How is Kipu


Our unique software-based products allow end users to solve relevant problems much earlier by slashing required physical qubit numbers down by several orders of magnitude.

Already starting from about 1,000 moderately noisy qubits, i.e. already during the current NISQ (Noisy Intermediate-Scale Quantum) era of hardware development, commercial usefulness can be achieved for certain applications.

At the heart of our offerings are novel digital compression and unique hardware-specific digital-analog compression capabilities.
These allow us to make quantum computers useful in the near future, using application- and hardware-specific algorithms.

Implementations of these methods will lead to practical usefulness through application-specific quantum computers, challenging or outperforming classical – i.e. non-quantum – high-performance computer systems at a fraction of the cost.

In contrast, fault-tolerant approaches to quantum computing require huge qubit counts typically numbering in the tens to hundreds of millions, and highly sophisticated qubit error-correction schemes.

Both of these requirements are far beyond the reach of current technological capabilities, i.e. they can at best only manifest themselves many years after application- and hardware-specific algorithms will have been established in the market.


Starting Point
  • Kipu selects a base algorithm
  • Example: Financial portfolio optimization problem with the appropriate number of assets is selected
Digital compression
  • Kipu adds so-called counterdiabatic driving terms to analog version of the algorithm
  • Result – see our paper
Digital-analog compression
  • Kipu tailors the algorithm towards the best suitable hardware system by adding digital-analog elements
  • Example: multi-qubit gates, each n-qubit gate replaces n two-qubit gates – here, ion traps are more suited
  • Result is an even more compact hardware-specific algorithm
Result: Problem solved
  • After applying Kipu’s compression, we create an ultra-compact algorithm that is application- and hardware-specific, requiring quantum processors of much lower complexity
  • Customers utilize the algorithm by licensing our software implementation or accessing it as a service on Kipu’s platform

Counterdiabatic protocols accelerate solution of problems in a variety of domains as they allow us to reliably shorten the time required until completion of the computation. When translated to digital devices, these protocols dramatically compress the algorithms rendering the solutions.

Unpredictable result
Starting point
Non-adiabatic evolution
Accelerated but the result is unpredicted
Slow evolution
Starting point
Adiabatic evolution
Slow solution
Starting point
Counter-diabatic evolution
Getting the solution faster


For a brief introduction into what makes Kipu Quantum special, please refer to our whitepapers:

White paper: Kipu Quantum’s core technology – Our path toward useful quantum computing
White paper: On the industrial usefulness of quantum computing

For deeper insights, we provide a list of Kipu’s most relevant research articles, containing both theory and experimental works in Digitized Counterdiabatic Quantum Computing (DCQC), Digital Analog Quantum Computing (DAQC), Embedding Quantum Simulators (EQS), as well as the first works on Modular Quantum Simulation and Modular Quantum Computing in their evolution along the past decade. It also showcases our strong network of collaborators at several universities and many leading companies.

Efficient DCQO Algorithm within the Impulse Regime for Portfolio Optimization

Alejandro Gomez Cadavid, Iraitz Montalban, Archismita Dalal, Enrique Solano, Narendra N. Hegade

We propose a faster digital quantum algorithm for portfolio optimization using the digitized-counterdiabatic quantum optimization (DCQO) paradigm in the impulse regime, that is, where the counterdiabatic terms are dominant. Our approach notably reduces the circuit depth requirement of the algorithm and enhances the solution accuracy, making it suitable for current quantum processors. We apply this protocol to a real-case scenario of portfolio optimization with 20 assets, using purely quantum and hybrid classical-quantum paradigms. We experimentally demonstrate the advantages of our protocol using up to 20 qubits on an IonQ trapped-ion quantum computer. By benchmarking our method against the standard quantum approximate optimization algorithm and finite-time digitized-adiabatic algorithms, we obtain a significant reduction in the circuit depth by factors of 2.5 to 40, while minimizing the dependence on the classical optimization subroutine. Besides portfolio optimization, the proposed method is applicable to a large class of combinatorial optimization problems.


Digital-analog quantum computing of fermion-boson models in superconducting circuits

Shubham Kumar, Narendra N. Hegade, Enrique Solano, Francisco Albarrán-Arriagada, Gabriel Alvarado Barrios

We proposed the digital-analog encoding for fermion-boson models using superconducting circuits outperforming digital methods in terms of circuit depth which scales quadratically with the smaller dimension of the lattice, (e.g. for a 5X5 or 5X10000 lattice, the scaling remains 25) and, for 1D chains we have a constant depth of 9, paving the way for advancements in material science, energy, and pharmaceuticals.


Digitized-counterdiabatic quantum factorization

Narendra N. Hegade, Enrique Solano.

