu Quantum, we are actively exploring the practical implications of the recent demonstration of [computational supremacy in quantum critical dynamic](https://www.science.org/doi/10.1126/science.ado6285)s using D-Wave Advantage 2, with a focus on real-world machine learning applications. By encoding datasets into those quantum processors (using 200+ qubits for molecular toxicity classification, a key task in early-stage drug design, and 111+ qubits for predicting myocardial infarction complications), we show that quantum-generated feature representations can significantly boost classical machine learning performances. This effectively transforms a computational quantum supremacy claim into a practical quantum advantage, providing quantum computing solutions for today's industry needs. #### Feature mapping utilizing quantum quench dynamics In our recent work, we have developed an approach that encodes statistical patterns from classical datasets into complex spin-glass Hamiltonians, subsequently evolving these quantum systems coherently through quantum quench dynamics. This evolution drives the system into highly entangled quantum states, creating rich and complex feature representations capable of capturing intricate data correlations that are challenging to replicate classically. Our results show that this analog quantum feature mapping through quantum quench dynamics significantly boosts the performance of classical machine learning models on two challenging benchmark datasets. We compared our method against state-of-the-art classical approaches using multiple evaluation metrics, demonstrating superior performance at the quantum-advantage level. In addition to directly employing quantum-generated features with classifiers like Gradient Boosting, we further demonstrate the applicability of these quantum feature maps within kernel-based methods, such as Support Vector Classification (SVC). To evaluate statistical robustness, we employ Stratified Cross-validation across two distinct models, randomly shuffling the dataset and splitting it multiple times into stratified folds. This process ensures proportional representation of each class in every fold and across repetitions, resulting in a more reliable and unbiased estimation of the models' generalization performance. ![Feature mapping performance comparison](/blog/feature-mapping-and-industrial-machine-learning-applications/featuremappingKIPUQUANTUM.jpg) For the medical dataset, leveraging the quantum feature maps, the model achieves an AUC improvement of 12.6%, a 13.6% enhancement in balanced accuracy, and a remarkable 85.9% increase in recall for the positive class, a critical metric for improving true positive rates in medical applications compared to the purely classical model. In the molecular toxicity dataset, the model with quantum feature maps shows a 41.0% boost in AUC, a 28.2% increase in F1-Score, and a 74.0% improvement in precision for the positive class. The recall for the positive class improves by 40.0%. These consistent gains demonstrate that quantum feature maps from the quench dynamics are more effective in capturing complex patterns. #### Broad Applicability This quantum feature mapping approach is not limited to the presented use-cases. It can be applied across a wide range of domains in science, technology, and industrial applications. One of the most promising aspects of this novel Kipu Quantum technology is its compatibility with many existing classical models: when classical performance improves, applying quantum feature mapping on top consistently leads to further gains. Utilizing current quantum processors with demonstrated quantum supremacy capacities to tackle real-world problems is a crucial step toward achieving practical quantum advantage now, as they unlock the full potential of current quantum computers in meaningful applications. We are excited about the potential of these tools and warmly invite researchers, practitioners, and enthusiasts to connect with us if they are interested in exploring our datasets or models to further validate, enhance, or build upon our findings. We are continuously proving that Kipu Quantum technologies are systematically delivering quantum-advantage level solutions. We will go ahead displaying impressive results next weeks and months, where our quantum computing products and solutions showcase quantum-advantage level for a variety of industries. ### Written by ![Anton Simen Albino](/_next/static/media/image-6.7bd35086.png) Anton Simen Albino Quantum Machine Learning Lead [Back to Blog Overview](/blog) --- # Hybrid Sequential Quantum Computing URL: https://kipu-quantum.com/blog/hybrid-sequential-quantum-computing [Back to Blog](/blog) # Hybrid Sequential Quantum Computing Complex Classical-Quantum Workflows Achieving Runtime Quantum-Advantage By Pranav Chandarana, Sebastián Romero, Alejandro Gómez Cadavid & Narendra Hegade•09.10.2025 Combinatorial optimization lies at the core of many industrial and scientific problems, from logistics and energy grids to finance, manufacturing, and materials design. Yet, as problem sizes increase, classical methods such as simulated annealing (SA), memetic tabu search (MTS), or exact solvers like CPLEX face steep scalability barriers. At Kipu Quantum, we explore a new way forward: non-trivial sequencing of classical and quantum optimization routines that yield measurable speedups at the runtime quantum-advantage level. Built upon Sequential Quantum Computing paradigm \[1\], this approach, introduced in our latest study 'Hybrid Sequential Quantum Computing (HSQC)' \[2\], demonstrates how carefully ordered computational stages can redefine runtime efficiency on today's quantum processors. ## Rethinking Hybridization: From Mixing to Orchestration Many hybrid algorithms alternate between quantum and classical phases in fixed feedback loops. HSQC instead focuses on runtime-adaptive sequencing, where each stage is deliberately positioned to exploit its specific computational strength and mitigate the weaknesses of the others. This composition is not trivial: the order, duration, and transfer of information between stages directly determine the achieved performance. One of the workflow examples proceeds as follows: 1. Classical exploration (SA): efficiently maps the energy landscape to identify promising low-energy configurations. 2. Quantum refinement (BF-DCQO) \[3,4\]: leverages digitized counterdiabatic quantum evolution and discovers deeper minima. 3. Classical exploitation (MTS or SA): refines the quantum-enhanced solutions locally, steering the system toward the ground state. ![Hybrid Sequential Quantum Computing schematic](/blog/hybrid-sequential-quantum-computing/Picture1.png) Hybrid sequential quantum computing (HSQC) schematic. The HSQC framework tested begins with a classical optimizer to find promising low-energy states, then seeds the BF-DCQO protocol on a QPU. The digitized counterdiabatic quantum evolution to escape to deeper minima, after which a final classical pass refines the obtained solutions to the ground state. ## Runtime Quantum-Advantage Level in Action We validated this sequential orchestration on dense higher-order unconstrained binary optimization (HUBO) problems executed on IBM's 156-qubit heavy-hex superconducting processors. Two runtime pipelines were tested: - SA → BF-DCQO → MTS, combining stochastic sampling, counterdiabaticity, and memetic local search. - SA → BF-DCQO → SA, where quantum outputs continue to a second simulated annealing process. Across all instances, sequential orchestration consistently surpassed standalone classical solvers. For the best-case instance: - HSQC reached the ground state in estimated ~3 seconds, - compared to estimated ~22 seconds for MTS and estimated ~1800 seconds for SA, achieving up to 700× faster convergence over SA and 9× faster over MTS. The runtime quantum-advantage level is clear: HSQC matches or exceeds the solution quality of exact solvers like CPLEX (≈ 23 s per instance) while operating an order of magnitude faster. ![Performance comparison](/blog/hybrid-sequential-quantum-computing/Picture2.png) N = 156, 2 SWAP layers, problem instance has 125 two-body terms and 616 three-body terms. HSQC achieves solutions nearly up to ~700× faster than simulated annealing (SA), ~10× faster than memetic tabu search (MTS) and CPLEX. ## Why Sequential Order Matters The advantage stems from the selective interplay between computational paradigms. - During the BF-DCQO stage, bias-field feedback transforms measurement statistics into adaptive guidance for the next classical phase. - The MTS refinement then exploits this structure, combining evolutionary exploration with tabu-guided local search to avoid retracing previous minima. - Runtime allocation between these stages is adaptive, optimizing efficiency based on the observed energy landscape ![Performance comparison between MTS/SA and HSQC](/blog/hybrid-sequential-quantum-computing/HSQC_blog1.png) Performance comparison between MTS/SA and HSQC. (a) For different numbers of generations, Gmax, optimality gaps 𝒢 obtained across the eight instances tested. Data points lying in the lower part of the plot mean that the HSQC approach performed better than MTS. (b) For different numbers of sweeps, optimality gaps were obtained across the same eight instances. Here, 𝒢 =100(Emin\-GS)/|GS| ## Comparing with Other Quantum Strategies To contextualize HSQC's results, we benchmarked against D-Wave's Advantage2\_system1.6 annealer and their hybrid solvers up to 4 seconds of time limit computation. Even with long annealing times ranging from 0.5 µs up to 2000 µs and additional classical post-processing, D-Wave solutions displayed 20-35% optimality gaps relative to the ground state, with a total QPU sampling time ranging from 5.5-9.5 s on average. In contrast, HSQC's non-trivial sequencing achieved near-optimal or exact solutions on IBM's digital quantum processors without the overhead of HUBO-to-QUBO mapping or auxiliary qubits required for posterior embedding. Much faster and better solutions were obtained with HSQC using 10x fewer qubits than D-Wave. These results highlight how quantum annealers are not well-suited for higher-order optimization, whose qubit overhead worsens with increasing problem density and k-locality of the many-body terms, and undermines the quality of the solutions and scalability. ![Performance comparison with D-Wave](/blog/hybrid-sequential-quantum-computing/Picture4.png) Performance comparison between D-wave Advantage, D-wave Hybrid-solver, HSQC and MTS. Minimum optimality gaps G obtained across the eight instances tested. Here, G=100(E\_min-"GS" )/|"GS" |, meaning the lower the gap the better. Omitted bars indicate that the ground state energy was reached. ## Towards Runtime-Optimized Quantum Workflows Sequential quantum optimization is more than an algorithmic design. It represents a modular and evolving workflow in which each stage can be independently upgraded as quantum hardware, heuristics, or compilation strategies advance. This modularity ensures scalability toward larger HUBO instances and compatibility with next-generation processors, in step with the rapidly accelerating roadmaps of quantum hardware providers, where qubit counts, connectivity, and chip architectures are improving at record pace. Future directions include deploying this sequencing framework on two-dimensional architectures with enhanced connectivity, and integrating a generative-AI agent capable of autonomously designing and orchestrating classical-quantum execution sequences in real time. Such an adaptive agent would learn from performance feedback, dynamically optimizing runtime allocation and stage ordering. These developments mark a decisive step toward quantum advantage in optimization, turning experimental research into real-world applications across logistics, manufacturing, and telecom. ## References 1. Romero, S. V. et al. 'Sequential Quantum Computing', [arXiv:2506.20655 (2025)](https://arxiv.org/abs/2506.20655). 2. Chandarana P. et al., 'Hybrid Sequential Quantum Computing', [arXiv:2510.05851 (2025)](https://arxiv.org/abs/2510.05851). 3. Chandarana P. et al., 'Runtime Quantum Advantage with Digital Quantum Optimization', [arXiv:2505.08663 (2025)](https://arxiv.org/abs/2505.08663). 4. Cadavid A. G. et al., 'Bias-Field Digitized Counterdiabatic Quantum Optimization', [Phys. Rev. Res. 7, L022010 (2025)](https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.L022010). ### Written by ![Pranav Chandarana](/_next/static/media/PranavChandarana.5348aefc.jpg) Pranav Chandarana Quantum Optimization Engineer ![Alejandro Gómez Cadavid](/_next/static/media/image-4.4deb7e83.png) Alejandro Gómez Cadavid Quantum Optimization Lead ![Dr. Narendra Hegade](/_next/static/media/NarendraHegade.0cf8d9ee.jpg) Dr. Narendra Hegade Fellow [Back to Blog Overview](/blog) --- # Kipu Quantum at AI in Drug Discovery 2025 URL: https://kipu-quantum.com/blog/kipu-quantum-at-ai-in-drug-discovery-2025 [Back to Blog](/blog) # Kipu Quantum at AI in Drug Discovery 2025 Pushing the Boundaries with Quantum-Powered AI By Matthias Kaiser, Robert Lahmann•24.03.2025 Earlier this month, Kipu Quantum had the privilege of attending the AI in Drug Discovery 2025 conference in London, organized by SAE Media Group. This event brought together leaders from the pharmaceutical, biotech, and AI sectors to discuss how cutting-edge computational methods are revolutionizing drug discovery and development. Representing Kipu Quantum, Robert Lahmann and Matthias Kaiser engaged in insightful discussions with AI researchers, pharmaceutical executives, and quantum computing experts. One of the most prominent themes at the event was the increasing role of artificial intelligence and machine learning in drug discovery, and how quantum computing could provide the next leap forward in solving pharmaceutical challenges. #### Key AI and Machine Learning Use Cases in Drug Discovery AI and machine learning have already made a significant impact on the drug discovery pipeline, addressing key bottlenecks that have traditionally slowed down pharmaceutical innovation. Here are some of the most promising AI applications discussed at the event: #### 1\. Molecular Docking & Binding Affinity Predictions **AI in Drug Discovery:** Molecular docking, predicting how a drug molecule binds to a target protein, is a critical step in drug development. Machine learning models, such as graph neural networks (GNNs) and transformer-based architectures, are now being used to analyze protein-ligand interactions. AI speeds up docking simulations by predicting binding affinities based on massive datasets of known drug-protein interactions. **Challenges:** While AI accelerates docking predictions, traditional physics-based simulations (such as molecular dynamics) are still required for precise energy calculations. Classical approaches struggle with: - Simulating large molecular systems accurately. - Capturing quantum effects, which influence binding affinity. - Accounting for complex protein conformations, which change in different environments. **How Quantum Computing Can Improve It:** Quantum computing offers an exponential advantage in simulating molecular interactions at a fundamental level. Quantum algorithms could: - Perform more accurate quantum chemistry calculations to refine AI-generated docking scores. - Enable hybrid AI-quantum models that incorporate real-time quantum simulations into AI predictions. - Reduce reliance on approximations, leading to more reliable drug candidate selection. #### 2\. AI-Driven Molecular Design & Lead Optimization **AI in Drug Discovery:** AI-driven generative models, such as Variational Autoencoders (VAEs) and Reinforcement Learning (RL)-based approaches, are increasingly used to design novel drug-like molecules. These models generate new chemical compounds based on desired properties such as solubility, toxicity, and metabolic stability. **Challenges:** Despite their promise, AI-based molecular design models still struggle with optimizing generated compounds due to: - High computational costs for quantum chemistry calculations. - Difficulty in accurately predicting electronic and structural properties of new molecules. - Challenges in chemical synthesizability, as many AI-generated molecules are theoretically interesting but impractical to manufacture. **How Quantum Computing Can Improve It:** Quantum computing enhances molecular design by: - Providing more precise energy calculations for AI-generated molecules, improving drug-like properties. - Using quantum-enhanced optimization algorithms to refine AI-suggested compounds. - Running quantum chemistry simulations to predict reaction pathways, ensuring compounds can be realistically synthesized in a lab. #### 3\. AI-Powered De Novo Drug Discovery & Virtual Screening **AI in Drug Discovery:** Pharmaceutical companies use AI to screen billions of drug-like molecules in virtual libraries. AI-driven models can rank molecules based on predicted effectiveness, filtering down to the most promising candidates before physical testing. **Challenges:** Even with AI, virtual screening faces limitations such as: - False positives and negatives due to limited accuracy in AI scoring functions. - Inability to explore the full chemical space, as AI still relies on classical databases and known molecules. - Computational cost constraints, requiring trade-offs between speed and accuracy. **How Quantum Computing Can Improve It:** Quantum computing can radically improve virtual screening by: - Exploring vast molecular spaces with quantum-enhanced AI, identifying molecules beyond known chemical