Quantinuum Researchers Demonstrate a new Optimization Algorithm that delivers solutions on H2 Quantum Computer
Algorithm reliably and consistently solves combinatorial optimization problems using minimal quantum resources
In a meaningful advance in an important area of industrial and real-world relevance, Quantinuum researchers have demonstrated a quantum algorithm capable of solving complex combinatorial optimization problems while making the most of available quantum resources.
Results on the new H2 quantum computer evidenced a remarkable ability to solve combinatorial optimization problems with as few quantum resources as those employed by just one layer of the quantum approximate optimization algorithm (QAOA), the current and traditional workhorse of quantum heuristic algorithms.
Optimization problems are common in industry in contexts such as route planning, scheduling, cost optimization and logistics. However, as the number of variables increases and optimization problems grow larger and more complex, finding satisfactory solutions using classical algorithms becomes increasingly difficult.
Recent research suggests that certain quantum algorithms might be capable of solving combinatorial optimization problems better than classical algorithms. The realization of such quantum algorithms can therefore potentially increase the efficiency of industrial processes.
However, the effectiveness of these algorithms on near-term quantum devices and even on future generations of more capable quantum computers presents a technical challenge: quantum resources will need to be reduced as much as possible in order to protect the quantum algorithm from the unavoidable effects of quantum noise.
Sebastian Leontica and Dr. David Amaro, a senior research scientist at Quantinuum, explain their advances in a new paper, “Exploring the neighborhood of 1-layer QAOA with Instantaneous Quantum Polynomial circuits” published on arXiv. This is one of several papers published at the launch of Quantinuum’s H2, that highlight the unparalleled power of the newest generation of the H-Series, Powered by Honeywell.
“We should strive to use as few quantum resources as possible no matter how good a quantum computer we are operating on, which means using the smallest possible number of qubits that fit within the problem size and a circuit that is as shallow as possible,” Dr. Amaro said. “Our algorithm uses the fewest possible resources and still achieves good performance.”
The researchers use a parameterized instantaneous quantum polynomial (IQP) circuit of the same depth as the 1-layer QAOA to incorporate corrections that would otherwise require multiple layers. Another differentiating feature of the algorithm is that the parameters in the IQP circuit can be efficiently trained on a classical computer, avoiding some training issues of other algorithms like QAOA. Critically, the circuit takes full advantage of, and benefits from features available on Quantinuum’s devices, including parameterized two-qubit gates, all-to-all connectivity, and high-fidelity operations.
“Our numerical simulations and experiments on the new H2 quantum computer at small scale indicate that this heuristic algorithm, compared to 1-layer QAOA, is expected to amplify the probability of sampling good or even optimal solutions of large optimization problems,” Dr. Amaro said. “We now want to understand how the solution quality and runtime of our algorithm compares to the best classical algorithms.”
This algorithm will be useful for current quantum computers as well as larger machines farther along the Quantinuum hardware roadmap.
How the Experiment Worked
The goal of this project was to provide a quantum heuristic algorithm for combinatorial optimization that returns better solutions for optimization problems and uses fewer quantum resources than state of the art quantum heuristics. The researchers used a fully connected parameterized IQP, warm-started from 1-layer QAOA. For a problem with n binary variables the circuit contained up to n(n-1)/2 two-qubit gates and the researchers employed only 20.32n shots.
The algorithm showed improved performance on the Sherrington-Kirkpatrick (SK) optimization problem compared to the 1-layer QAOA. Numerical simulations showed an average speed up of 20.31n compared to 20.5n when looking for the optimal solution.
Experimental results on our new H2 quantum computer and emulator confirmed that the new optimization algorithm outperforms 1-layer QAOA and reliably solves complex optimization problems. The optimal solution was found for 136 out of 312 instances, four of which were for the maximum size of 32 qubits. A 30-qubit instance was solved optimally on the H2 device, which means, remarkably, that at least one of the 776 shots measured after performing 432 two-qubit gates corresponds to the unique optimal solution in the huge set of 230 > 109 candidate solutions.
These results indicate that the algorithm, in combination with H2 hardware, is capable of solving hard optimization problems using minimal quantum resources in the presence of real hardware noise.
Quantinuum researchers expect that these promising results at small scale will encourage the further study of new quantum heuristic algorithms at the relevant scale for real-world optimization problems, which requires a better understanding of their performance under realistic conditions.