This work shows how a simple adaptation of the work carried out by by B. Yan et al., arXiv:2212.12372 (2022) can be outperformed with a non-hybrid digitized-counterdiabatic by a factor of 6, factorizing 48-bit integer using trapped-ion hardware.


Digitized-Counterdiabatic Quantum Algorithm for Protein Folding

Pranav Chandarana, Narendra N. Hegade, Iraitz Montalban, Enrique Solano, Xi Chen.

We apply our method of Hybrid Digitized Counterdiabatic Quantum Computing (hybrid DCQC) to proteins with up to 9 amino acids, using up to 17 qubits on quantum hardware. Specifically, we benchmark our quantum algorithm with Quantinuum’s trapped ions, Google’s and IBM’s superconducting circuits, obtaining high success probabilities with low-depth circuits as required in the NISQ era.


Digitized-Counterdiabatic Quantum Optimization

Narendra N. Hegade, Xi Chen, Enrique Solano

Kipu’s battlehorse for combinatorial optimization outperforming state-of-the-art techniques to solve some of the most challenging industry problems.


Digitized-counterdiabatic quantum approximate optimization algorithm

Pranav Chandarana, Narendra N. Hegade, K. Paul, Francisco Albarrán-Arriaga, Enrique Solano, Adolfo del Campo, Xi Chen.

QAOA being one of the most use variational techniques for combinatorial optimization, addition of counterdiabatic protocols shows enhancement from solving combinatorial optimization problems to finding the ground state of many-body quantum systems.


Approximating the quantum aproximate optimization algorithm with digital-analog interactions

David Headley, Thorge Müller, Ana Martin, Enrique Solano, Mikel Sanz, Frank K. Wilhelm.

By embracing the analog capacity for multi-qubit interactions, we exploit the recently proposed digital-analog quantum computation paradigm, in which the versatility of programmable universal quantum computers and the error resilience of quantum simulators are combined to improve platforms for quantum computation, specially suited to the variational quantum approximate optimisation algorithm


Pioneering Quantum Algorithm for solving Black-Scholes Equation

J. Gonzáles-Conde, A. Rodríguez-Rozas, E. Solano, and M. Sanz, “Quantum Algorithm for Pricing Financial Derivatives


General theory of digital-analog quantum computing (DAQC)

Adrian Parra-Rodriguez, Pavel Lougovski, Lucas Lamata, Enrique Solano, and Mikel Sanz, “Digital-Analog Quantum Computation”, Phys. Rev. A 101, 022305 (2020).

This paper is the kick-off of the general theory on Digital-Analog Quantum Computing. Essentially, we proved there that we can be universal with DAQC, although we will use this mostly for bespoke Co-Design Quantum Computers and application to key use cases. I think this paper will be a reference for decades in quantum computing, until error correction may become meaningful, perhaps next century.


Implementing quantum Fourier transform via digital-analog methods (DAQC)

A. Martin, L. Lamata, E. Solano, and M. Sanz, “Digital-analog quantum algorithm for the quantum Fourier transform”, Phys. Rev. Research 2, 013012 (2020).

A key example of the power of DAQC applied to the quantum Fourier transform algorithm, which is the basis of quantum phase estimation article, which is at the basis of Shor algorithm, most quantum chemistry  algorithms, and material design algorithms. A pillar for what comes soon from Co-Design QC as quantum products fo key use cases.


Enhancing connectivity through digital-analog approach (DAQC)

A. Galicia, B. Ramon, E. Solano, and M. Sanz, “Enhanced connectivity of quantum hardware with digital-analog control”,  arXiv:1912.09331, accepted in Phys. Rev. Research (2020).

Another key paper on the unpredictable flexibility and power of DAQC methods.


Digital-analog quantum simulation of quantum approximate optimization algorithm (DAQS)

D. Headley, T. Müller, A. Martin, E. Solano, M. Sanz, and F. K. Wilhelm, “Approximating the Quantum Approximate Optimisation Algorithm”, arXiv:2002.12215 (2020).

A masterpiece of Co-Design Quantum Computers developed with Mercedes Benz researchers, Saarbrücken researchers that coordinate the Quantum Computing European consortium, and our QUTIS Center in Bilbao, Spain, where most of these ideas were developed in last 10 years. We proved that all what other quantum software/hardware companies are proposing for QAOA is misusing the available quantum hardware and quantum software.


Pioneering Connection between Active Learning and Quantum Information

Y.-C. Ding, J.-D. Martín-Guerrero, M. Sanz, R. Magdalena-Benedicto, X. Chen, and E. Solano, “Retrieving Quantum Information with Active Learning”, Phys. Rev. Lett. 124, 140504 (2020).


Pioneering Quantum Computing Realization of Models of Financial Crashes

Y.-C. Ding, L. Lamata, J.-D. Martín-Guerrero, E. Lisazo, S. Mugel, R. Orús, E. Solano, and M. Sanz, “Towards Prediction of Financial Crashes with a D-Wave Quantum Computer”, arXiv:1904.05808 (2020).