databases. - Running quantum-enhanced similarity searches, better predicting how novel compounds behave in biological systems. - Enhancing molecular docking models by incorporating quantum-mechanical interactions that classical AI models miss. #### 4\. AI for Precision Medicine & Biomarker Discovery **AI in Drug Discovery:** AI is revolutionizing precision medicine by analyzing genomic, proteomic, and clinical data to identify biomarkers that predict how patients will respond to treatments. Deep learning models can sift through enormous datasets to uncover patterns that would take humans decades to find. **Challenges:** Despite its potential, AI-based precision medicine still faces hurdles, including: - Difficulty in integrating multi-omics data (genomics, transcriptomics, proteomics, etc.). - High-dimensional data complexity, making it challenging to pinpoint disease-causing factors. - Limited predictive accuracy, as AI relies on statistical correlations rather than fundamental physical insights. **How Quantum Computing Can Improve It:** Quantum computing could enhance precision medicine by: - Enabling quantum-enhanced machine learning for faster, more accurate biomarker discovery. - Simulating protein and genetic interactions with far greater precision than classical models. - Running quantum-boosted feature selection, identifying the most important disease-related genes with greater accuracy. #### Kipu Quantum's Commitment to the Future of Drug Discovery The AI in Drug Discovery 2025 conference reaffirmed that AI is already transforming drug development, and that quantum computing will provide the next breakthrough. Our participation in this event reinforced the growing demand for high-performance computing solutions that address the pharmaceutical industry's toughest challenges. At Kipu Quantum, we are committed to bridging the gap between AI, quantum computing, and life sciences. By combining the power of AI with quantum-enhanced simulations, we aim to accelerate drug discovery, improve success rates, and revolutionize personalized medicine. If you're interested in exploring how quantum computing and AI can revolutionize your drug discovery pipeline, let's connect and join our new webinar about quantum computing in the pharma industry. [Join our webinar on quantum computing in pharma here](https://events.teams.microsoft.com/event/ef0c98cc-ca53-4095-9080-be17e5e6a7ef@bedf7ecf-b90d-4fda-a837-66edcb69e0d2) ### Written by ![Matthias Kaiser](/blog/kipu-quantum-at-ai-in-drug-discovery-2025/800-Kipu_Q_037-3.jpg) Matthias Kaiser Account Executive ![Robert Lahmann](/blog/kipu-quantum-at-ai-in-drug-discovery-2025/800-JPEGimage-417E-ABD0-AC-0.jpeg) Robert Lahmann Customer Success Manager [Back to Blog Overview](/blog) --- # Kipu's Quantum One-Stop-Shop for Industrial Usefulness URL: https://kipu-quantum.com/blog/industrial-quantum-usefulness [Back to Blog](/blog) # Kipu Quantum Builds the Quantum One-Stop-Shop for Industrial Quantum Usefulness By Narendra Hegade & Robert Lahmann•January 2025 Through expanded collaboration with IBM, Kipu Quantum starts to provide developers with quantum algorithms capable of outperforming classical baselines of 48 x 2.3 GHz and 123 GB RAM on IBM Quantum hardware. ## Industrial Quantum Usefulness Quantum usefulness in industry applications depends on delivery. Two challenges stand between research results and business value: turning algorithms into production-ready tools and finding problems worth solving. The first is infrastructure: APIs that let developers build without having quantum PhDs. The second is discovery: matching quantum's strengths to real business pain points. Not every hard problem needs quantum. Not every quantum solution solves a problem anyone has. Kipu's expanded role with IBM aligns with handling the full lifecycle: build the science, sell it in APIs, service end-user applications. ## Beating Classical with Quantum Algorithms Using a 156-qubit IBM Quantum Heron processor, you can find approximate solutions for a class of HUBO (Higher-Order Unconstrained Binary Optimization) problems faster than classical baselines. The Quantum Optimization Benchmarking Library, maintained by the Quantum Optimization Working Group, provides standardized HUBO test instances for comparing quantum and classical approaches. On selected benchmarks, Kipu's optimization technology surpassed CPLEX and Gurobi (with access to at least 48 cores x 2.3 GHz and 123 GB RAM) as well as best-in-class classical Tabu Search. ### Speed Advantage: - **Bias Field-DCQO:** 80x faster binary optimization than CPLEX, and 12x faster than Simulated Annealing (using 156 qubits of IBM Heron processor-powered quantum computers: ibm\_marrakesh, and ibm\_kingston) - **Hybrid Sequential Quantum Computing:** 700x vs. Simulated Annealing, 9x vs. Tabu Search using Classical (SA) → Quantum (BF-DCQO) → Classical (MTS/SA) sequence (using 156 qubits of IBM Heron processor-powered quantum computers: ibm\_kingston, ibm\_marrakesh, and ibm\_aachen) ### Efficiency Advantage: - **Hybrid Classical-Quantum Sampling:** 10³ fewer samples needed for low-temperature Boltzmann distributions (using 156 qubits of IBM Heron processor-powered quantum computer: ibm\_marrakesh) - **Quantum Reasoning-LLM (using Iskay):** 5x fewer tokens while reaching o3-level reasoning performance on BIG-Bench Hard benchmark with non-reasoning native GPT-4o (using 120 qubits of IBM Heron process-powered quantum computer: ibm\_aachen) ### Scaling Advantage: - **LABS Optimization:** Quantum Enhanced-Memetic Tabu Search scales as O(1.24N) vs. best classical O(1.34N) and quantum QAOA O(1.46N), achieving 6x less circuit depth (experimental validation up to 20 qubits on IBM Heron processor-powered quantum computer: ibm\_marrakesh) ### Accuracy Advantage: - **Quantum Feature Extraction (Machine Learning):** +5% Area under the Curve (AUC) boost in Support Vector Classification, outperforming Google Vision (0.919) with 11×10⁶ parameters (using 156 qubits on IBM Heron processor-powered quantum computer: ibm\_kingston) These results mark the shift, where quantum hardware combined with world-class software offers superior capabilities for a class of mathematical problems in scaling, accuracy, speed, and energy. Validated benchmarks, as compared between certain, finite classical resources and utility-scale quantum hardware shift the objective: expand the expected advantage catalog and discover where quantum outperforms classical business computations. ## From Notebooks to Services On November 12, 2025, a developer at the IBM Quantum Developer Conference loaded ms\_5\_100, a specific problem definition of the Market Split problem from the Quantum Benchmarking Library that's classically hard to solve and demanding on quantum hardware. The developer ran Kipu's Iskay Quantum Optimizer via the Qiskit Functions Catalogue, deployed to an IBM quantum computer over the cloud using Qiskit. The problem required a high circuit depth with 40 qubits. It solved. Minutes to result. No quantum expertise required. What made this possible? Iskay integrates tunable pre- and post-processing with a counterdiabatic quantum approach, compressing circuit depth to fit within hardware constraints. The result: a problem that would exhaust both quantum and classical computers becomes solvable. Algorithms like Iskay now deploy through standardized APIs, letting domain experts build quantum workflows without writing quantum code. [Try it yourself](https://login.hub.kipu-quantum.com/realms/planqk/protocol/openid-connect/registrations?client_id=planqk-login&redirect_uri=https%3A%2F%2Fhub.kipu-quantum.com%2Fmarketplace%23error%3Dlogin_required%26state%3D891af9db-e673-45a7-b927-6327e0a2553b%26iss%3Dhttps%3A%2F%2Flogin.hub.kipu-quantum.com%2Frealms%2Fplanqk&state=41134f37-b5da-439a-9c2f-1d462e588306&response_mode=fragment&response_type=code&scope=openid&nonce=c777df0c-7404-4d53-a5e3-04a7ec1ca66f&code_challenge=kTMNLq-qM5tp9gX3jx0Etcxx0P75D1pICJBiR8Z7aWs&code_challenge_method=S256) ## About Kipu Quantum Kipu Quantum operates in the Industrial Quantum Usefulness era. With computational quantum advantage achieved across optimization, machine learning, and AI applications, the German company focuses on market-ready platform productization through the Kipu Quantum Hub. Kipu's roadmap prioritizes curated quantum-advantage technologies, customer-validated prototypes, and strategic hardware partnerships. The company pioneers Agentic Quantum Computing: integrating AI agents directly into quantum workflows to accelerate industrial usefulness. Over 300 organizations currently use the Kipu Quantum Hub. ## References 1. Pranav Chandarana, Alejandro G. Cadavid, et al. (2025). "Runtime Quantum Advantage with Digital Quantum Optimization \[using BF-DCQO\]" [arXiv:2505.08663](https://arxiv.org/abs/2505.08663) 2. Pranav Chandarana, Sebastián V. Romero, et al. (2025). "Hybrid Sequential Quantum Computing" [arXiv:2510.05851](https://arxiv.org/abs/2510.05851) 3. Narendra N. Hegade, Nachiket L. Kortikar, et al. (2025) "Digitized Counterdiabatic Quantum Sampling" [arXiv:2510.26735](https://arxiv.org/abs/2510.26735) 4. Carlos Flores-Garrigos, Gaurav Dev, et al. (2025). "Quantum Combinatorial Reasoning for Large Language Models" [arXiv:2510.24509](https://arxiv.org/abs/2510.24509) 5. Alejandro G. Cadavid, Pranav Chandarana, et al. (2025). "Scaling advantage with quantum-enhanced memetic tabu search for LABS" [arXiv:2511.04553](https://arxiv.org/abs/2511.04553) 6. Anton Simen, Sebastián V. Romero, et al. (2025). "Branch-and-Bound Digitized Counterdiabatic Quantum Optimization." [arXiv:2504.15367](https://arxiv.org/abs/2504.15367) 7. Anton Simen, Carlos Flores-Garrigós, et al. (2025). "Digitized Counterdiabatic Quantum Feature Extraction" [arXiv:2510.13807](https://arxiv.org/abs/2510.13807) ### Written by ![Dr. Narendra Hegade](/_next/static/media/NarendraHegade.0cf8d9ee.jpg) Dr. Narendra Hegade Fellow ![Robert Lahmann](/_next/static/media/RobertLahmann.30835849.jpg) Robert Lahmann Customer Success Manager [Back to Blog Overview](/blog) --- # Material Design at the Quantum-Advantage Level URL: https://kipu-quantum.com/blog/pushing-boundaries-in-material-design-at-the-quantum-advantage-level [Back to Blog](/blog) # Pushing Boundaries in Material Design at the Quantum-Advantage Level By Alejandro Gómez Cadavid, Dr. Narendra Hegade•11.03.2025 Discovering and designing advanced materials requires substantial computational resources, significant financial investments, and considerable energy consumption. Even today's most powerful supercomputers, operating at high-performance computing (HPC) centers and equipped with thousands of GPUs, often struggle with accurately simulating the complex quantum behaviors that underpin innovative material designs. Quantum computing offers a promising alternative. By directly leveraging quantum mechanics, quantum computers can efficiently simulate complex quantum systems, surpassing the capabilities of classical computational methods. At Kipu Quantum, we have made significant progress demonstrating the practical potential of quantum algorithms. ### Quantum simulation at the quantum-advantage level: solving problems that are intractable with classical methods In our recent research paper, "Digitized Counterdiabatic Quantum Critical Dynamics" ([arXiv:2502.15100](https://arxiv.org/abs/2502.15100)), we implemented digitized counterdiabatic (CD) quantum protocols on IBM's superconducting quantum hardware, scaling our experiments to 156 qubits, the largest and most complex quantum simulation performed to date on gate-based quantum processors. Our protocols specifically address and significantly reduce defect formation, a property arising during rapid quantum phase transitions. Compared to leading quantum annealing methods, our approach achieved up to a 48% reduction in defect formation. Recent studies indicate that simulating even modest 3D quantum systems consisting of just a few hundred qubits is classically intractable, potentially requiring millions of years on conventional computers (read more in [Nature](https://www.nature.com/articles/s41586-022-04940-6) and [Science](https://www.science.org/doi/10.1126/science.ado6285)). Although previous analog quantum simulations successfully demonstrated quantum supremacy for certain specific systems, they were restricted by stringent hardware limitations, preventing broader applicability and flexibility in addressing complex, industry-relevant challenges. In contrast, our digital quantum simulation framework effectively addresses these limitations, providing a versatile and adaptable approach for solving significant problems, particularly in materials design. Given ongoing rapid advancements in quantum hardware, we anticipate practical demonstrations of quantum advantage in solving these classically intractable yet commercially and scientifically valuable challenges in the near future. ![Quantum simulation animation](/blog/pushing-boundaries-in-material-design-at-the-quantum-advantage-level/animation11.gif) ![Quantum simulation results](/blog/pushing-boundaries-in-material-design-at-the-quantum-advantage-level/image3.jpg) ### 100 times faster compared to advanced matrix product state simulator Moreover, our digital quantum simulations demonstrated substantial performance improvements over classical computational methods, achieving runtimes that are more than 100 times faster compared to classical Matrix Product State (MPS) approaches. In the figure depicted below we show the runtime comparison of quantum simulation from IBM quantum computer and MPS simulation of the quantum circuits using MIMIQ software from MPS-expert company [QPerfect](https://qperfect.io/index.php/mimiq/). Additionally, our digital quantum protocols uniquely enable precise simulation of non-stoquastic quantum dynamics, intricate quantum behaviors that are beyond the capabilities of current quantum annealers, including [those](https://www.science.org/doi/10.1126/science.ado6285) that recently demonstrated quantum advantage. This distinctive capability significantly broadens the scope and applicability of our method, highlighting its versatility and potential impact on quantum materials discovery and design. ![Runtime comparison between quantum and classical simulations](/blog/pushing-boundaries-in-material-design-at-the-quantum-advantage-level/runtime51.jpg) ### Looking Ahead With the rapid advancements announced in commercial quantum hardware roadmaps, anticipating higher qubit counts, connectivity, and enhanced accuracies, we expect our digitized counterdiabatic quantum methods to increasingly demonstrate a consolidated quantum advantage in materials science. Our Kipu Quantum technologies not only overcome classical computational capabilities but also significantly accelerates quantum computing innovation, enabling more efficient, accurate, and reliable development of next-generation materials. Understanding and controlling quantum critical dynamics, the behavior of quantum systems near phase transitions, is essential in many scientific and technological areas, including spintronics, energy conversion, and superconductivity. Improved control over defect formation will lead to significant advances in technologies impacting design of batteries, efficient solar cells, enhanced MRI magnets, and more robust power grids. ### Written by ![Alejandro Gómez Cadavid](/_next/static/media/image-4.4deb7e83.png) Alejandro Gómez Cadavid Quantum Optimization Lead ![Dr. Narendra Hegade](/_next/static/media/NarendraHegade.0cf8d9ee.jpg) Dr. Narendra Hegade Fellow [Back to Blog Overview](/blog) --- # Molecular Toxicity via Neutral-Atom Quantum Processors URL: https://kipu-quantum.com/blog/reading-toxicity-of-molecules-with-neutral-atom-quantum-processors [Back to Blog](/blog) # Reading Toxicity of Molecules with Neutral-Atom Quantum Processors ## A solid step toward neutral-atom quantum feature extraction with accuracy quantum advantage for molecular toxicity classification By Antonio Ferrer Sánchez, Carlos Flores & Alejandro Gómez Cadavid Deciding whether a molecule is toxic is one of the most important questions in drug discovery and chemical safety. Testing every candidate in a laboratory is slow and costly, so researchers lean on machine learning models that learn to predict toxicity from the structure of a molecule. These models are only as good as the numbers we feed them, the so-called features, and a large part of the work in this field is finding better ways to turn a molecule into a short list of informative numbers. This blog describes an early experiment in doing exactly that by using the Molecular toxicity dataset \[1\]. ## The idea behind quantum feature extraction The experiment builds on our recent works on quantum feature extraction, where we showed that a quantum computer can act as a kind of transformation engine, using massive multiqubit entanglement, that takes classical data and re-expresses it in a richer form \[2\], \[3\], \[4\]. In this case, each data point, for example, the description of a molecule, is written into the settings of a multipartite quantum system. The system is then allowed to evolve according to the laws of quantum physics, and during that evolution the exponentially many parts of the system influence one another in ways that are hard to reproduce with classical formulas. When the system is finally measured, the outcomes carry a fingerprint of all those interactions. Those measurement outcomes become new features, and they are handed to a standard machine learning classifier that makes the final toxic or non-toxic decision. The appealing finding from these works is that the