# Kipu’s Roadmap

*Kipu’s Roadmap Towards Commercial Quantum Advantage*

*The pre-industrial era of quantum computing: driven by hardware progress*

Mature quantum computing is projected to unlock hundreds of billions in value-at-stake for large organizations. It is poised to reshape industries alongside the current advancements in artificial intelligence. While GenAI continues to revolutionize the way we interact with technology, quantum computing is becoming a game-changing reality that’s already around the corner.

IBM Quantum heralded in the era of pre-industrial quantum computing when they made the first quantum computers cloud-accessible in 2016. In just a few years, quantum hardware companies have steadily increased qubit counts while improving gate quality, delivering on promises that once seemed overly ambitious. Today, cloud-accessible quantum processors are almost a commodity. We have access to quantum processors with hundreds of qubits, covering several modalities. Quantum computers made their way into data centers, and even small, portable quantum computers for educational purposes that cost less than a premium TV are now for sale. Quantum computers capable of running thousands of gates and harnessing hundreds of qubits will soon tackle problems that are beyond the reach of classical computers, marking that the future of computing is not on the horizon—it’s already taking shape today.

*The Big Mismatch: algorithms are the next bottleneck to overcome*

However, despite progress on hardware, most of the existing quantum algorithms are still even more greedy for quantum resources than the hardware can provide. This mismatch between algorithmics resource demand and hardware capabilities prevents us from unlocking the real potential of what quantum computing has to offer. With conventional approaches, quantum is more than ten years away from solving any real problem.

Hence, the new bottleneck of quantum computing is efficient and scalable quantum algorithms. Let us look at the famous Grover algorithm, also known as the quantum search algorithm: it can be used to find the optimal solution to an NP-hard optimization problem like job-shop scheduling. Using the *Azure Quantum Resource Estimator *and assuming error-correction methods*,* we estimated the resources required to solve the scheduling problem of 50 variables. This problem, which is solvable by classical means, would demand around 1 million physical qubits and 2 billion logical quantum gates.

Another example is the quantum interior-point methods algorithm. This algorithm is a quantum boosted version of the classical interior-point methods which is used in optimization. Researchers from *AWS* and *Goldman Sachs *studied the end-to-end application of the quantum algorithm for portfolio optimization^{1}. They found that optimizing a portfolio with 100 assets would require more than 10^{29} quantum gates. We note optimizing 100 assets is also still solvable classically.

Although IBM’s roadmap is forecasting a quantum computer capable of executing the impressive number of 1 billion (10^{9}) gates in 2033^{2}, the required number of gates is 20 orders of magnitude higher. To bring this into perspective, a supercomputer compared to a laptop can “only” perform 6 orders of magnitude more calculations per second. The size of a hydrogen atom compared to the size of the earth corresponds to 20 orders of magnitude. We at Kipu Quantum are optimists by nature, but waiting for quantum hardware (or, in fact, ANYTHING in the realm of technology) to improve by this much is unlikely to happen during our lifespan.

The quantum resource overhead (number of qubits and gates) makes current algorithms like Grover highly impractical for current quantum processors and applications. The quantum industry needs algorithms that not only utilize quantum speedup, but also maximize resource efficiency.

*The birth of a new algorithmic paradigm, the death of old labels*

To overcome this, the development of scalable and efficient quantum algorithms needs to address the following challenges: reducing circuit depth, the number of algorithmic layers, each including simultaneously applied quantum gates, and reducing the required circuit width, the number of qubits needed to encode/map industrially relevant problems.

This is where Kipu Quantum technologies steps in. We are driven by the idea of realizing practical quantum computing applications rather soon. To this end, we develop application- and hardware-specific quantum computing solutions with original and proprietary digital, analog, and digital-analog quantum computing paradigms. We solve problems with drastically reduced circuit depth (up to 10.000 times). Kipu’s catalyzed algorithms match current hardware and problem encoding to harness the full power of quantum computing.