Speedup of IQP over QAOA
Numerical simulations of 256 SK random instances for each problem size from 4 to 29 qubits. Graph A shows the probability of sampling the optimal solution in the IQP circuit, for which the average is 2-0.31n. Graph B shows the enhancement factor compared to 1-layer QAOA, for which the average is 20.23n. These results indicate that Quantinuum’s algorithm has significantly better runtime than 1-layer QAOA.
About Quantinuum
Quantinuum, the world’s largest integrated quantum company, pioneers powerful quantum computers and advanced software solutions. Quantinuum’s technology drives breakthroughs in materials discovery, cybersecurity, and next-gen quantum AI. With over 500 employees, including 370+ scientists and engineers, Quantinuum leads the quantum computing revolution across continents.
This month, Quantinuum welcomed its global user community to the first-ever Q-Net Connect, an annual forum designed to spark collaboration, share insights, and accelerate innovation across our full-stack quantum computing platforms. Over two days, users came together not only to learn from one another, but to build the relationships and momentum that we believe will help define the next chapter of quantum computing.
Q-Net Connect 2026 drew over 170 attendees from around the world to Denver, Colorado, including representatives from commercial enterprises and startups, academia and research institutions, and the public sector and non-profits - all users of Quantinuum systems.
The program was packed with inspiring keynotes, technical tracks, and customer presentations. Attendees heard from leaders at Quantinuum, as well as our partners at NVIDIA, JPMorganChase and BlueQubit; professors from the University of New Mexico, the University of Nottingham and Harvard University; national labs, including NIST, Oak Ridge National Laboratory, Sandia National Laboratories and Los Alamos National Laboratory; and other distinguished guests from across the global quantum ecosystem.
Congratulations to Q-Net Connect 2026 Award Recipients!
The mission of the Quantinuum Q-Net user community is to create a space for shared learning, collaboration and connection for those who adopt Quantinuum’s hardware, software and middleware platform. At this year’s Q-Net Connect, we awarded four organizations who made notable efforts to champion this effort.
- JPMorganChase received the ‘Guppy Adopter Award’ for their exemplary adoption of our quantum programming language, Guppy, in their research workflows.
- Phasecraft, a UK and US-based quantum algorithms startup, received the ‘Rising Star’ award for demonstrating exceptional early impact and advancing science using Quantinuum hardware, which they published in a December 2025 paper.
- Qedma, a quantum software startup, received the ‘Startup Partner Engagement’ award for their sustained engagement with Quantinuum platforms dating back to our first commercially deployed quantum computer, H1.
- Anna Dalmasso from the University of Nottingham received our ‘New Student Award’ for her impressive debut project on Quantinuum hardware and for delivering outstanding results as a new Q-Net student user.
Congratulations, again, and thank you to everyone who contributed to the success of the first Q-Net Connect!
Become a Q-Net Member
Q-Net offers year‑round support through user access, developer tools, documentation, trainings, webinars, and events. Members enjoy many exclusive benefits, including being the first to hear about exclusive content, publications and promotional offers.
By joining the community, you will be invited to exclusive gatherings to hear about the latest breakthroughs and connect with industry experts driving quantum innovation. Members also get access to Q‑Net Connect recordings and stay connected for future community updates.
In a follow-up to our recent work with Hiverge using AI to discover algorithms for quantum chemistry, we’ve teamed up with Hiverge, Amazon Web Services (AWS) and NVIDIA to explore using AI to improve algorithms for combinatorial optimization.
With the rapid rise of Large Language Models (LLMs), people started asking “what if AI agents can serve as on-demand algorithm factories?” We have been working with Hiverge, an algorithm discovery company, AWS, and NVIDIA, to explore how LLMs can accelerate quantum computing research.
Hiverge – named for Hive, an AI that can develop algorithms – aims to make quantum algorithm design more accessible to researchers by translating high-level problem descriptions in mostly natural language into executable quantum circuits. The Hive takes the researcher’s initial sketch of an algorithm, as well as special constraints the researcher enumerates, and evolves it to a new algorithm that better meets the researcher’s needs. The output is expressed in terms of a familiar programming language, like Guppy or NVIDIA CUDA-Q, making it particularly easy to implement.
The AI is called a “Hive” because it is a collective of LLM agents, all of whom are editing the same codebase. In this work, the Hive was made up of LLM powerhouses such as Gemini, ChatGPT, Claude, Llama, as well as NVIDIA Nemotron, which was accessed through AWS’ Amazon Bedrock service. Many models are included because researchers know that diversity is a strength – just like a team of human researchers working in a group, a variety of perspectives often leads to the strongest result.