quantum features often add information the classical ones miss, and in several cases, they improved the accuracy of the classifier. ## Neutral atoms Our earlier works ran on superconducting quantum chips, the kind of digital quantum computer that executes sequences of discrete gates. The experiment described here asks a natural question, whether the same idea can be carried out on neutral-atom quantum hardware. Neutral-atom machines hold single atoms in place with tightly focused laser beams, arrange them into patterns in space, and then shine them with light into a highly excited state known as a Rydberg state. When two atoms sit close together and one of them is excited, it changes the behavior of its neighborhood, and this natural interaction is what does heavy lifting. Instead of programming a long list of gates, these devices require a sequence of smooth control signals, and the collective dynamics of the atoms evolves continuously. Currently, these devices offer a larger qubit count with respect to digital quantum computers, and it is there where their true advantage is. As long as a smart quantum-classical workflow is developed for feature extraction, more qubits imply more features involved in the problem. We assign a set of driving schedules to each molecule in the dataset. We also specify how far apart the atoms should sit, which sets how strongly neighbors interact. Those numbers are considered to build a physical program for the hardware. The two hundred atoms are laid out on a grid of fourteen by fifteen positions, spaced a few micrometers apart. The whole sequence lasts a little under four microseconds, after which the state of every atom is read out. See Figure 1 for a detailed diagram of the graph. ## What we ran These programs ran on QuEra's Aquila, a neutral-atom processor with up to 256 atoms, which we reached through Kipu Quantum's Hub platform \[5\]. We submitted the training set of the toxicity dataset one molecule at a time and with 500 independent measurements. In total, 122 samples were processed this way, with roughly two thirds carrying the non-toxic label and one third on the toxic label. ![The atomic layout for one molecule from the toxicity dataset, showing a 14 by 15 grid of neutral atoms positioned a few micrometers apart.](/blog/reading-toxicity-of-molecules-with-neutral-atom-quantum-processors/figure-1-atomic-layout.png) Figure 1. The atomic layout for one molecule from the toxicity dataset. ## The output Reading the states of the atoms gives strings of excited and unexcited sites per measurement and gathering many of those strings for a molecule produces a statistical portrait of how the atoms responded to it. From these, we built a set of about a thousand quantum features per molecule. To judge the competitiveness of this method, we compared it against a classical baseline of few hundreds of features derived from the molecule in the usual way, and we also tried the two feature sets joined together. ![Test scores for each classifier using classical features, quantum features, and the two combined, shown across raw accuracy, balanced accuracy, F1-score and AUC.](/blog/reading-toxicity-of-molecules-with-neutral-atom-quantum-processors/figure-2-classifier-scores.png) Figure 2. Test scores for each classifier using classical features, quantum features and the two combined, shown across the four metrics. We then handed each feature set to a family of standard machine-learning classifiers, including gradient-boosted decision-tree ensembles such as XGBoost and CatBoost, a random forest, a support vector machine, and Google Research's TabFM \[6\], a zero-shot tabular foundation model for classification and regression based on in-context learning. These results are depicted in Figure 2. All the considered classifiers were trained and scored on molecules it had never seen, and to avoid lucky cases, we repeated the whole procedure over one hundred random splits and averaged the results. In addition, we also considered an extra source of error coming from random subsampling of the test samples; to probe the robustness of the model and to make sure we are not falling into lucky scenarios. We looked at four performance metrics, from plain accuracy through to balanced accuracy, F1 score and the area under the ROC curve (AUC), since the toxicity data is imbalanced and plain accuracy on its own can flatter a model that simply leans toward the majority class. Aiming to be as fairest as possible, several feature selection algorithms were performed on the classical features and on the quantum ones, leading to a “best-to-best” comparison in which the best-performing model on classical baseline is compared to the corresponding best-performing one on the quantum mapping. Across every classifier, the quantum features matched or beat the tested classical baselines. On plain accuracy, the classical features already do a reasonable job, and the quantum features add a modest increase, pushing the strongest models close to the 0.78 mark. On balanced accuracy and F1 score, the difference is much larger. The classical baseline sits around 0.55 for balanced accuracy and near 0.3 for F1, which is the tell-tale sign of a model that mostly predicts the common class, while the quantum features raise balanced accuracy to about 0.7 and roughly double the F1 score to around 0.6. The support vector machine driven by quantum features was the strongest combination overall, reaching about 0.78 accuracy and the best area under the curve in the study. ## Looking ahead As a conclusion, the neutral-atom-based feature mapping used here has achieved meaningful results, demonstrating a case where only the quantum features can improve quantitatively the performance not only on raw accuracy and AUC, but also in terms of the balanced accuracy which is known to constitute a more robust metric. These results constitute a first solid step towards more general models, where each type of quantum device provides significant features, which alone or combined with classical features, give the most accurate classification of the data. We have showed experimental evidence that an industrial use of analog quantum processors, involving neutral atoms, superconducting qubits, or trapped ions, is possible for the wide class of tabular-data and time-series machine-learning problems, as feature extraction or image classification. We believe that hardware providers as QuEra, D-Wave, Pasqal, Atom Computing, Oratomic, and Planqc will have to consider today's industrial applications with immediate added value for customers. We will soon report on further findings, services, products, and production-level possibilities with surrogate quantum machine-learning techniques. ## References 1. Molecular toxicity dataset. [archive.ics.uci.edu/dataset/728/toxicity-2](https://archive.ics.uci.edu/dataset/728/toxicity-2). 2. Kipu Quantum. Digitized Counterdiabatic Quantum Feature Extraction. [Read the blog post](/blog/digitized-counterdiabatic-quantum-feature-extraction). 3. Kipu Quantum. Analog Quantum Feature Selection with Neutral Atoms. [Read the blog post](/blog/analog-quantum-feature-selection-with-neutral-atoms). 4. Kipu Quantum. Classical Surrogates for Quantum-Advantage Feature Extraction. [Read the blog post](/blog/classical-surrogates-for-quantum-feature-extraction). 5. Kipu Quantum Hub platform. [hub.kipu-quantum.com](https://hub.kipu-quantum.com). 6. Google Research. TabFM: a zero-shot tabular foundation model for classification and regression based on in-context learning. ### Written by ![Antonio Ferrer Sánchez](/_next/static/media/image-7.690c24d3.png) Antonio Ferrer Sánchez Quantum Algorithm Engineer ![Carlos Flores](/_next/static/media/image-9.4413cb6e.png) Carlos Flores Quantum Machine Learning Engineer ![Alejandro Gómez Cadavid](/_next/static/media/image-4.4deb7e83.png) Alejandro Gómez Cadavid Quantum Optimization Lead [Back to Blog Overview](/blog) --- # Quantum Advantage with Digital-Analog Computing (DAQC) URL: https://kipu-quantum.com/blog/unlocking-quantum-advantage-with-digital-analog-quantum-computing-daqc [Back to Blog](/blog) # Unlocking Quantum Advantage with Digital-Analog Quantum Computing (DAQC) By •10.04.2025 Quantum computing is entering a transformative era, with rapid advancements bringing promising new paradigms into focus. One of the exciting and emerging approaches is Digital-Analog Quantum Computing (DAQC), a hybrid strategy uniquely positioned to harness quantum processor's computational power to address more complex problems with existing commercial devices. Despite its great potential, DAQC has largely been overlooked by hardware providers of programmable quantum processors, with some successful but exceptional experimental confirmations ([see Google's Nature paper last year](https://www.nature.com/articles/s41586-024-08460-3)). This represents a critical gap in technology and provides an opportunity for companies to tap into DAQC's immediate advantages. #### The Essence of Digital-Analog Quantum Computing DAQC merges two complementary quantum computing approaches: the precise, discrete control of digital quantum gates and the continuous multipartite or multimode dynamics of quantum processors. Digital quantum computing relies on the sequential application of precisely defined quantum gates. Companies such as IBM, Google, and IonQ are a few that make use of digital quantum algorithms. On the other hand, analog quantum computing leverages continuous quantum evolutions of bosonic and multiqubit operations, exemplified by quantum annealers such as D-Wave's processors and neutral-atom processors like those developed by QuEra and Pasqal. DAQC integrates these two strategies, offering greater flexibility, scalability, and potential for an early practical quantum advantage. #### How DAQC Could Deliver Quantum Advantage In practical terms, DAQC exploits the natural analog quantum dynamics of quantum processors in conjunction with digital quantum gates in an optimal manner, significantly simplifying complex computations. Via the smart encoding of complex problems into quantum hardware, DAQC can solve specific tasks with less algorithmic runtime, lower gate counts, minimal use of analog blocks, and reduced susceptibility to errors. This makes it especially appealing in the current noisy intermediate-scale quantum (NISQ) era, where error mitigation remains crucial. This clearly indicates that if quantum advantage can be achieved today with digital quantum computers, the systematic deploy of DAQC will make it even better. For example, in superconducting circuits, the natural qubit-resonator couplings can be utilized to encode fermion-boson models natively, such as the Hubbard-Holstein model defined on a square lattice of size (l ×h) \[[DAQC of Fermion-Boson models with Superconductors](https://www.nature.com/articles/s41534-025-01001-4)\], see Fig. (left). This model has relevance in material design and chemistry, where describing electron-phonon interactions accurately is essential for understanding superconductivity, charge-density waves, and other correlated electron phenomena. Moreover, with Digital-Analog Counterdiabatic Quantum Optimization (DACQO) one can solve larger optimization problems at the quantum advantage level with a smaller gate count and less runtime using digital-analog encodings \[[DAQC for optimization with trapped ions](https://iopscience.iop.org/article/10.1088/2058-9565/ad8b64)\], see Fig. (right). We have provided preliminary evidence of scaling up for optimization problems using DACQO with trapped ions, and we are now extending this approach to other hardware platforms, including superconducting circuits, neutral atoms, photonic, and semiconductor quantum processors. We have demonstrated that such digital-analog encodings, which combine native analog hardware interactions with digital gate operations, can lead to significant speedups in time-to-solution and improvements in solution quality. ![DAQC vs Digital HH model comparison](/blog/unlocking-quantum-advantage-with-digital-analog-quantum-computing-daqc/DAQC_vs_DigitalHH_model.jpg) #### Real-World Applications of DAQC Recent experiments done by Google \[[Google's Digital-Analog Quantum Processor](https://www.nature.com/articles/s41586-024-08460-3)\] and QuEra have showcased the remarkable capabilities of leveraging analog interactions in superconducting circuits and neutral atoms for studying quantum phase transitions and advancing Quantum Error Correction, respectively. These breakthroughs highlight the potential of the Digital-Analog Quantum Computing (DAQC) paradigm across a range of high-impact applications: - Drug Discovery: Accelerating molecular simulations to enable faster and more accurate screening of drug candidates. - Optimization Problems: Efficiently tackling complex challenges in logistics, supply chains, and scheduling. - Finance: Enhancing predictive modeling and risk analysis through quantum-accelerated computation. - Materials: Simulating quantum many-body systems and exploring novel material phases with high precision, aiding the discovery of superconductors, catalysts, and quantum materials. These achievements underscore DAQC's transformative potential, bridging the gap between theoretical quantum advantage and practical, real-world outcomes across industries #### A Call to Hardware Providers Despite its demonstrated benefits, DAQC remains underexplored by hardware providers of programmable quantum processors for demonstrating quantum advantage. To realize DAQC's full potential, quantum hardware companies must recognize and invest in its unique capabilities. By doing so, they will not only facilitate the immediate practical application of quantum technologies but also position themselves at the forefront of quantum innovation. There is a potential to demonstrate quantum advantage using DAQC in Superconducting processors of Google, Rigetti and IQM, Neutral Atom processors of Quera and Pasqal, Trapped ion processors of AQT and eleQtron, Photonic processors of Quandela, and Spin-Qubit processor of Diraq. #### Looking Ahead The hybrid nature of DAQC can unlock immediate quantum advantage for wide classes of use cases and lay the groundwork for future quantum computing advancements. As quantum hardware matures, DAQC methodologies will seamlessly integrate and evolve, ensuring continual growth in computational capabilities. DAQC offers quantum hardware providers a compelling opportunity to bridge the gap between theoretical promise and practical impact. Now is the moment to embrace digital-analog quantum computing and accelerate towards meaningful quantum advantage. At Kipu Quantum, we are actively advancing the DAQC paradigm for quantum simulations of material properties, quantum chemistry, and complex optimization tasks. Our goal is to outperform classical techniques such as tensor network methods, Gurobi, simulated annealing, and CPLEX. ### Written by [Back to Blog Overview](/blog) --- # Quantum Optimization Benchmark: Intractable Decathlon URL: https://kipu-quantum.com/blog/quantum-optimization-benchmark-library-the-intractable-decathlon [Back to Blog](/blog) # Quantum Optimization Benchmark Library: "The Intractable Decathlon" By Dr. Narendra Hegade, Alejandro Gómez Cadavid•16.04.2025 Combinatorial optimization problems play a crucial role across diverse industries such as logistics, finance, pharmaceuticals, telecommunications, and many others. They enable effective decision-making and resource allocation. But as these problems grow in complexity and size, classical computational methods often struggle, becoming impractical or inefficient. Quantum computing emerges as a promising solution, with the potential to handle such problems beyond classical capabilities. Recently, as part of the Quantum Optimization Working Group, a community that includes optimization experts from companies such as Kipu Quantum, IBM, NTT, E.ON, among others, and several academic institutions, we took part in a major benchmarking initiative detailed in our latest article, "Quantum Optimization Benchmark Library: The Intractable Decathlon" \[1\]. This initiative aims to systematically benchmark quantum and classical optimization algorithms fairly and rigorously, identifying promising problem classes and tracking progress towards achieving quantum advantage. Among the ten challenging optimization problems featured, the Low-Autocorrelation Binary Sequence (LABS) problem stands out for its exceptional complexity. Even for problems involving just 67 binary variables, an optimal solution remains unknown, posing a significant challenge for classical solvers. #### Why LABS Matters: A Real-World Impact Minimizing autocorrelation is critical in applications like radar systems, digital communications, and coding theory. For example, radar systems transmit binary signals and analyze their reflections. High autocorrelation leads to interference and false detections, whereas low autocorrelation enhances signal clarity and accuracy. LABS optimization specifically seeks sequences that minimize this off-peak autocorrelation, improving performance in numerous practical scenarios (see Fig. 1) ![Random sequence example](/blog/quantum-optimization-benchmark-library-the-intractable-decathlon/random.gif)![Optimal sequence of length 30](/blog/quantum-optimization-benchmark-library-the-intractable-decathlon/low.gif) Figure 1. Example of a random sequence (top) compared to the optimal sequence of length 30 (bottom). The optimal sequence, with low autocorrelation, has a dominant peak with respect to the sidelobes, unlike the random sequence. #### Kipu Quantum's Contribution: BF-DCQO and