Several key players in academia and industry have presented credible claims that quantum computers can surpass classical ones in performance. The terminology surrounding current quantum computing and its capabilities like NISQ (Noisy Intermediate-Scale Quantum), FTQC (Fault-Tolerant Quantum Computing) or even PISQ (Perfect Intermediate-Scale Quantum computing) can be confusing and often overlaps, complicating the evaluation of such claims. The underlying assumption that quantum computing will progress from NISQ to FTQC in a linear or even exponential manner is overly simplistic. There is no agreed-upon threshold at which a NISQ device transitions into a FTQC system. There is no clear-cut position point. By framing the development of quantum computing in terms of two discrete eras, the NISQ phase and FTQC phase, separated by a hypothetical thin line, the community clearly oversimplifies.

Two years ago, creating Kipu’s first tech roadmap, we emphasized that our novel algorithmic methods are crucial for commercial usefulness already in the NISQ era. Today, we realize that framing the future development along the terms of NISQ and FTQC is utterly irrelevant. It is especially irrelevant for industry which seeks quantum-powered solutions for their businesses. A more nuanced and flexible approach that recognizes the commercial outcome and steady emergence of quantum developments may be more reflective.

*A meandering river, not a razor-sharp line*

This is why we at Kipu Quantum are convinced that we should shift from technical terminology to a more practical, impactful and consumer-oriented perspective. We believe that we are at the beginning of an era where neither mathematicians nor computer scientists should be the final judges of when quantum computers become commercially useful, but the people and organizations that pay for it. Quantum computing should no longer be viewed as a far-off and experimental technology, but rather as a solution that will soon deliver real business outcome and immediate or imminent added value for paying industry customers. The latter is more plausible when packaged in adjusted workflows and combined with the best-of-kind classical tools that run on CPUs, GPUs, and FPGAs. The users of quantum technology are in a better position to assess whether quantum computing solves their problems faster, cheaper, consuming less energy, or better than classical approaches, making them the true judges of quantum advantage.

Recently we presented the largest optimization problem with industry relevance via an experiment running on an IBM quantum processor using all 156 qubits by applying Kipu Quantum’s powerful algorithms (read here). While this result is not yet intractable, it constitutes a significant leap. We consider this result as a first landmark result at the beginning of the fluid era of Commercial Quantum Advantage.

We like to think about quantum advantage as a meandering river, whose journey is complex, dynamic, and unpredictable. There is a confluence of many efforts in both: hardware, algorithms, and application areas. As rivers carve their landscape within time, different industries will experience their quantum advantage moments at different times and in different ways, just as various parts of a river’s landscape change uniquely. We also expect classical technologies to further improve, which in some cases may even lead them to leapfrog what quantum computers could do, resulting in a longer neck-by-neck race of different ways to solve industrial problems. Quantum advantage is not universal.

*Quantifying Progress in Quantum Algorithms with KCI*

In the new era of Commercial Quantum Advantage, we at Kipu Quantum want to quantify our technological progress on solving challenging problems with our catalyzed and accelerated algorithms. Going forward, we will measure our own progress in a metric that depends on several factors like the size, density, and locality of the chosen use case, as well as the connectivity of the used hardware. We define our metric for NP-hard optimization problems just because these problems are often benchmarked on classical as well as on quantum hardware, while having many applications in various industries. Therefore, we introduce the Kipu complexity index (KCI) given by:

For the proposed KCI, we characterize the problem size with the number of qubits* N*. The problem density 𝑑 quantifies how many terms the quantum formulation of the problem contains with respect to the maximum number of terms possible.^{[1]} We also consider the locality 𝑘 of the problem corresponding to the polynomial order of the optimization problems.^{[2]} Since our algorithms are naturally tested on quantum hardware, we also consider the connectivity of the corresponding quantum processor architecture. Here, we use the average number of connections per qubit* c*.^{[3]}

KCI strongly weights the problem density and the locality. This means that solving a fully connected HUBO problem has a higher complexity than a sparse QUBO with a larger number of qubits. The reason for this weight is that higher order terms require more gates to implement them. The problem density has also high weight since the number of gates also directly scales with the problem density. We will present a detailed discussion of KCI in a scientific report in the upcoming weeks.