Pioneering Quantum Computing Implementation of Pricing Financial Derivatives

A. Martin, B. Candelas, A. Rodríguez-Rozas, J.-D. Martín-Guerrero, X. Chen, L. Lamata, R. Orús, E. Solano, and M. Sanz, “Towards Pricing Financial Derivatives with an IBM Quantum Computer”, arXiv:1904.0583 (2020).


Reaching quantum supremacy via co-design approach (CDQC)

F. Hu, L. Lamata, C. Wang, X. Chen, E. Solano, and M. Sanz, “Quantum Supremacy in Cryptography with a Low-Connectivity Quantum Annealer”, arXiv:1906.08140 (2019).

A prove that we can reach quantum supremacy and quantum advantage with variants, some of them even simpler, of D-Wave architectures. A key result for cryptography.


Digital-analog quantum computation of scattering in quantum electodynamics in trapped ions (CDQS)

X. Zhang, K. Zhang, Y. Shen, J. Zhang, M.-H. Yung, J. Casanova, J. S. Pedernales, L. Lamata, E. Solano, and K. Kim, “Fermion-antifermion scattering via boson exchange in a trapped ion”, Nat. Comm. 9, 195 (2018).

An impressive implementation in the lab of our proposals on CDQS


Review article on digital-analog quantum simulations (DAQS)

Lucas Lamata, Adrián Parra-Rodriguez, Mikel Sanz, and Enrique Solano, “Digital-Analog Quantum Simulations with Superconducting Circuits”, Advances in Physics X: 3, 1457981 (2018).

A review article on what we had achieved up to 2018 on DAQS proposals.


Pioneering proposal for a nonlinear non-Markovian quantum element (DAQS)

P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, “Quantum Memristors”, Sci. Rep. 6, 29507 (2016). 

Here, we invented the Quantum Memristor, as a new fundamental quantum device in superconducting circuits for opening the field of Neuromorphic Quantum Computing.


Digital-analog quantum computing for mapping quantum chemistry and biomolecules on a physical architecture (DAQS)

L. García-Álvarez, U. Las Heras, A. Mezzacapo, M. Sanz, E. Solano, and L. Lamata, “Quantum chemistry and charge transport in biomolecules with superconducting circuits”, Sci. Rep. 6, 27836 (2016).


Digital-analog mapping of spin models on a trapped-ion architecture (DAQS)

I. Arrazola, J. S. Pedernales, L. Lamata, and E. Solano, “Digital-Analog Quantum Simulation of Spin Models in Trapped Ions”, Sci. Rep. 6, 30534 (2016).

These original ideas for trapped ions inspired us to go ahead with further models in superconducting circuits and other quantum platforms.


Digital-analog quantum simulation of interacting fermions via exchange of bosons in quantum field theories (DAQS)

L. García-Álvarez, J. Casanova, A. Mezzacapo, I. L. Egusquiza, L. Lamata, G. Romero, and E. Solano, “Fermion-Fermion Scattering in Quantum Field Theory with superconducting circuits”, Phys. Rev. Lett. 114, 070502 (2015).

In this work, we were able to describe a modular architecture for quantum computation of scattering processes between fermions, like electrons, via exchange of a continuum of bosonic modes, like photons in open air. Our proposal shows that you may reach quantum advantage with rather few quantum elements (qubits, cavities, open transmission lines), while the proposal of John Preskill and others, published in Science 2011 requires millions of qubits.


Mapping unphysical operations on a physical architecture in ion traps (CDQS)

X. Zhang, Y. Shen, J. Zhang, J. Casanova, L. Lamata, E. Solano, M.-H. Yung, J.-N. Zhang, and K. Kim, “Time Reversal and Charge Conjugation in an Embedding Quantum Simulator”, Nat. Commun. 6, 7917 (2015).

Key experiment proving our prediction on how modular co-design concepts work nicely in the lab, in this case trapped ions.


Digital-analog quantum simulator of fluid dynamics (DAQS)

A. Mezzacapo, M. Sanz, L. Lamata, I. L. Egusquiza, S. Succi, and E. Solano, “Quantum Simulator for Transport Phenomena in Fluid Flows”, Sci. Rep. 5, 13153 (2015).

The pioneeing article dealing with the problem on how to approach quantum simulation/computation of fluid dynamics model. The highly nonlinear case may only be develop in Co-Design Quantum Computers.


Digital-analog quantum simulation of quantum chemistry (DAQS)

M.-H. Yung, J. Casanova, A. Mezzacapo, J. McClean, L. Lamata, A. Aspuru-Guzik, and E. Solano, “From transistor to trapped-ion computers for quantum chemistry”, Sci. Rep. 4, 3589 (2014).