Potential for Quantum Advantage At Kipu Quantum, we have actively engaged with the LABS problem using our Bias-field Digitized Counterdiabatic Quantum Optimization (BF-DCQO) algorithm \[2\]. Our results demonstrate significant scaling advantages over established commercial exact solvers like CPLEX (1.73N) and Gurobi (1.61N), achieving a promising scaling factor of approximately 1.26N for sequence lengths up to N = 30. Moreover, we compared our method to the Quantum Approximate Optimization Algorithm (QAOA) with 12 layers. QAOA has demonstrated a scaling advantage over the best classical algorithm for LABS, namely Memetic Tabu Search \[3\]. Impressively, BF-DCQO achieved performance comparable to that of the twelve-layer QAOA while requiring 6x fewer entangling gates. This remarkable efficiency and resource reduction highlight the practicality of our approach for current and near-term quantum hardware. ![Runtime scaling comparison](/blog/quantum-optimization-benchmark-library-the-intractable-decathlon/classical_methods_comparison.png) Figure 2. Runtime scaling of CPLEX and Gurobi compared to BF-DCQO for sequence lengths up to 30. #### Setting New Quantum Benchmarks on Quantum Hardware Our experiments pushed the practical quantum computing frontier forward, successfully solving LABS instances up to 20 qubits on IBM's quantum hardware. This achievement sets a new benchmark, surpassing the previous record of 18 qubits held by the JPMorgan team using Quantinuum's system \[3\]. One remarkable aspect of BF-DCQO is that it bypasses the need for variational classical optimization entirely, significantly simplifying its implementation and making it highly suitable for early-stage quantum hardware. #### Looking Ahead This collaborative benchmarking effort underscores the potential of quantum computing in addressing challenging optimization problems and accelerates the journey toward quantum advantage. At Kipu Quantum, we continue refining our algorithms, extending the scope of our research, and encouraging the broader community to explore and contribute to this exciting and rapidly evolving field. **References** \[1\] [Koch, Thorsten, et al. "The Quantum Optimization Benchmarking Library." Nature Computational Science (2026).](https://doi.org/10.1038/s43588-026-00991-1) \[2\] [Romero, Sebastián V., et al. "Bias-field digitized counterdiabatic quantum algorithm for higher-order binary optimization." arXiv preprint arXiv:2409.04477 (2024).](https://arxiv.org/abs/2409.04477) \[3\] [Shaydulin, Ruslan, et al. "Evidence of scaling advantage for the quantum approximate optimization algorithm on a classically intractable problem." Science Advances 10.22 (2024): eadm6761.](https://www.science.org/doi/10.1126/sciadv.adm6761) ### Written by ![Dr. Narendra Hegade](/_next/static/media/NarendraHegade.0cf8d9ee.jpg) Dr. Narendra Hegade Fellow ![Alejandro Gómez Cadavid](/_next/static/media/image-4.4deb7e83.png) Alejandro Gómez Cadavid Quantum Optimization Lead [Back to Blog Overview](/blog) --- # Quantum-Enhanced Memetic Tabu Search URL: https://kipu-quantum.com/blog/scaling-advantage-quantum-enhanced-memetic-tabu-search [Back to Blog](/blog) # Scaling Advantage with Quantum-Enhanced Memetic Tabu Search By Alejandro Gómez Cadavid, Pranav Chandarana & Sebastián Romero•2025 In optimization, scaling is everything. Solvers eventually hit the wall where effort grows exponentially with problem size. Facing that wall, lowering the scaling base, is how we measure real computational progress. At Kipu Quantum, in collaboration with NVIDIA, we have recently shown that hybrid quantum-classical optimization pipelines can accelerate purely classical ones. Our latest work introduces the Quantum-Enhanced Memetic Tabu Search (QE-MTS) for the Low-Autocorrelation Binary Sequence (LABS) problem. The result: a measurable scaling advantage for one of the hardest combinatorial benchmarks known. The Low-Autocorrelation Binary Sequence (LABS) problem has long been a proving ground for optimization methods. It involves finding binary sequences that minimize unwanted correlations. In simple terms, building patterns that produce a sharp signal without echoes or interference. This challenge materializes in radar pulse design and communication protocols, where improvements in sequence quality translate into clearer signals and enhanced target detection. ![Low Autocorrelation Binary Sequence visualization](/blog/scaling-advantage-quantum-enhanced-memetic-tabu-search/N30_011100111010101101101111110000-ezgif.com-video-to-gif-converter.gif) Figure 1. Example of a low autocorrelation binary sequence, which reduces interference and false detections, hence enhancing signal clarity and accuracy from the peak at zero lag. ![Density of local minima comparison](/blog/scaling-advantage-quantum-enhanced-memetic-tabu-search/density_local_minima.png) Figure 2. Density of single-flip local minima across different system sizes N for the LABS problem and the spin-glass SK case. This quantifies the number of configurations in which no single flip reduces the energy, compared to the total number of configurations. This supports why LABS is a more challenging problem than a common spin-glass benchmark. Every sequence length defines a single, unique instance, forcing algorithms to confront a unique rugged landscape. When compared to other typical benchmarks, such as the spin-glass Sherrington-Kirkpatrick (SK) model, LABS exhibits more local minima. In other words, low non-optimal points where optimizers have a hard time escaping. ## A new type of hybrid providing scaling advantage The idea behind QE-MTS is simple: let the quantum computer do what it is best at, generating low-energy samples via digitized counterdiabatic quantum optimization, and let the classical optimizer refine them. These quantum-informed candidates seed a population-based memetic tabu search, guiding it through the rugged energy landscape. Across sequence lengths from 27 to 37, QE-MTS shows a typical scaling of O(1.24N), improving upon the O(1.34N) scaling of the best classical baseline. That difference may look small on paper, but in exponential growth, it is transformative. The analysis projects a crossover around N ≈ 47, where QE-MTS becomes faster than classical MTS for typical runs, widening its advantage as system size increases. The quantum part of QE-MTS, digitized counterdiabatic quantum optimization, achieves this with a sixfold reduction in circuit depth compared to QAOA methods, keeping it suitable for early fault tolerant quantum computers. ![Median time-to-solution for MTS and QE-MTS](/blog/scaling-advantage-quantum-enhanced-memetic-tabu-search/plot_medians_vs_N.png) Figure 3. Median time-to-solution for MTS and QE-MTS. Time-to-solution is measured as the number of function evaluations required to reach the known optimal solution. ## Additional hardware and implementation details GPUs (Graphics Processing Units) are highly effective for simulating quantum circuits since they are designed to handle massive computations. Quantum circuit simulations involve manipulating large state vectors, whose size grows exponentially with the number of qubits. NVIDIA GPUs together with the CUDA-Q SDK provide an intuitive and powerful tool to simulate these demanding quantum circuits. In our case, all quantum circuits were simulated on NVIDIA B200 GPUs using CUDA-Q, with up to N = 37 qubits via Amazon EC2 P6-b200.48xlarge instance. With QE-MTS, we see clear evidence that quantum enhancement can reshape classical scaling. This observation is not unique to LABS, but goes beyond other optimization problems, where hybrid sequential classical-quantum pipelines are leading. At Kipu Quantum, we believe this is how progress looks in the present, near and mid-term: smarter hybrids, measurable scaling gains, and tangible industrial impact. ![Runtime to simulate quantum circuits using GPUs](/blog/scaling-advantage-quantum-enhanced-memetic-tabu-search/h200_vs_a100.png) Figure 4. Runtime to simulate the quantum circuits using 8 B200 GPUs with 1440GB. This multi GPU setup can reach the simulation of up to 37 qubits circuits. ## Why this matters With QE-MTS, we see clear evidence that quantum enhancement can reshape classical scaling. This observation is not unique to LABS, but goes beyond other optimization problems, where hybrid sequential classical-quantum pipelines are leading. At Kipu Quantum, we believe this is how progress looks in the present, near and mid-term: smarter hybrids, measurable scaling gains, and tangible industrial impact. ## References 1. Chandarana, P., Romero, S. V., Cadavid, A. G., Simen, A., Solano, E., & Hegade, N. N. (2025). Hybrid Sequential Quantum Computing. [arXiv preprint arXiv:2510.05851](https://arxiv.org/abs/2510.05851) 2. Cadavid, A. G., Chandarana, P., Romero, S. V., Trautmann, J., Solano, E., Patti, T. L., & Hegade, N. N. (2025). Scaling advantage with quantum-enhanced memetic tabu search for LABS. [arXiv preprint arXiv:2511.04553](https://arxiv.org/abs/2511.04553) 3. Hegade, N. N., Cadavid, A. G. (2025). Quantum Optimization Benchmark Library: "The Intractable Decathlon" Kipu Quantum, Knowledge Hub, Blog. 4. CUDA-Q Development Team, CUDA-Q (2025), [https://nvidia.github.io/cuda-quantum/0.6.0/using/python.html](https://nvidia.github.io/cuda-quantum/0.6.0/using/python.html) accessed: 2025-07-14. ### Written by ![Alejandro Gómez Cadavid](/_next/static/media/image-4.4deb7e83.png) Alejandro Gómez Cadavid Quantum Optimization Lead ![Pranav Chandarana](/_next/static/media/PranavChandarana.5348aefc.jpg) Pranav Chandarana Quantum Optimization Engineer [Back to Blog Overview](/blog) --- # Quantum-Reasoning LLM (QR-LLM): Quantum Intelligence URL: https://kipu-quantum.com/blog/quantum-intelligence [Back to Blog](/blog) # Quantum-Reasoning LLM (QR-LLM): Emergence of Quantum Intelligence By Carlos Flores & Narendra Hegade•03.10.2025 ## From Chain-of-Thought to Combinatorial Reasoning As large language models (LLMs) become central to AI applications, a key challenge remains: how to make their reasoning capacity both more accurate, reliable, faster, and scalable. While chain-of-thought \[1\] prompting helps models explain their steps, it also produces redundant, inconsistent, and low-quality fragments. We address here this limitation by reformulating reasoning as a combinatorial optimization problem \[2\], which we solve with suitably designed and engineered hybrid classical-quantum workflows involving digital, analog, or digital-analog quantum computing encodings. From this point of view, our QR-LLMs can be implemented with a variety of homogeneous or heterogeneous individual, iterated, or sequential runs on commercial quantum processors like IBM, IonQ, QuEra, Atom Computing, Pasqal, Quantinuum, Rigetti, D-Wave, IQM, Xanadu, and Origin Quantum, among many others. In our approach, each reasoning fragment, or "reason", extracted from multiple GPT-4-1 completions is treated as a binary decision variable: either it is selected or discarded. By combining these fragments into a Higher-Order Unconstrained Binary Optimization (HUBO) Hamiltonian formulation, we explicitly capture the individual importance (linear terms), pairwise consistency (quadratic terms), and higher-order coherence (k-local terms). This optimization is far more expressive than the majority voting or simple filtering methods. It ensures that the final answer is built from the most relevant and diverse reasons, avoiding redundancy and improving interpretability. ![QR-LLM Pipeline](/blog/quantum-intelligence/Workflow_Chatqpt_white.png) Figure 1. Pipeline of QR-LLM: reasoning fragments extracted from multiple LLM completions are mapped into a HUBO formulation and solved with a quantum optimizer (BF-DCQO), producing the final answer. ## Why Quantum Computing Matters? The power of this method comes with a cost: as the number of candidate reasons grows, the HUBO Hamiltonian quickly becomes dense. With just 120 reasons, we already face ~7,000 pairwise interactions and ~280,000 triplets; moving to k-body terms (k>>1) makes the problem explode in complexity. **Classical solvers like simulated annealing collapse in runtime** under this growth, struggling to navigate flat, degenerate energy landscapes. This is where quantum solvers come in. We employ our proprietary **Bias-Field Digitized Counterdiabatic Quantum Optimization** (BF-DCQO) \[3\], which smoothly runs on today's digital quantum hardware, like IBM and IonQ, and can operate with high k-body Hamiltonian terms. Presently, IBM's quantum systems are the only commercial quantum processors where we can scale up to 156 reasons (156 physical qubits). With next generations, along IBM's roadmap, including the preannounced NightHawk 2D chips and their modular Flamingo architectures \[4\], we expect to solve each time more complex tasks and question prompts. With current quantum processors, we are currently identifying the class of complex questions that would unavoidably require reaching quantum-advantage level in our quantum algorithms, giving rise to the era of Quantum Intelligence. ## Benchmarking Results We tested this framework against some of the **most demanding BBEH benchmarks** \[5\] for reasoning: **Causal Understanding, DisambiguationQA, and NYCC**. These datasets are widely regarded as essential for evaluating new LLMs, as they probe multi-step inference, semantic disambiguation, and conceptual combination. Our results show that our **Quantum Combinatorial Reasoning outperforms reasoning-native models**, such as OpenAI **o3-high**: - **+4.9%** in Causal Understanding. - **+2.7%** in DisambiguationQA. - **+8.7%** in NYCC. This establishes a clear quantum-advantage trajectory for strategic and complex LLM reasoning. ![DisambiguationQA Benchmark Results](/blog/quantum-intelligence/chqpt_benchmark.png) Figure 2. Accuracy results on the DisambiguationQA benchmark. QR-LLM achieves the highest performance (61.0), surpassing reasoning-native models such as o3-high (58.3) and DeepSeek R1 (50.0). ![BBEH Benchmarks Comparison Table](/blog/quantum-intelligence/Screenshot2025-10-03at11.05.04.png) Table 1. Accuracy (%) for three BBEH benchmarks: Causal Understanding, DisambiguationQA, and NYCC. QR-LLM consistently outperforms reasoning-native models such as o3-high and DeepSeek R1, with the best results in all tasks. ## Towards Quantum Intelligence - **Order and structure of reasons:** combining HUBO with Tree-of-Thoughts \[6\] to capture sequential dependencies. - **Ranking of reasons:** moving beyond binary selection to importance-weighted outputs. - **Quantum Intelligence:** exploiting k-body interactions to model reasoning at very high relational levels where quantum advantage is a sine qua non condition. - **Hierarchical reasoning:** hybrid pipelines where simple questions are solved classically, while complex, multi-hop problems invoke quantum solvers. - **Sequential architectures on heterogeneous hardware:** leveraging hybrid pipelines that combine CPUs, GPUs, and quantum processors to deliver more complex answers across diverse computational backend for quantum-intelligence industrial applications. This roadmap points toward a new paradigm: Quantum Intelligence (QI), where quantum optimization will be able to progressively and incessantly augment quantum-reasoning LLMs. The consolidation of QI, as the next step of classical AI, will allow us to solve reasoning tasks once considered out of reach for classical methods, outperforming the reasoning capabilities of human brains/minds. Therefore, it is currently unpredictable to guess how QI may shake humanity and where it will place our technological societies in a troubled world. ## Bibliography 1. WEI, Jason, et al. Chain-of-thought prompting elicits reasoning in large language models. Advances in neural information processing systems, 2022, vol. 35, p. 24824-24837. 2. Esencan, Mert, et al. "Combinatorial reasoning: selecting reasons in generative AI pipelines via combinatorial optimization." arXiv preprint arXiv:2407.00071, 2024. 3. CADAVID, Alejandro Gomez, et al. Bias-field digitized counterdiabatic quantum optimization. Physical Review Research, 2025, vol. 7, no 2, p. L022010. 4. IBM QUANTUM. How IBM will build the world's first large-scale, fault-tolerant quantum computer. [https://www.ibm.com/quantum/blog/large-scale-ftqc](https://www.ibm.com/quantum/blog/large-scale-ftqc), 2025. 5. KAZEMI, Mehran, et al. Big-bench extra hard. arXiv preprint arXiv:2502.19187, 2025. 