*Threshold for Commercial Quantum Advantage: 100+ qubits for dense-enough problems *

We believe that commercial quantum advantage will be in the region where we can solve NP-hard problems of 100+ qubits at a sufficiently high problem density. We conclude this by using exact classical algorithms to find the optimal solution, which becomes impractical due to the exponentially scaling computational resources. Often classical heuristic algorithms are used instead that deliver suboptimal solutions. However, quantum algorithms are very promising to give the optimal solution. The difference between a suboptimal and the optimal one can mean a huge difference in terms of commercial value, which is exactly one pillar of the proposed denomination of commercial quantum advantage.

However, not only solution quality has a commercial impact. Also, the time required to solve the problem, the problem size and energy demand required to obtain a solution are unmet requirements. There is also a strong indication that already a fully-connected HUBO problem of 80 variables could be intractable with classical solvers. Nevertheless, the next hardware generations of quantum computers will offer the capability to tackle the problem.

The key question remains: can we identify industry problems that align with the connectivity and number of variables required for these advanced solutions? We are eager to explore this opportunity in collaboration with an industry partner.

*Kipu’s Roadmap Towards Commercial Quantum Advantage*

This roadmap, developed using a sophisticated metric, outlines our strategic paths and measures our technological progress across three dimensions: co-designed algorithm complexity, novel applications, and innovative services on our platform. It is to be considered a work in progress and will be amended. In today’s version, we list our expected advancements by quarter until the end of 2025.

Each dimension is key to driving forward our mission of realizing the level of useful quantum computing. By advancing our algorithms, we aim to tackle increasingly complex problems defined by *KCI. *

At the same time, we are committed to exploring novel applications and commercial use cases that demonstrate the usefulness of our technology across various verticals and industry sectors. Finally, we continue to innovate with services and quantum tools that enhance the value of our product platform, providing our customers with frictionless quantum computing. The roadmap serves as a strategic guide, ensuring that our technological development and innovation remain aligned with industry demands, ultimately empowering our customers and partners

*Outlook: Quantum Destiny is all*

Quantum computing, while one of the most complex technologies to understand and develop, is also set to fundamentally change the way we live and conduct business. At Kipu Quantum, we are fully committed to accelerating this transformation, advancing quantum computing solutions years ahead of what the quantum industry anticipates.

Our bold and forward-looking strategy, driven by a rigorous focus on application- and hardware-specific algorithms, positions us as the leader in the rapidly evolving market. Our highly motivated and diverse team, always thinking two steps ahead, is driven by constant and creative innovation, steadily working on solutions that push beyond conventional limits.

Our roadmap is designed to clearly outline how we will address the key areas of technological performance, application development, and quantum-enabled services. We believe it offers a succinct view of our planned contributions to the quantum landscape.

Looking ahead, the year 2025 holds special significance for Kipu Quantum, as the United Nations has declared it the International Year of Quantum Science and Technology (IYQ). This global initiative celebrates a century of breakthroughs in quantum mechanics—building on the foundational work of pioneers like Werner Heisenberg and Erwin Schrödinger. We also see 2025 as a pivotal moment for quantum technology, emphasizing our confidence that it will be a year full of achievements, the quantum industry has never ever seen before.

**Quantum destiny is all.**

^{[1]} For example, a fully connected problem has the density 𝑑=1.

^{[2]} To solve problems on a quantum computer many of them are formulated with polynomials of order/locality 𝑘=2 corresponding to the *quadratic unconstrained binary optimization* (QUBO) problems. However, one can also find formulations containing polynomials of higher order 𝑘>2 which belong to the so-*called higher-order unconstrained binary optimization* (HUBO) problems.

^{[3]} For example, for a heavy grid of the IBM hardware, we obtain 𝑐=1.6 and qubits connected on a square grid, like the Google chip, we get 𝑐=1.75. An all-to-all connected hardware corresponds to 𝑐=N. Therefore, the factor 1+1/𝑐 is has a maximum of 2 for qubits connected on an 1-dimensional line and asymptotically approaches 1 for an-to-all connected hardware.