Once the LLMs are assembled, the Hive calls on them to do the work writing the desired algorithm; no new training is required. The algorithms are then executed and their ‘fitness’ (how well they solve the problem) is measured. Unfit programs do not survive, while the fittest ones evolve to the next generation. This process repeats, much like the evolutionary process of nature itself.
After evolution, the fittest algorithm is selected by the researchers and tested on other instances of the problem. This is a crucial step as the researchers want to understand how well it can generalize.
In this most recent work, the joint team explored how AI can assist in the discovery of heuristic quantum optimization algorithms, a class of algorithms aimed at improving efficiency across critical workstreams. These span challenges like optimal power grid dispatch and storage placement, arranging fuel inside nuclear reactors, and molecular design and reaction pathway optimization in drug, material, and chemical discovery—where solutions could translate into maximizing operational efficiency, dramatic reduction in costs, and rapid acceleration in innovation.
In other AI approaches, such as reinforcement learning, models are trained to solve a problem, but the resulting "algorithm" is effectively ‘hidden’ within a neural network. Here, the algorithm is written in Guppy or CUDA-Q (or Python), making it human-interpretable and easier to deploy on new problem instances.
This work leveraged the NVIDIA CUDA-Q platform, running on powerful NVIDIA GPUs made accessible by AWS. It’s state-of-the art accelerated computing was crucial; the research explored highly complex problems, challenges that lie at the edge of classical computing capacity. Before running anything on Quantinuum’s quantum computer, the researchers first used NVIDIA accelerated computing to simulate the quantum algorithms and assess their fitness. Once a promising algorithm is discovered, it could then be deployed on quantum hardware, creating an exciting new approach for scaling quantum algorithm design.
More broadly, this work points to one of many ways in which classical compute, AI, and quantum computing are most powerful in symbiosis. AI can be used to improve quantum, as demonstrated here, just as quantum can be used to extend AI. Looking ahead, we envision AI evolving programs that express a combination of algorithmic primitives, much like human mathematicians, such as Peter Shor and Lov Grover, have done. After all, both humans and AI can learn from each other.
As quantum computing power grows, so does the difficulty of error correction. Meeting that demand requires tight integration with high-performance classical computing, which is why we’ve partnered with NVIDIA to push the boundaries of real-time decoding performance.
Realizing the full power of quantum computing requires more than just qubits, it requires error rates low enough to run meaningful algorithms at scale. Physical qubits are sensitive to noise, which limits their capacity to handle calculations beyond a certain scale. To move beyond these limits, physical qubits must be combined into logical qubits, with errors continuously detected and corrected in real time before they can propagate and corrupt the calculation. This approach, known as fault tolerance, is a foundational requirement for any quantum computer intended to solve problems of real-world significance.
Part of the challenge of fault tolerance is the computational complexity of correcting errors in real time. Doing so involves sending the error syndrome data to a classical co-processor, solving a complex mathematical problem on that processor, then sending the resulting correction back to the quantum processor - all fast enough that it doesn’t slow down the quantum computation. For this reason, Quantum Error Correction (QEC) is currently one of the most demanding use-cases for tight coupling between classical and quantum computing.
Given the difficulty of the task, we have partnered with NVIDIA, leaders in accelerated computing. With the help of NVIDIA’s ultra-fast GPUs (and the GPU-accelerated BP-OSD decoder developed by NVIDIA as part of NVIDIA CUDA-Q QEC library), we were able to demonstrate real-time decoding of Helios’ qubits, all in a system that can be connected directly to our quantum processors using NVIDIA NVQLink.
While real-time decoding has been demonstrated before (notably, by our own scientists in this study), previous demonstrations were limited in their scalability and complexity.
In this demonstration, we used Brings’ code, a high-rate code that is possible with our all-to-all connectivity, to encode our physical qubits into noise-resilient logical qubits. Once we had them encoded, we ran gates as well as let them idle to see if we could catch and correct errors quickly and efficiently. We submitted the circuits via both NVIDIA CUDA-Q as well as our own Guppy language, underlining our commitment to accessible, ecosystem-friendly quantum computing.
The results were excellent: we were able to perform low-latency decoding that returned results in the time we needed, even for the faster clock cycles that we expect in future generation machines.
A key part of the achievement here is that we performed something called “correlated” decoding. In correlated decoding, you offload work that would normally be performed on the QPU onto the classical decoder. This is because, in ‘standard’ decoding, as you improve your error correction capabilities, it takes more and more time on the QPU. Correlated decoding elides this cost, saving QPU time for the tasks that only the quantum computer can do.
Stay tuned for our forthcoming paper with all the details.