6. YAO, Shunyu, et al. Tree of thoughts: Deliberate problem solving with large language models. Advances in neural information processing systems, 2023, vol. 36, p. 11809-11822. ### Written by ![Carlos Flores](/_next/static/media/image-9.4413cb6e.png) Carlos Flores Quantum Machine Learning Engineer ![Dr. Narendra Hegade](/_next/static/media/NarendraHegade.0cf8d9ee.jpg) Dr. Narendra Hegade Fellow [Back to Blog Overview](/blog) --- # Runtime Quantum Advantage with BF-DCQO (I) URL: https://kipu-quantum.com/blog/runtime-quantum-advantage-with-bf-dcqo [Back to Blog](/blog) # Runtime Quantum Advantage with BF-DCQO (I) By Pranav Chandarana, Alejandro Gómez Cadavid, Dr. Narendra Hegade•25.04.2025 In the challenging domain of combinatorial optimization, higher-order unconstrained binary optimization (HUBO) problems are renowned for their computational complexity. Classical solvers like CPLEX and simulated annealing (SA) often struggle with severe runtime bottlenecks when higher-order terms come into play, exponentially increasing computational demands and limiting scalability. Our team set out to precisely explore this unfriendly territory. At Kipu Quantum, we have introduced Bias-Field Digitized Counterdiabatic Quantum Optimization (BF-DCQO), a transformational quantum algorithm tailored specifically for tackling complex optimization problems. BF-DCQO combines well-established counterdiabatic quantum dynamics protocols with a clever measurement-driven bias-update strategy, efficiently navigating complex energy landscapes where classical solvers typically stumble. We deployed BF-DCQO on IBM's latest 156-qubit Heron machines and benchmarked the time required to produce high-quality solutions. The results are impressive: BF-DCQO is able to consistently achieve comparable quality in the yielded solutions for the tested instances up to **80 times** faster than CPLEX, or up to **12 times** faster than SA. This occurs despite the quantum chip's modest shot rate (~10 kHz) compared to classical hardware, which evaluates around 10^8 samples per second. Moreover, the performance gap grows as the system size increases, clearly indicating that we are trespassing quantum-advantage level for wide classes of combinatorial optimization problems as compared to the tested solvers. This experimental achievement of Kipu Quantum algorithms running in commercial quantum processors, in absence of sophisticated error mitigation, error correction, or fault-tolerant encodings, proves that utility scale and quantum-advantage level in quantum computing is possible today, even with noisy qubits. We can easily imagine that, when error-corrected or fault-tolerant quantum computers may start to be available in the future, Kipu Quantum algorithmic solutions will show even more powerful results on logical qubits. Given the ambitious roadmaps and reliability of most quantum hardware providers, we consider that systematic quantum advantage will naturally happen and consolidate along this year 2025. #### Quantum vs. Classical: Performance Benchmarks To rigorously validate BF-DCQO, we performed extensive benchmarks on the ibm marrakesh backend, which features 156 transmon qubits arranged in a heavy-hex architectural lattice. We tested our quantum algorithm on dense HUBO problems involving up to three-body terms and coefficients drawn from heavy-tailed distributions. The chosen coefficients closely mirror real-world optimization problems encountered in wide classes of use cases in finance, risk management, and regulatory compliance. Similar cases can be developed for logistics, manufacturing, telecommunications networks, energy distribution, robotics, chemistry, navigation, and life sciences. ![Enhancement factor vs system size](/blog/runtime-quantum-advantage-with-bf-dcqo/SystemsizeBF-DCQO.jpg) Figure 1. Enhancement factor, meaning ratio of CPLEX runtime to BF-DCQO runtime, as a function of system size or number of qubits. Each box summarizes results across multiple problem instances; the line inside shows the median, the box covers the middle 50% of data, and dots indicate outliers, cases with exceptionally high speed-up. Fig.1 shows how fast our BF-DCQO is, as compared to CPLEX across different system sizes or number of qubits \[1\]. As this size increases, we see that not only does the average improvement grow, but the potential for dramatic speed-ups becomes even more pronounced. We can clearly see that for some instances the runtime improvements are modest, while for most of them, drastic enhancements happen. ![Accuracy comparison SA vs BF-DCQO](/blog/runtime-quantum-advantage-with-bf-dcqo/Figure2blogKipu.jpg) Figure 2. Accuracy of simulated annealing (SA) and BF-DCQO across two instances corresponding to two system sizes with 130 and 156 qubits. ![Runtime comparison for N=156](/blog/runtime-quantum-advantage-with-bf-dcqo/Figure3Kipublog.png) Figure 3. Runtime to find 99.8% of the optimal solution for an N=156 qubit instance using BF-DCQO, CPLEX, and SA. On the other hand, Fig. 2 demonstrates how BF-DCQO outperforms SA in both accuracy and runtime. For both methods, accuracy is evaluated relative to the optimal solution. Although SA achieves near-optimal accuracy, BF-DCQO consistently delivers superior results, particularly for the larger problem instance. Execution times in seconds are annotated above each bar, highlighting BF-DCQO's faster convergence, achieved even with comparable or better accuracy. Notably, SA requires exploring at least four orders of magnitude more samples than BF-DCQO to reach similar accuracy. Both Fig. 1 and Fig. 2 clearly illustrate that BF-DCQO's performance advantage grows significantly with system size. In larger scenarios, such as the 100- and 156-qubit cases, we observe speed-ups exceeding an order of magnitude. Also, in Fig. 3, we show results for simultaneously outperforming both CPLEX and SA for a 156-qubit instance. The takeaway is clear: the larger the optimization problem, the greater the advantage of BF-DCQO, showing signatures of scaling quantum advantage. #### Decoding Runtime Quantum Advantage BF-DCQO's superior performance is rooted in four key design principles: 1. **Digitized Counterdiabatic Protocol:** By minimizing unwanted excitations among energy levels during rapid counterdiabatic quantum evolution, BF-DCQO, its digitized counterpart, significantly increases the probability of obtaining optimal or near-optimal solutions. 2. **Measurement-driven Bias Updates**: BF-DCQO leverages measurement information from each DCQO iteration to adaptively navigate complex energy landscapes, resulting in faster convergence. 3. **Nonvariational Quantum Algorithmics:** our BF-DCQO is in essence and by construction an iterative purely quantum algorithm without any drawback coming from others' variational approaches. 4. **Native Embedding of Complex Interactions:** Classical solvers like CPLEX typically decompose higher-order terms into large sets of linear constraints and additional binary variables, introducing substantial computational overhead. Although SA can directly tackle HUBO problems, it often struggles since it gets stuck in local minima within rugged energy landscapes. In contrast, BF-DCQO can efficiently handle higher-order terms, providing an encoding advantage, significantly improving the speed of convergence and the quality of the solution. #### Quantum Advantage and the Path to Commercial Realization Our success with BF-DCQO represents a significant milestone, clearly demonstrating superior speed and accuracy compared to advanced classical solvers. Today's quantum processors already enable remarkable algorithmic performance. However, upcoming quantum platforms, such as IBM's 1000+ qubit "Flamingo" systems will further enhance BF-DCQO's capabilities, promising substantial breakthroughs in solving previously intractable optimization problems. Quantum algorithms like BF-DCQO will soon tackle even denser HUBO problems that are challenging for classical computations, firmly consolidating and establishing the era of commercial quantum advantage. We actively welcome collaborations and partnerships with industry leaders and top researchers to accelerate together the exciting present and future of quantum optimization. *\[1\] We thank Stefan Woerner from IBM for sharing his expertise on using CPLEX through private communication and for his valuable feedback.* ### Written by ![Pranav Chandarana](/_next/static/media/PranavChandarana.5348aefc.jpg) Pranav Chandarana Quantum Optimization Engineer ![Alejandro Gómez Cadavid](/_next/static/media/image-4.4deb7e83.png) Alejandro Gómez Cadavid Quantum Optimization Lead ![Dr. Narendra Hegade](/_next/static/media/NarendraHegade.0cf8d9ee.jpg) Dr. Narendra Hegade Fellow [Back to Blog Overview](/blog) --- # Runtime Quantum Advantage with BF-DCQO (II) URL: https://kipu-quantum.com/blog/runtime-quantum-advantage-with-bf-dcqo-ii [Back to Blog](/blog) # Runtime Quantum Advantage with BF-DCQO (II) Comparison against Quantum Annealing and QAOA By Pranav Chandarana, Alejandro Gómez Cadavid, Dr. Narendra Hegade•22.05.2025 The Bias-Field Digitized Counterdiabatic Quantum Optimization (BF-DCQO) algorithm has recently demonstrated a compelling runtime quantum advantage in tackling higher-order unconstrained binary optimization (HUBO) problems. Notably, it can outperform established classical solvers such as CPLEX and Simulated Annealing (SA) in both speed and quality of solutions \[1\]. In this post, we explore how BF-DCQO stacks up against prominent quantum algorithmic approaches, such as Quantum Annealing (QA) and the Quantum Approximate Optimization Algorithm (QAOA). By examining these comparisons, the aim is to understand where BF-DCQO stands in the evolving landscape of quantum optimization. ### Quantum versus Quantum: Performance Benchmarks In our [previous blog](/blog/runtime-quantum-advantage-with-bf-dcqo), we showed how BF-DCQO, when executed on IBM's digital quantum hardware, can outperform classical solvers such as CPLEX and SA for a class of complex problems. This runtime quantum advantage is particularly striking given the hardware disparity: the quantum processor operates at a relatively modest shot rate of ~10 kHz, whereas classical systems can evaluate up to 10⁸ samples per second on a regular computer. Despite this, BF-DCQO showed a performance boost, which would grow with system size, as the evidence suggested. But outperforming classical solvers is only one part of the story. To fully gauge its potential, we must also compare BF-DCQO with other quantum optimization strategies. Here, we shift our focus to a quantum-versus-quantum comparison, evaluating BF-DCQO alongside prominent contenders in both digital and analog quantum processors. Let's begin by comparing BF-DCQO running on IBM's digital quantum hardware with (analog) quantum annealing on D-Wave's Advantage Prototype 2.6. This next-generation annealer features 1200+ qubits and is designed to naturally solve large-scale Quadratic Unconstrained Binary Optimization (QUBO) problems, which is the quadratic version of the more general HUBO class. However, tackling HUBO problems on D-Wave requires a transformation pipeline. First, the HUBO instance must be reduced to a QUBO form through a mapping procedure. Then, a suitable embedding onto the quantum annealer's hardware graph must be found. These steps introduce an overhead in the form of auxiliary qubits and added constraints, which are not intrinsic to the original problem. In contrast, BF-DCQO can address HUBO instances natively, avoiding this added complexity, offering up to a 4.3x reduction in the number of qubits for the instances here tested. To make a runtime comparison with BF-DCQO, we executed the QA experiments using different annealing times between 0.5 µs and 2000 µs, while keeping the best performing. After recent scaling speedup claims using QAOA, in addition to QA, we also benchmarked BF-DCQO against a hardware-friendly version of QAOA, known as **Linear-Ramp QAOA (LR-QAOA)** \[2\]. Here we used up to 5 layers and kept the best performing on hardware. BF-DCQO entirely sidesteps the bottleneck of classical parameter optimization, a feature shared by LR-QAOA, which was one of the motivating factors behind including it in our comparisons. By leveraging a linear ramp instead of variational feedback loops, LR-QAOA becomes a far more feasible candidate for execution on near-term quantum devices. #### Performance Overview In **Figure 1**, we present a comparative analysis of the accuracy achieved by BF-DCQO, QA, and LR-QAOA. Each bar in the plot represents the percent accuracy with respect to the optimal solution, and the corresponding *runtime* is displayed on top of each bar for clarity. To ensure a balanced comparison, we applied the same post-processing pipeline, originally developed for BF-DCQO, to all quantum algorithms under evaluation. The results reveal a consistent trend: **BF-DCQO delivered higher solution accuracy across all benchmark instances**. More importantly, this improvement was not just in solution quality, it also came with **a significantly reduced runtime** compared to both QA and LR-QAOA. These findings strongly suggest that **BF-DCQO offers a more effective path to high-quality approximate solutions of HUBO problems on near-term quantum hardware**. Not only did it outperform both digital (LR-QAOA) and analog (QA) quantum solvers in accuracy, but it also did so faster, even when running on digital quantum hardware with modest capabilities. This solidifies BF-DCQO as a frontrunner for achieving runtime quantum advantage in practical optimization scenarios. ![BF-DCQO Performance Comparison](/blog/runtime-quantum-advantage-with-bf-dcqo-ii/Dwave_compare3.png) Figure 1: Accuracy (%) for five 156-qubit HUBO instances tackled with BF-DCQO, QA and LR-QAOA. Each bar represents the best experimentally achieved accuracy with the runtimes shown on top in seconds. Each of the instance is generated using up to 3 local terms and specific distributions. \[1\] #### Conclusions When we pit BF-DCQO against QA and LR-QAOA, **BF-DCQO consistently outperformed both in accuracy, runtime and resources (in terms of qubit overhead for QA and circuit depth for LR-QAOA) in the tested instances**. Thanks to its integration of counterdiabatic terms directly into a digitized evolution framework and the use of a bias field, BF-DCQO achieves significantly faster convergence on challenging 156-qubit instances. Despite running on hardware with a relatively low shot rate of ~10 kHz, BF-DCQO demonstrated **a reduction in runtime to reach an approximate solution, compared to** QA on D-Wave's Advantage2 system and LR-QAOA on IBM Kingston. But the story doesn't end at fixed problem sizes. One of BF-DCQO's most powerful advantages is **its scalability**. While analog quantum annealing may suffer from embedding overheads and LR-QAOA may require time-consuming parameter searches, BF-DCQO maintains efficiency as the problem size grows. Its bias-field calibration and embedded counterdiabatic corrections require minimal classical overhead and scale naturally with system size. Importantly, it continues to exploit the same Hamiltonian structure, regardless of qubit count. In practice, this positions BF-DCQO as a **hardware-efficient, scalable approach to runtime quantum advantage on industrial use-cases**. BF-DCQO not only demonstrated superiority on current quantum hardware but also set the stage for even greater gains as quantum processors improve in coherence, connectivity, and gate fidelity. #### References 1. Chandarana P, Cadavid AG, Romero SV, Simen A, Solano E, Hegade NN. Runtime Quantum Advantage with Digital Quantum Optimization. arXiv preprint [arXiv:2505.08663](https://arxiv.org/abs/2505.08663). 2025 May 13. 2. Montanez-Barrera JA, Michielsen K. Towards a universal QAOA protocol: Evidence of a scaling advantage in solving some combinatorial optimization problems. arXiv preprint [arXiv:2405.09169](https://arxiv.org/abs/2405.09169). 2024 May 15. ### Written by ![Pranav Chandarana](/_next/static/media/PranavChandarana.5348aefc.jpg) Pranav Chandarana Quantum Optimization Engineer ![Alejandro Gómez Cadavid](/_next/static/media/image-4.4deb7e83.png) Alejandro Gómez Cadavid Quantum Optimization Lead ![Dr. Narendra Hegade](/_next/static/media/NarendraHegade.0cf8d9ee.jpg) Dr. Narendra Hegade Fellow [Back to Blog Overview](/blog) --- # Sequential Quantum Computing URL: https://kipu-quantum.com/blog/sqc [Back to Blog](/blog) # Sequential Quantum Computing Integrating multiple quantum processors for better solutions By Alejandro Gómez Cadavid, Pranav Chandarana, Dr. Narendra Hegade•30.06.2025 Today's quantum landscape offers a range of processors, each with unique strengths and limitations. But can we harness the best of every device? At Kipu, we've pioneered Sequential Quantum Computing (SQC) \[1\]: a paradigm that links different quantum processors in series to overcome individual bottlenecks and unlock advanced capabilities on today's hardware. ### How does SQC work? Similar to the preparation of a gourmet dish, where sourcing each ingredient from specialized shops is preferred over a single supermarket with average-quality items, SQC employs a sequential workflow, utilizing different quantum processors to acquire higher-quality solutions. Individually, digital and analog quantum processors offer distinct advantages but also specific constraints. SQC mitigates individual limitations by sequentially transferring information between commercial quantum processors, creating seamless quantum algorithmics that enhance the performance of the targeted tasks. We announce the launch of a diverse range of quantum computing solutions, encompassing both sequential and parallel, classical and quantum, as well as homogeneous and heterogeneous quantum processing workflows. This novel SQC paradigm will provide enhanced performance and earlier quantum advantage for industry applications as quantum computers evolve from noisy to error-corrected to fault-tolerant quantum devices. #### Experimental Breakthrough ![Sequential Quantum Computing Schematic](/blog/sqc/sqc_schematics.jpg) **Figure 1.