This is the pioneering paper where celebrated VQE algorithm was applied to quantum chemistry models in trapped ions. These ideas were taken by top experimental groups in trapped ions (IQOQI, Innsbruck, Austria) and superconducting circuits (Google, Santa Barbara, US), and implemented in the lab.


Transforming an analog block into another one by single-qubit pulses (DAQS)

J. S. Pedernales, R. Di Candia, D. Ballester, E. Solano, “Quantum Simulations of Relativistic Quantum Physics in Circuit QED”, New J. Phys. 15, 055008 (2013).

Here, we applied a known co-design method and found a mysterious coincidence in mathematical structure between light-matter interactions and relativistic Dirac equations, similar to the ones appearing in monolayer and bilayer graphene.


Embedding quantum simulators to measure entanglement (EQS)

R. Di Candia, B. Mejia, H. Castillo, J. S. Pedernales, J. Casanova, and E. Solano, “Embedding Quantum Simulators for Quantum Computation of Entanglement”, Phys. Rev. Lett 111, 240502 (2013).

In this manuscript, we develop the full theory of embedding quantum simulators/computers to reproduce antilinear operations, which are unphysical but present in useful applications. In particular, it is present in the definition of measures of entanglement, so here we manage to prove that measuring entanglement in dynamical systems works better in quantum computers with Co-Design embedding concepts.


Transforming an analog block into another one by single-qubit pulses (DAQS)

D. Ballester, G. Romero, J. J. García-Ripoll, F. Deppe, and E. Solano, “Quantum simulation of the ultrastrong coupling dynamics in circuit QED”, Phys. Rev. X 2, 021007 (2012).

Here, we developed first tools for creating Co-Design counter-rotating terms, associated with a pseudo-violation of energy conservation, onto a conventional light-matter interaction model. In that way we could move towards collective Dicke model and towards superradiance phenomena.


Quantum simulation of materials with interacting fermions and bosons (DAQS)

A. Mezzacapo, J. Casanova, L. Lamata, and E. Solano, “Digital Quantum Simulation of the Holstein Model in Trapped Ions”, Phys. Rev. Lett. 109, 200501 (2012).

In this work, we developed the pioneering Co-Design quantum simulation/computation of materials involving fermions coupled to bosons, where bosons are represented by bosons, as it should be for efficiency reasons. Along these lines, many important models in material design for quantum computers can reach quantum advantage with a few dozens of quantum elements, be qubits, qutrits, cavity modes, or open transmission lines.


Mapping unphysical operations on a physical architecture (EQS)

J. Casanova, C. Sabín, J. León, I. L. Egusquiza, R. Gerritsma, C. Roos, J. J. García-Ripoll, and E. Solano, “Quantum Simulation of the Majorana Equation and Unphysical Operations”, Phys. Rev. X 1, 021018 (2011).

Here, we enhanced the architecture possibilities of quantum simulations/computations involving mathematical models that do not have a direct mapping on a physical system. This is the case, for example, of Black-Scholes equations in financial models. It is this paper the original proposal of what later we named Embedding Quantum Simulators or, equivalently, Embedding Quantum Computers. This requires ancillary qubits with a suitable mapping of model onto architecture that was inexistent previously.


Quantum simulation of quantum field theories for trapped ions (DAQS)

J. Casanova, L. Lamata, I. L. Egusquiza, R. Gerritsma, C. F. Roos, J. J. García-Ripoll, and E. Solano, “Quantum simulation of quantum field theories in trapped ions”, Phys. Rev. Lett. 107, 260501 (2011).

In this work, we develop for the first time the possibility of combining qubits and motional modes in trapped ions for a quantum computation of quantum field theories in the co-design paradigm. Harmonic oscillator excitations are not mapped onto qubits, in-built harmonic oscillators in the architecture represent harmonic oscillators in the model. This proposal was tested in the lab and published later.



Kipu algorithms outperform competing approaches - This translates into tangible advantages for end users, even on current hardware

Achieved improvement on today's quantum hardware




Increased success probability


circuit depth



Exemplary use cases

Protein folding for pharma & biotech

Portfolio optimization for finance

Combinatorial optimization for logistics

Electronic structure simulation for chemistry & pharma

Kipu Quantum’s algorithms allow end users to pilot our products even on today’s hardware.

We are currently prototyping the technology on use cases that are relevant for workflows in the pharmaceutical and chemical industries, automotive & manufacturing, logistics, as well as the finance & insurance sectors.

With its team’s many years of combined relevant expertise in the technical and commercial aspects of quantum computing, Kipu Quantum is well-positioned to provide leading-edge technological solutions for end users.





Oil & Gas


Automotive & Aerospace

Finance & Insurance

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