** Sequential quantum computing schematic. Different quantum hardware architectures offer distinct advantages. SQC integrates homogeneous and heterogeneous quantum processors, combining their strengths and addressing their limitations to enhance solution quality while minimizing resource utilization. The promise of SQC is not just theoretical or conceptual. We have already demonstrated its potential by addressing a combinatorial optimization problem with interactions involving hundreds of three-body terms. We considered a 156-qubit problem adapted to IBM Heron devices up to three-body terms with randomly chosen Sidon set couplings. These are known to yield non-degenerate landscapes \[2\]. For such a task, our bias-field digitized counterdiabatic quantum optimization (BF-DCQO) algorithm was used, since it has proven superior performance on digital platforms \[3, 4, 5, 6\]. It turns out that within the SQC paradigm, BF-DCQO is also a suitable quantum algorithm if the state initialization utilizes quantum annealing (QA) for computing the biases. Along these lines, for the sake of a balanced benchmarking, three approaches are considered: - Standalone QA (D-Wave): Hundreds of thousands of measurements. - Standalone BF-DCQO (IBM): Ten iterations with tens of thousands of measurements. - SQC (D-Wave+IBM): one iteration of BF-DCQO on IBM with five thousand shots, warm-started with a solution from QA with three thousand samples. Therefore, the overall routine required fewer than ten thousand shots. The logic behind this combination is to obtain fast, high-quality results from D-Wave as a warm start of a BF-DCQO algorithm run on IBM. Digital quantum processors admit the computation of nonstoquastic terms, which can yield better results as an outcome. In consequence, not only were the obtained solutions better, but they also required fewer resources, showcasing a clear advantage of sequentially combining both quantum processors (see Table 1). In particular, the significant reduction in the number of required measurements was 36x for QA and 6x for BF-DCQO. Table 1. Performance of the instance plotted in Figure 2 under different approaches, where the best results are in bold. For IBM platforms, we assume a sampling rate of 10 kHz. For quantum annealers, the runtime is computed as the product of the number of shots and the annealing time, assuming sampling rates of a few MHz. Approach Number of shots AR Best AR Best energy Qubits Standalone QA (large) 290000 (26.1 s) 96.63% 98.89% \-184.78 678 Standalone BF-DCQO 50000 (5.0 s) 90.10% 97.52% \-182.21 156 Standalone QA (low) 3000 (0.6 s) 90.70% 98.51% \-184.07 678 SQC 8000 (1.1 s) 94.95% 100% \-186.86 678/156 ![SQC Performance Results](/blog/sqc/final.jpg) **Figure 2.** Results for the heavy-hexagonal 156-qubit NN HUBO. (a) Using D-Wave, post-processed distributions using 290000 and 3000 samples (dark blue and lavender, respectively) and annealing time of 90 μs. Using IBM, best post-processed distribution after ten iterations of BF-DCQO (purple). Using both D-Wave and IBM (SQC approach, yellow), one iteration of BF-DCQO after initializing the bias fields with the post-processed D-Wave distribution of 3000 samples. (b)-(c) Approximation ratios and best approximation ratios obtained. #### Stability To evaluate performance across multiple instances, we considered 17 randomly distributed Sidon instances, as described above. Then, we compared the following three methods: - Standalone QA (D-Wave) with 50K measurements. - Standalone BF-DCQO (IBM) with 5 iterations and 10K measurements per iteration. - SQC (D-Wave+IBM) with 4K QA shots and 3 IBM iterations with 10K measurements. In Fig. 3, we show the distribution of approximation ratios for these three methods. We observed that the combined SQC approach performed better on average than the individual workflow. Furthermore, the spread of the data was smaller. This indicates that there are a significant number of cases where SQC offers advantages. ![SQC Statistics](/blog/sqc/sqc_stats.jpg) **Figure 3.** Approximation ratio distribution over the studied instances for the three methods: BF-DCQO on digital IBM, QA on analog D-Wave, and the combination of both as a SQC approach. #### Why SQC matters SQC represents a powerful and versatile approach to addressing computational challenges that the currently evolving quantum hardware struggles with. The ability of the SQC paradigm to integrate different quantum platforms promises significant advancements in performance and efficiency. SQC is not limited to optimization problems. In fact, it has a broader applicability. Future efforts will focus on expanding SQC to domains such as quantum simulation of materials, quantum chemistry, and quantum machine learning, paving the way for more groundbreaking discoveries. Sequential quantum computing is more than just a technological innovation: it is a leap forward in quantum science and commercial quantum computing under realistic conditions. By combining the strengths of various quantum processors, SQC opens up new possibilities for solving complex problems efficiently while pushing the boundaries of what current quantum hardware can achieve separately. Whether it is quantum chemistry, materials science, quantum artificial intelligence, or large-scale optimization challenges, SQC is poised to reshape the landscape of computational research. #### References 1. Romero SV, Cadavid AG, Solano E, Hegade NN. Sequential Quantum Computing. arXiv preprint [arXiv:2506.20655 (2025)](https://arxiv.org/abs/2506.20655). 2. Katzgraber HG, Hamze F, Zhu Z, Ochoa AJ, Munoz-Bauza H. Seeking Quantum Speedup Through Spin Glasses: The Good, the Bad, and the Ugly. [Phys. Rev. X. 5:031026](https://journals.aps.org/prx/abstract/10.1103/PhysRevX.5.031026). 2015 Sep 1. 3. Cadavid AG, Dalal A, Simen A, Solano E, Hegade NN. Bias-field Digitized Counterdiabatic Quantum Optimization. [Phys. Rev. Research 7:L022010](https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.L022010). 2025 Apr 9. 4. Romero SV, Visuri AM, Cadavid AG, Solano E, Hegade NN. Bias-Field Digitized Counterdiabatic Quantum Algorithm for Higher-Order Binary Optimization. arXiv preprint [arXiv:2409.04477](https://arxiv.org/abs/2409.04477). 2024 Sep 5. 5. Simen A, Romero SV, Cadavid AG, Solano E, Hegade NN. Branch-and-bound Digitized Counterdiabatic Quantum Optimization. arXiv preprint [arXiv:2504.15367](https://arxiv.org/abs/2504.15367). 2025 Apr 21. 6. Chandarana P, Cadavid AG, Romero SV, Simen A, Solano E, Hegade NN. Runtime Quantum Advantage with Digital Quantum Optimization. arXiv preprint [arXiv:2505.08663](https://arxiv.org/abs/2505.08663). 2025 May 13. ### Written by ![Alejandro Gómez Cadavid](/_next/static/media/image-4.4deb7e83.png) Alejandro Gómez Cadavid Quantum Optimization Lead ![Pranav Chandarana](/_next/static/media/PranavChandarana.5348aefc.jpg) Pranav Chandarana Quantum Optimization Engineer ![Dr. Narendra Hegade](/_next/static/media/NarendraHegade.0cf8d9ee.jpg) Dr. Narendra Hegade Fellow [Back to Blog Overview](/blog) --- # The Timeless Thread of Information URL: https://kipu-quantum.com/blog/the-timeless-thread-of-information [Back to Blog](/blog) # The Timeless Thread of Information From Ancient Knots to Cosmic Networks By •10.02.2025 ![Quipu display at Computer History Museum](/blog/the-timeless-thread-of-information/1739207733163-2.jpg) Picture made at the [Computer History Museum](https://www.computerhistory.org) In a cosmic twist that even the most imaginative storytellers couldn't create, astronomers have recently unveiled the universe's largest known structure, a colossal formation stretching 1.3 billion light-years and boasting a mass of approximately 200 quadrillion suns! They have rightly named this Quipu, drawing inspiration from the ancient Incan system of knotted cords used for record-keeping and computing. Our company's name, KIPU QUANTUM, is derived from the same Incan quipu - a sophisticated method of encoding information through intricate knots. These early "data storage" systems were not just a way to record numbers: they were a fundamental tool for organizing society, tracking knowledge, and passing information across generations. Interestingly, Quipu is the Spanish word (also used in English) for this system, corresponding to Khipu in Quechua, the language of the Incas. Khipu means "knot," and these knots, arranged along colored strings, carried complex encoded information. In some Quechua variants, the word Kipu is also used interchangeably with Khipu, giving us a trilogy of names: Quipu, Khipu, and Kipu. The quipu's structure - a main cord with various subsidiary cords, each with knots positioned to convey meaning, reflects the complexity we explore in quantum computing today. It's fascinating how this ancient system resonates with modern technological concepts, revealing that the way we structure, and process information has always been a defining part of human advancement. So, the next time someone inquiries about our name, it carries an even deeper significance, a connection between history, technology, and the cosmos itself. From the Incas' knotted networks to the vast interwoven galaxies of Quipu, from early symbolic dataencoding to the future of quantumcomputing ### Written by [Back to Blog Overview](/blog) --- # Unlocking the Power of Quantum Computing URL: https://kipu-quantum.com/blog/iskay-quantum-optimizer-by-kipu-quantum [Back to Blog](/blog) # Unlocking the Power of Quantum Computing With the Iskay Quantum Optimizer by Kipu Quantum By •2024 The Iskay Quantum Optimizer is an innovative tool that allows the user to solve complex optimization problems using IBM® quantum computers. Although the basis is a complex disruptive technology, the Iskay Quantum Optimizer is easy to use. Here is packed one of the most-efficient quantum algorithms operating in a simple user interface design that can replace a classical optimization solver in the workflow of those who need it. The Iskay Quantum Optimizer combines Kipu's best technology: BF-DCQO ([1](https://doi.org/10.48550/arXiv.2409.04477), [2](https://doi.org/10.48550/arXiv.2405.13898)) running highly-compressed quantum circuits with efficient pre- and post-processing performed all automatically under the quantum hood. As it is compatible with all IBM quantum processors, its performance will follow the always-accelerating development of superconducting quantum computers. #### Powerful solver: To solve an optimization problem, the Iskay Optimizer only requires the objective function of the problem. It can handle optimization tasks involving up to 156 qubits, utilizing the full capacity of IBM's quantum devices. With a 1-to-1 mapping between classical variables and qubits, you can tackle optimization problems with up to 156 binary variables (size of the largest IBM chip at the time of the writing). The Iskay Quantum Optimizer is designed to solve unconstrained binary optimization problems, supporting both the widely used QUBO (Quadratic Unconstrained Binary Optimization) formulation and HUBO (Higher-order Unconstrained Binary Optimization) problems. Utilizing a non-variational quantum algorithm, the majority of the computational hardware power comes from quantum operating at the quantum advantage level. The iterative protocol of our algorithm offers a massive reduction in cost of use and time to solution by greatly reducing the number of shot-sampling from the quantum hardware. Look up the benchmarking table on IBM Qiskit Function page and feel free to compare with other available quantum solutions, we are that confident in our Iskay! Have a look: [Iskay quantum optimizer documentation](https://docs.quantum.ibm.com/guides/kipu-optimization) #### Versatile tool: Now for more concrete use of the Iskay Quantum Optimizer: its versatility allows to tackle a variety of complex optimization problems. Here are some examples of key use cases you can solve with Iskay: - **Max-k-SAT:** The Max-k-SAT problem involves finding the maximum number of satisfiable clauses in a Boolean formula. This is a crucial problem in fields such as artificial intelligence and computational theory, where efficient solutions can significantly enhance performance. It is a famous example of an NP-hard optimization problem. - **Portfolio Optimization:** In the financial sector, portfolio optimization is essential for maximizing returns while minimizing risk. The Iskay Quantum Optimizer can efficiently handle the complex calculations required to balance portfolios, adapting to market changes. - **Protein Folding:** Understanding how proteins fold is critical in biology and medicine, as it impacts drug design and disease treatment. The Iskay Quantum Optimizer can simulate protein folding processes, providing insights that are difficult to achieve with classical methods. As a matter of fact, Kipu Quantum holds the world-record of largest protein folded on an IBM quantum computer ([read here](https://arxiv.org/abs/2212.13511)). - **Vehicle Routing Problem:** The vehicle routing problem involves determining the most efficient routes for a fleet of vehicles to deliver goods or services. This is a common challenge in logistics and transportation. The Iskay Quantum Optimizer can find optimal solutions that reduce costs and improve efficiency. By leveraging the power of quantum computing at the quantum advantage level, the Iskay Quantum Optimizer offers innovative solutions to these and other complex problems, driving advancements across various industries. #### Learn more about the Iskay Quantum Optimizer Join us live to see Iskay in action and learn how to integrate it into your workflow: [Register for our upcoming webinar](/webinars) You can also access the full documentation of our Iskay quantum optimizer at: [Iskay quantum optimizer documentation](https://docs.quantum.ibm.com/guides/kipu-optimization) #### Other quantum computing solvers from Kipu? We consider the Iskay Quantum Optimizer as a milestone, but the height of the quantum technology tower of Kipu has been consistently growing and will continue to grow. Did you have a look at our [PLANQK platform](https://platform.planqk.de/home)? It allows you to access various quantum hardware and Kipu's quantum algorithm. In addition, you can speed up your development of your own quantum applications leveraging our cloud technology. Create an [account](https://platform.planqk.de/home) on PLANQK today and stay up-to-date with our latest quantum computing achievements packaged in industry-ready convenient solutions. Quantum destiny is all! ### Written by [Back to Blog Overview](/blog) --- # EETimes: BASF and Kipu on Quantum Computing Mastery URL: https://kipu-quantum.com/news/basf-partnership [Back to News](/news) 05.12.2024 # EETimes: BASF and Kipu Focus on End-User Mastery of Quantum Computing ![Chemical Industry](/_next/static/media/photo-1532634922-8fe0b757fb13.c3d1f1a4.jpg) At Kipu Quantum, we provide our partners with the most advanced hardware- and application-specific quantum algorithms for a variety of industrial-level use cases, running on commercially accessible hardware. Partnering with industry leaders like BASF motivates us to bring quantum advantage-level products to market as soon as possible. ### Reshaping the Chemical Industry In a recent EETimes article, Horst Weiss and Michael Kühn from BASF, along with our CEO, Daniel Volz, shared insights into how quantum computing can reshape the chemical industry. We're proud to be part of this BASF journey. ### Quantum Algorithms in Action In our recent collaboration, we successfully developed tailored quantum algorithms that optimize complex logistics processes in BASF's chemical operations. This achievement underscores the power of hardware- and application-specific quantum solutions to solve industry-relevant challenges. ### Looking Ahead > "There has already been enough hardware progress. Now, it's about bringing the hardware and algorithms together to make it over the tipping point." > > Daniel Volz, CEO of Kipu Quantum We believe that the power of quantum computing lies in the synergy of customized algorithms and advanced quantum hardware. **Read more:** - [EE Times article: BASF and Kipu Focus on End-User Mastery of Quantum Computing](https://www.eetimes.eu/basf-and-kipu-focus-on-end-user-mastery-of-quantum-computing/) - [Read the press release](https://lnkd.in/db-CWkf2) [Back to News](/news) --- # Kipu and NVIDIA Advance Hybrid Quantum Optimization URL: https://kipu-quantum.com/news/nvidia-cineca-partnership [Back to News](/news) 23.04.2025 # Kipu Quantum Teams With NVIDIA to Advance Hybrid Quantum Optimization Using CINECA's Leonardo Supercomputer ![Supercomputer](/_next/static/media/photo-1558494949-ef010cbdcc31.8295e319.jpg) Building on our recent work on [quantum-enhanced memetic tabu search](https://arxiv.org/abs/2511.04553), we have extended our numerical experiments to 43 qubits, continuing the scaling trajectory from 27 to 37 and now 43 qubits. These new results were enabled by large-scale simulations performed on the CINECA supercomputing infrastructure and developed using the [NVIDIA CUDA-Q platform](https://developer.nvidia.com/cuda-q), allowing us to explore the behavior of our approach on larger structured optimization instances. ### The LABS Challenge This work focuses on the Low Autocorrelation Binary Sequence (LABS) problem, a challenging combinatorial optimization task with a rugged energy landscape that makes it a demanding benchmark for both classical and quantum methods. Our hybrid framework combines quantum sampling with classical memetic tabu search, using quantum-generated states to guide the classical solver toward promising regions of the solution space. ### Scaling to 43 Qubits The new simulations extend the system sizes considered in our earlier work and contribute additional data points for studying the scaling behavior of the hybrid approach. By reaching 43 qubits, we continue to examine how hybrid quantum-classical strategies behave as problem sizes increase and structured optimization instances become more demanding. The work was enabled by simulations on the Leonardo supercomputer at CINECA. Prof. Francesco Ubertini, President of CINECA highlighted the importance of HPC infrastructures in advancing the integration of accelerated classical computing and quantum technologies: > "The collaboration between CINECA, Kipu Quantum, and NVIDIA highlights the strategic role of HPC infrastructures in advancing the integration of classical accelerated computing and quantum technologies. Supporting this large-scale simulation on the Leonardo cluster (a system funded by EuroHPC and the Italian Ministry of University and Research (MUR)) demonstrates how European and national investments in world-class supercomputing infrastructures enable the development and validation of hybrid quantum-classical algorithms, contributing in a concrete way to the architectural foundations of next-generation supercomputing. CINECA will continue to invest in this direction, fostering high-value international collaborations at the intersection of science and advanced computing." We thank NVIDIA for the collaboration and CINECA for providing the supercomputing resources that made these experiments possible. More details will be shared soon. [Back to News](/news) --- # Kipu Expands Team with World-Renowned Scientists URL: https://kipu-quantum.com/news/team-expansion [Back to News](/news) 2024 # Kipu Quantum Expands Team with World-Renowned Quantum Scientists ![Team Expansion](/_next/static/media/photo-1522071820081-009f0129c71c.083b1c33.jpg) Kipu Quantum announces strategic hires that strengthen research capabilities across quantum algorithms, hardware optimization, and industrial applications, positioning the company for accelerated innovation and market expansion. ### World-Class Expertise The new team members bring extensive experience from leading research institutions and quantum computing companies, with proven track records in developing cutting-edge quantum algorithms and demonstrating quantum advantage in real-world applications. ### Strategic Focus Areas These strategic additions strengthen Kipu Quantum's capabilities in key areas including quantum error mitigation, hardware-aware algorithm design, and industry-specific quantum applications for pharmaceuticals, materials science, and optimization challenges. The expanded team will accelerate development of Kipu Quantum's quantum-centric intelligence platform and enable deeper collaboration with enterprise customers across multiple industries. [Back to News](/news) --- # Kipu Quantum Named a Quantum Computing Leader URL: https://kipu-quantum.com/news/industry-recognition [Back to News](/news) 2024 # Industry Recognition: Kipu Quantum Named Quantum Computing Leader ![Industry Recognition](/_next/static/media/photo-1552664730-d307ca884978.47d85c1e.jpg) Independent analyst report recognizes Kipu Quantum's innovative approach to industrial quantum applications and quantum advantage demonstrations, positioning the company as a leader in the quantum computing industry. ### Industry Leadership Validated A comprehensive industry analysis by leading technology research firm highlights Kipu Quantum's unique position in delivering practical quantum advantage across multiple industrial applications. The report emphasizes the company's hardware-aware algorithmic approach and demonstrated performance improvements over classical methods. ### Key Differentiators The analysis identifies several key factors driving Kipu Quantum's leadership position, including deep expertise in quantum algorithm development, strong partnerships with quantum hardware providers, and a proven track record of demonstrating quantum advantage in real-world applications across pharmaceuticals, materials science, and optimization domains. ### Market Impact This recognition validates Kipu Quantum's strategy of focusing on near-term quantum advantage applications and building practical solutions that deliver measurable value to enterprise customers. The company's approach of co-designing quantum algorithms with specific hardware platforms has proven particularly effective in achieving superior performance. As quantum computing transitions from research to commercial deployment, industry recognition reinforces Kipu Quantum's position as a trusted partner for organizations seeking to harness quantum computing's transformative potential. [Back to News](/news) --- # Kipu Starts Commercial Quantum Advantage Era URL: https://kipu-quantum.com/news/commercial-quantum-advantage-era [Back to News](/news) 08.09.2024 # Kipu Starts Commercial Quantum Advantage Era ## Solving optimization problems with industry relevance on IBM 156-Qubit quantum processors ![Quantum Computing](/_next/static/media/photo-1635070041078-e363dbe005cb.c06dc1c4.jpg) Developing quantum algorithms to tackle complex large-scale combinatorial optimization problems is one of the holy grails of quantum computing, especially when they can efficiently run on accessible cloud-based commercial quantum computers. The most sophisticated optimization problems have a massive impact on industries like logistics, finance, telecommunication, energy, chemistry, artificial intelligence, materials, and manufacturing. Classical computing just cannot keep up with the complexity of these challenges. ### No Need to Wait for the Far Future Kipu Quantum's innovative quantum algorithms catalyze the involved quantum dynamics and drastically reduce the requirements for solving complex problems running on today's quantum hardware. No need to keep waiting for the far future. We are starting the commercial era of quantum computing: the period in which customers can reliably decide to request and invest in quantum computing services that will bring immediate or imminent added value to their products and business. ### 156 Qubits on IBM Quantum Processors Three months ago, we introduced our game-changing innovation from the realm of digital catalysis and accelerated compression: Bias-Field Digitized Counterdiabatic Quantum Optimization (BF-DCQO), stemming from a new generation of Kipu's technologies using counterdiabatic protocols. Today, we are proud to present the largest optimization quantum algorithm via an experiment running on an IBM quantum processor using all 156 qubits by applying Kipu's powerful algorithms. This is just the beginning, as our methods can be directly applied on larger processors, including the one with 433 qubits and beyond, which brings about a fundamental change in the perspective of current quantum computing possibilities. ### Key Benefits of BF-DCQO By utilizing a fully quantum, non-variational approach, we successfully solved highly complex and hard-to-tackle higher-order unconstrained binary optimization (HUBO) problem without mapping it to lower-order quadratic (QUBO) formulations, which benefits in: - Enhanced solution quality - Lower resource consumption - Reduced circuit depths - Execution on today's quantum processors - Commercial quantum advantage level These benefits show that Kipu's tech makes the most of current quantum hardware, even with its natural limitations. This means businesses in several industry sectors can start seeing the real value of quantum computing now, without waiting for the far future. ### The Start of a New Era We consider these results of our case studies as the start of the Commercial Quantum Advantage era, Kipu dixit, and soon more and better when our technologies are extended to denser and more complex industry-level problems. These results disclosed today are just the appetizer of what Kipu is currently working on, always two steps ahead of our time and what is openly shared. To all quantum computing stakeholders, including investors, governments, customers, technologists, artists, and providers: Are you ready for Kipu Quantum's Commercial Quantum Advantage era? **Read the latest results:** Bias-Field Digitized Counterdiabatic Quantum Algorithm for Higher-Order Binary Optimization Quantum destiny is all. [Back to News](/news) --- # Kipu: Quantum-centric Intelligence URL: https://kipu-quantum.com/news/quantum-centric-intelligence [Back to News](/news) 23.04.2026 # Kipu: Quantum-centric Intelligence ## From intent to quantum solution in minutes Quantum computing today demands weeks of specialist work to get a result. Kipu changes that by providing the quantum-centric intelligence platform. Our platform lets teams describe what they want to solve - and get to a working quantum solution in minutes. ![From intent to quantum solution in minutes](/_next/static/media/image-11.ce858265.png) ### Three Things Make This Possible #### 1) The Kipu Quantum Hub A unified platform with access to all major quantum backends, classical CPU and GPU resources, and a built-in marketplace of quantum services. #### 2) Quantum Solvers Quantum solvers in optimization and machine learning with demonstrated applications on real industry problems from logistics optimization to protein folding to predictive maintenance. #### 3) An AI Agent An AI agent that ties it all together: it translates user intent into quantum workflows, selects the right solver and backend, configures the execution, and interprets the results, so the user doesn't need quantum expertise themselves. This is quantum computing for people who need answers, not a PhD. ### Available Today and Beyond We are releasing the products and tools that bring this vision to life step by step. Some capabilities described above are available today through the Kipu Quantum Hub; others are on our near-term roadmap. **Explore what is already possible today:** [Register for our upcoming webinar](/webinars) Stay tuned for more. [Back to News](/news) --- # Major Breakthrough in Quantum Error Correction URL: https://kipu-quantum.com/news/quantum-error-correction-breakthrough [Back to News](/news) 2025 # Kipu Quantum Announces Major Breakthrough in Quantum Error Correction ![Quantum Error Correction](/_next/static/media/photo-1635070041078-e363dbe005cb.c06dc1c4.jpg) Revolutionary approach to digital-analog quantum error correction demonstrates unprecedented accuracy rates on commercial quantum hardware, paving the way for large-scale quantum applications. ### Groundbreaking Achievement Kipu Quantum has achieved a significant milestone in quantum error correction, demonstrating unprecedented accuracy rates using a novel digital-analog approach on commercial quantum hardware platforms. This breakthrough represents a crucial step toward enabling large-scale quantum applications across industries. ### Technical Innovation The new error correction method combines the precision of digital quantum gates with the power of analog quantum dynamics, creating a hybrid approach that significantly outperforms traditional quantum error correction techniques. This innovation allows for more robust quantum computations on current noisy intermediate-scale quantum (NISQ) devices. ### Industry Impact This breakthrough has immediate implications for pharmaceutical companies, materials science researchers, and financial institutions seeking to leverage quantum computing for complex optimization and simulation tasks. The improved error rates enable longer quantum circuits and more sophisticated algorithms to run reliably on today's quantum processors. Kipu Quantum continues to push the boundaries of what's possible with current quantum hardware, demonstrating that quantum advantage is achievable today with the right algorithmic approaches and hardware-aware optimization techniques. [Back to News](/news) --- # New Collaboration with Lufthansa Industry Solutions URL: https://kipu-quantum.com/news/lufthansa-collaboration [Back to News](/news) 21.01.2025 # New Collaboration with Lufthansa Industry Solutions ![Aviation Operations](/_next/static/media/photo-1436491865332-7a61a109cc05.3e1d4ee0.jpg) Flight operations must continuously adapt to meet rising demands for efficiency and sustainability. For airlines, operational profitability is no longer just about expanding routes or increasing fleet size; it hinges on maximizing resource utilization through strategic and tactic planning processes. These tasks range from long-term strategies, such as designing optimal annual flight schedules, to highly dynamic short-term adjustments, including real-time route optimization and day-to-day crew management. The intricacy of these challenges, driven by countless variables and constraints, often pushes traditional methods to their limits, making it clear that innovative solutions are needed to stay competitive in an evolving industry. Quantum computing can tackle such complexity. ### QCI QCMobility Project As part of the "QCI QCMobility" project, Lufthansa Industry Solutions has been awarded the contracts for the two sub-projects "Strategic Planning Processes" and "Tactical Planning Processes." We are proud to announce that Lufthansa Industry Solutions is supported in this project by Kipu Quantum as a subcontractor. ### Three Optimization Challenges In the project, our team aims to address three interconnected optimization problems fundamental to strategic flight operations planning: - **Aircraft Rotation Optimizer** - **Tail Assignment** - **Short Term Planning** Together with LHIND, we will model these challenges using QUBO (Quadratic Unconstrained Binary Optimization) and HUBO (Higher-Order Unconstrained Binary Optimization) formulations to implement solutions on quantum computers. These problems will be solved using highly efficient quantum algorithms and evaluated on both classical and quantum hardware. The evaluation will include benchmarking for scalability and applicability to real-world flight operations. ### Real-World Scale and Complexity The data for this project will come directly from Eurowings' operational planning systems, encompassing over 100 aircraft operating across 13 locations. This adds significant complexity to the optimization tasks and provides a rigorous testing ground for the solutions. Our team at Kipu Quantum is excited to contribute our expertise in application- and hardware-specific quantum solutions. By adapting Kipu's advanced algorithms to the aviation sector, we look forward to supporting the success of this groundbreaking project. **For more information:** - [Read the press release](https://www.presseportal.de/pm/128057/5953646) - [Visit DLR QCI QCMobility website](https://qci.dlr.de/en/lufthansa-industry-solutions-supports-qcmobility/) [Back to News](/news) --- # QInnovision Consortium Welcomes Kipu Quantum URL: https://kipu-quantum.com/news/qinnovision-consortium [Back to News](/news) 27.05.2024 # QInnovision Consortium Welcomes Kipu Quantum as First International Startup ![Partnership and Collaboration](/_next/static/media/photo-1552664730-d307ca884978.47d85c1e.jpg) We are thrilled to announce that Kipu Quantum, a world-leading player in algorithms for quantum computers, has joined the QInnovision Consortium as our first international startup member. ### Unparalleled Quantum Solutions Kipu Quantum stands out for its unwavering focus on application- and hardware-specific quantum solutions. Its technology, offering unparalleled compression through digital, analog, and digital-analog encoding, empowers customers in the pharmaceutical, chemical, logistics, and financial sectors to execute highly complex processes on current quantum hardware. Kipu's technology significantly accelerates the time to market for quantum computing applications. ### Prof. Enrique Solano Joins as International Advisor We are also delighted to share that Prof. Enrique Solano has recently joined QInnovision Consortium as an International Advisor to the steering committee. > "I am honored by the decision of Vernewell Group Executives to appoint me to the Steering Committee. I am confident that the consortium is committed to bringing the benefits of quantum computing to industry, and I am excited about the opportunities ahead." > > Prof. Enrique Solano ### Building a Quantum Ecosystem We are also proud to share the success of the recent Pasqal Perspectives on Quantum event, held at Sorbonne University Abu Dhabi. This event served as a platform for fostering our shared vision of building a thriving quantum computing ecosystem. Pasqal, a strategic partner of Kipu Quantum, played a pivotal role in advancing all parties' shared goals and initiatives, further solidifying our commitment to collaboration and ecosystem development. With Kipu Quantum joining our consortium, we are poised to drive significant advancements in quantum computing applications across various industries. We look forward to the innovative contributions they will bring to our community. Stay tuned for further announcements during Make it in the Emirates, where Kipu Quantum and Vernewell Group will be present. ### About QInnovision Consortium QInnovision Consortium is dedicated to accelerating the adoption and advancement of quantum computing technologies across industries. By bringing together leading organizations and innovators, we aim to foster collaboration, share knowledge, and drive the practical application of quantum computing. ### About Kipu Quantum GmbH Kipu Quantum is a German company based in Karlsruhe and Berlin that operates at the intersection of quantum computer hardware and application software layers, developing disruptive application- and hardware-specific quantum algorithms for a wide range of industries. These algorithms are based on a one-of-a-kind compression technology that requires orders of magnitude less quantum processor resources to solve a given problem than comparable approaches. Kipu Quantum's technology has the potential to solve industry-relevant problems in the order of 1,000 physical qubits and is compatible with any leading quantum hardware. The company is currently testing its technology with customers in the pharmaceutical, chemical, logistics and financial industries. **For more information:** - [Visit QInnovision Consortium](https://www.qinnovision.com) - [Learn more about Kipu Quantum](https://www.kipu-quantum.com) [Back to News](/news) --- # Quantum Advantage Demonstrated in Material Design URL: https://kipu-quantum.com/news/quantum-advantage-material-design [Back to News](/news) 2024 # Quantum Advantage Demonstrated in Material Design Applications ![Material Design](/_next/static/media/photo-1451187580459-43490279c0fa.fd364230.jpg) Kipu Quantum has demonstrated significant runtime improvements over classical methods in simulating complex material properties at the quantum-advantage level, marking a major milestone in the practical application of quantum computing to materials science. ### Breaking Classical Barriers Our research shows that quantum computing can now outperform traditional computational methods in simulating the quantum behavior of materials, opening new possibilities for discovering novel materials with specific properties for applications ranging from superconductors to advanced batteries. ### Real-World Impact This breakthrough enables materials scientists and engineers to explore a much larger space of potential materials more efficiently, accelerating the development of next-generation technologies including improved solar cells, more efficient catalysts, and stronger, lighter structural materials. The quantum-advantage-level performance demonstrated in these applications represents a crucial validation of quantum computing's practical value for industrial research and development. [Back to News](/news) --- # Quantum Hub Platform Launch: Enhanced Features URL: https://kipu-quantum.com/news/quantum-hub-platform-launch [Back to News](/news) 2024 # New Quantum Hub Platform Launches with Enhanced Features ![Quantum Hub Platform](/_next/static/media/photo-1639322537228-f710d846310a.ae0231e8.jpg) Kipu Quantum unveils major platform update offering improved user experience, expanded documentation, and seamless integration with leading quantum hardware providers. ### Enhanced User Experience The updated Quantum Hub platform features a redesigned interface that simplifies the process of developing, testing, and deploying quantum applications. New workflow tools enable faster iteration and more efficient collaboration between quantum and classical computing resources. ### Expanded Capabilities The platform now includes comprehensive documentation, interactive tutorials, and example applications across multiple industry verticals. Enhanced integration with quantum hardware providers gives users access to a wider range of quantum processors and simulation capabilities. ### Enterprise-Ready Features New enterprise features include advanced security controls, team collaboration tools, resource management capabilities, and detailed usage analytics to help organizations maximize the value of their quantum computing investments. [Back to News](/news) --- # Quantum-Enhanced AI, Deployable in Production URL: https://kipu-quantum.com/news/quantum-enhanced-ai-production [Back to News](/news) 20.05.2026 # Kipu Quantum Makes Quantum-Enhanced AI Deployable in Production ## Train on a quantum processor, deploy entirely on classical hardware ![Quantum-enhanced predictions with classical speed: the Off-line DQFE pipeline trains a surrogate on quantum-extracted features, then runs inference entirely on classical hardware across satellite imagery, drone monitoring, customer churn, medical imaging and molecular toxicity use cases.](/_next/static/media/offlineDQFE.68eb3fb8.png) The Off-line DQFE pipeline: quantum features extracted once, surrogate trained, inference at classical speed across high-value industrial use cases. New hybrid framework removes the single biggest barrier to enterprise adoption of quantum machine learning: the requirement to run a quantum processor for every prediction. **Berlin, Germany — 20 May 2026 —** Kipu Quantum today released a new hybrid quantum-classical framework that allows quantum-enhanced machine learning models to be trained on a quantum processor and deployed entirely on classical hardware — at the speed, cost and operational profile that enterprise production pipelines require. Quantum feature extraction has been delivering measurably richer data representations than classical feature engineering across multiple peer-reviewed studies, validated by Kipu Quantum and others on IBM quantum processors, including a 156-qubit IBM Quantum Heron r2 processor. ### How the framework works Current workflows can be slowed down by queue times. The new framework developed by Kipu Quantum changes the ability to extract useful features. The quantum processor is used only during a targeted training stage, where it learns the correlations that quantum feature extraction is uniquely good at producing. Those quantum-derived representations are then transferred into a lightweight classical surrogate model. From that point on, deployment is fully classical: microsecond inference latency, retrainable on a normal MLOps cadence, and managed on the same procurement terms as any classical model. In practice, the quantum processor is run on as little as 20% of the classical training data — a representative subsample — delivering the same accuracy at one fifth of the quantum hardware cost, a ratio that improves further as data volumes grow. This is possible because quantum feature mappings are stable and reproducible across hardware backends — consistent enough for a classical model to learn the mapping from a manageable set of training examples and generalize reliably at scale. The role of the quantum computer changes in the process. It stops being an expensive real-time inference engine and is used once, where it adds unique value, then absent from the production system. The predictive lift that quantum feature extraction delivers is preserved. The cost, latency and operational profile of the deployed model collapse to classical. ### Demonstrated across commercially significant workloads The framework has been demonstrated across commercially significant workloads — delivering approximately 10% accuracy improvement on molecular toxicity classification, a 0.932 AUC on medical image diagnostics against a 0.866 ResNet-50 baseline, and 3% on satellite imagery, all over strong classical baselines, with further validation across industrial monitoring, predictive analytics, and customer churn reduction. On a satellite benchmark, the surrogate model matched the full quantum result exactly, achieving 87% accuracy against an 84% classical baseline. The work is part of Kipu Quantum’s Rimay product suite, within the company’s quantum machine learning platform. ### Industry response IBM > “The quantum feature extraction technique that Kipu Quantum has developed for how quantum and classical compute can work together is yet another great example of finding a cost-effective way to run hybrid, QML workflows. And we at IBM are excited about the Kipu team’s work to show how our quantum hardware efficiently delivers accurate results across a wide range of applications—which we hope will in turn generate more interest from industry in the kinds of problems quantum computing can help solve.” — Scott Crowder, Vice President, IBM Quantum Adoption Global Quantum Intelligence (GQI) > “Kipu’s off-line surrogate framework achieves economic quantum advantage by capturing the 2–3% absolute accuracy gains of a quantum processor while running inference entirely on classical hardware. By processing only a small representative subsample (e.g., 20%) on actual quantum hardware, the framework reduces expensive quantum executions by a factor of 5 or more. The methodology is actively applied to high-volume enterprise problems, such as satellite drone imagery (TreeSatAI benchmark), medical diagnostics (Breast MedMNIST), and customer intent routing.” — André König, CEO at Global Quantum Intelligence NTT DATA > “There is a compelling shift happening in how quantum computing will create value, i.e. not by replacing classical systems, but by teaching them something they could not learn alone. Kipu Quantum’s quantum feature surrogate framework is a masterclass in exactly that — marrying quantum-derived representations with the classical infrastructure enterprises already own and trust. For organizations like NTT DATA, serving critical sectors at global scale, this is the inflection point we’ve been preparing for: measurable accuracy gains, zero quantum dependency at inference, and seamless integration into existing production pipelines. We are ready.” — Rika Nakazawa, Chief Commercial Innovation at NTT DATA MOEVE > “Through the Kipu Quantum Hub platform, we are achieving promising milestones that can optimize classical models in image classification for predictive maintenance. The Proof of Concept we implemented delivered positive results by using thermographic drone imagery and adopting hybrid classical-quantum technology for the early detection of issues in our energy parks. Additionally, we have partnered with Kipu Quantum through our Quantum Center of Excellence to analyze mechanical components.” — Estela Vilches, Head of Digital Innovation at MOEVE KPMG > “The scope of this technology is intentionally broad and industry-agnostic, providing a scalable solution for a wide range of immediately viable use cases. From satellite image classification and advanced customer analytics to the rapid screening of pharmaceutical candidates, Kipu’s approach allows enterprises to leverage the specific computational advantages of quantum systems across their entire portfolio of data-intensive challenges today.” — Aaron Kemp, Senior Director Quantum Research & Enterprise Innovation at KPMG US **Read the work:** - [Engineering blog: Classical Surrogates for Quantum Feature Extraction](/blog/classical-surrogates-for-quantum-feature-extraction) - [Arxiv Paper: Off-line quantum-advantage feature extraction for industrial production](https://arxiv.org/abs/2605.19801) [Back to News](/news) --- # R, Cinfo and Kipu Optimize Telecommunication Networks URL: https://kipu-quantum.com/news/r-cinfo-telecom-optimization [Back to News](/news) 23.01.2024 # R, Cinfo, and Kipu Quantum Design Algorithm for Optimizing Telecommunication Networks ## Pioneering quantum solution for network resilience using D-Wave and QuEra quantum processors ![Telecommunication Network Infrastructure](/_next/static/media/photo-1544197150-b99a580bb7a8.faa223bc.jpg) Galician telecommunication network operator R has developed a pilot to analyze its optical fiber communication network, to improve its resiliency. The project was done with Cinfo and their technology partner Kipu Quantum. Ultimately, the work may enable the evaluation of thousands of nodes in shorter time scales. It has been used to calibrate R's core network, aiming to increase its resilience and significantly improve its quality of service. ### Quantum Hardware: D-Wave and QuEra The designed algorithm was executed on two different types of quantum hardware, on quantum annealers from D-Wave and on neutral-atom quantum processors from QuEra, using up to 180 and 46 qubits on each of them, respectively. Based on recent roadmaps for quantum hardware, the piloted algorithm may cross the threshold for usefulness as early as 2025, which would enable the MASMOVIL Group to expand this initial work on a specific core network of R cable to larger networks prone to more errors. ### Identifying Critical Network Nodes The project, promoted by Cinfo and Kipu Quantum on the R infrastructure, applies the computing capacity offered today by quantum computing to the Galician operator's optical fiber backbone network, examining its robustness and resilience to potential outages and/or critical situations. The newly designed quantum algorithm identifies the most sensitive nodes, the ones that could have the greatest impact on the service in the event of a disconnection or breakdown. This relevant information makes it possible to focus on those points detected with current quantum technology and anticipate counteractions, achieving a maximum index of network availability and service excellence. Cinfo, which has prepared the network model adapted to the capabilities of accessible quantum computers, has been supported by Kipu Quantum, which was in charge of preparing the model of the quantum algorithm to analyze the R backbone network. > "The considered use case is a realistic instance that allows a significant improvement in the quality and guarantee of the service that, as a telecommunications operator, we want to offer our customers." > > Norberto Ojinaga, Director of Technology Solutions at R and MASMOVIL Group > "We manifest our strong engagement to provide our customers with a robust and resilient network in case of most adverse circumstances; therefore, we cannot neglect the advances quantum computing offers now to simulate and prepare our environments to be managed with a maximal guarantee." > > Isidro Fernández de la Calle, Director of Business at R and MASMOVIL Group ### Two-Phase Analysis: Quantum Annealers and Neutral Atoms Unlike classical computing, and thanks to the large number of qubits of neutral-atom quantum computers (256 today and about 1,000 expected in about a year), the piloted quantum algorithm consumes the same time regardless of the number of network nodes. In the first phase of the R-Cinfo-Kipu project, an analysis has been carried out for each node with currently available quantum computers. Specifically, an initial classification of the network topology has been performed with a quantum annealer on 180 of the 5,627 qubits available in the quantum computers of the D-Wave company, allowing a sensible network segmentation. In the second phase, the one related to the examination of sublattices, QuEra's quantum computer based on neutral-atom technology was used with 20 qubits for the solution of the main lattice structure and 46 qubits for the combined structure of sublattices. This pioneering hybrid solution architecture employing various quantum computing technologies has been made possible due to the commercial access offered by providers through cloud services. QuEra platform access is enabled by AWS Braket service, while D-Wave provides its own services. Cloud quantum computing capabilities made these combined solutions possible by extracting the best from each of them. ### Industry Perspectives > "At Cinfo, we have accepted the challenge of creating valuable use cases in quantum computing for industry. To this end, we are developing a team of professionals (graduates in Physics from the University of Santiago de Compostela) and selecting technology partners that will introduce us to the design of quantum algorithms and to the understanding of the different capabilities of existing quantum computers, such as Kipu Quantum." > > Antonio Rodríguez del Corral, CEO of Cinfo > "Quantum computers with digital, analog, and digital-analog encoding will move closer to quantum advantage for industrial use cases this year. Projects such as the one developed with R and Cinfo are a step forward towards the practical use of quantum processors with hundreds of qubits. Kipu Quantum is proud to contribute to the leaders and pioneers of the Galician quantum pole in the use of quantum technologies." > > Enrique Solano, Chief Visionary Officer, Kipu Quantum > "This project should lay the foundations for a long and fruitful collaboration with Cinfo, with the Galician industry and business community, as well as with the Spanish technological ecosystem in our joint path towards the usefulness of quantum computers in Europe." > > Daniel Volz, CEO of Kipu Quantum ### Path to Quantum Advantage Both quantum hardware companies and algorithm vendors have embraced the challenge of achieving quantum advantage in the short term, possibly in a couple of years. The startup Kipu Quantum aims to achieve this as soon as possible with its application- and hardware-specific algorithms, which are adapted to existing hardware. In addition, Kipu Quantum has the highest compression (i.e. reduction of algorithms in quantum devices) with digital, analog, and digital-analog encoding in optimization, logistics, finance, and artificial intelligence, as well as in the design of chemical molecules and materials. In this way, the best solutions can be extracted from quantum processors with qubits encoded in trapped ions, neutral atoms, or superconducting circuits. ### Looking Forward to 2025 As quantum computers become more powerful, a larger number of more complex variables can be incorporated into the algorithmic study. In this way, the path established by this Cinfo project, in collaboration with its expert partner Kipu Quantum, will go ahead and exploit the more than predictable quantum hardware enhancements. In fact, it is expected that by 2025 these supercomputers may already be able to process the algorithm for a complex network such as the backbone of R and the entire MASMOVIL Group; basically, as the infrastructure grows, it is optimized and perfected. All this shows that the use of quantum computing for the analytical and complete resolution of common problems in the industry is imminent. This will allow us to discard current approaches based on brute force and experience, which are not always effective in anticipating all scenarios. #### About the Partners **R** is the leading Galician operator of advanced telecommunications services, where it has become the flagship of the MASMOVIL Group since 2021 ([R.gal](https://www.r.gal)). **Cinfo** is a Galician technology company specialized in high-performance systems for telecommunications networks and at the intersection between video and artificial intelligence ([cinfo.es](https://www.cinfo.es)). [Back to News](/news)