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.
In an experiment led by Princeton and NIST, we’ve just delivered a crucial result in Quantum Error Correction (QEC), demonstrating key principles of scalable quantum computing developed by Drs Peter Shor, Dorit Aharonov, and Michael Ben-Or. In this latest paper, we showed that by using “concatenated codes” noise can be exponentially suppressed — proving that quantum computing will scale.
When noise is low enough, the results are transformative
Quantum computing is already producing results, but high-profile applications like Shor’s algorithm—which can break RSA encryption—require error rates about a billion times lower than what today’s machines can achieve.
Achieving such low error rates is a holy grail of quantum computing. Peter Shor was the first to hypothesize a way forward, in the form of quantum error correction. Building on his results, Dorit Aharanov and Michael Ben-Or proved that by concatenating quantum error correcting codes, a sufficiently high-quality quantum computer can suppress error rates arbitrarily at the cost of a very modest increase in the required number of qubits. Without that insight, building a truly fault-tolerant quantum computer would be impossible.
Their results, now widely referred to as the “threshold theorem”, laid the foundation for realizing fault-tolerant quantum computing. At the time, many doubted that the error rates required for large-scale quantum algorithms could ever be achieved in practice. The threshold theorem made clear that large scale quantum computing is a realistic possibility, giving birth to the robust quantum industry that exists today.
Realizing a legendary vision
Until now, nobody has realized the original vision for the threshold theorem. Last year, Google performed a beautiful demonstration of the threshold theorem in a different context (without concatenated codes). This year, we are proud to report the first experimental realization of that seminal work—demonstrating fault-tolerant quantum computing using concatenated codes, just as they envisioned.
The benefits of concatenation
The team demonstrated that their family of protocols achieves high error thresholds—making them easier to implement—while requiring minimal ancilla qubits, meaning lower overall qubit overhead. Remarkably, their protocols are so efficient that fault-tolerant preparation of basis states requires zero ancilla overhead, making the process maximally efficient.
This approach to error correction has the potential to significantly reduce qubit requirements across multiple areas, from state preparation to the broader QEC infrastructure. Additionally, concatenated codes offer greater design flexibility, which makes them especially attractive. Taken together, these advantages suggest that concatenation could provide a faster and more practical path to fault-tolerant quantum computing than popular approaches like the surface code.
We’re always looking forward
From a broader perspective, this achievement highlights the power of collaboration between industry, academia, and national laboratories. Quantinuum’s commercial quantum systems are so stable and reliable that our partners were able to carry out this groundbreaking research remotely—over the cloud—without needing detailed knowledge of the hardware. While we very much look forward to welcoming them to our labs before long, its notable that they never need to step inside to harness the full capabilities of our machines.
As we make quantum computing more accessible, the rate of innovation will only increase. The era of plug-and-play quantum computing has arrived. Are you ready?
Quantum computing companies are poised to exceed $1 billion in revenues by the close of 2025, according to McKinsey & Company, underscoring how today’s quantum computers are already delivering customer value in their current phase of development.
This figure is projected to reach upwards of $37 billion by 2030, rising in parallel with escalating demand, as well as with the scale of the machines and the complexity of problem sets of which they will be able to address.
Several systems on the market today are fault-tolerant by design, meaning they are capable of suppressing error-causing noise to yield reliable calculations. However, the full potential of quantum computing to tackle problems of true industrial relevance, in areas like medicine, energy, and finance, remains contingent on an architecture that supports a fully fault-tolerant universal gate set with repeatable error correction—a capability that, until now, has eluded the industry.
Quantinuum is the first—and only—company to achieve this critical technical breakthrough, universally recognized as the essential precursor to scalable, industrial-scale quantum computing. This milestone provides us with the most de-risked development roadmap in the industry and positions us to fulfill our promise to deliver our universal, fully fault-tolerant quantum computer, Apollo, by 2029.
In this regard, Quantinuum is the first company to step from the so-called “NISQ” (noisy intermediate-scale quantum) era towards utility-scale quantum computers.
Unpacking our achievement: first, a ‘full’ primer
A quantum computer uses operations called gates to process information in ways that even today’s fastest supercomputers cannot. The industry typically refers to two types of gates for quantum computers:
- Clifford gates, which can be easily simulated by classical computers, and are relatively easy to implement; and
- Non-Clifford gates, which are usually harder to implement, but are required to enable true quantum computation (when combined with their siblings).
A system that can run both gates is classified as universal and has the machinery to tackle the widest range of problems. Without non-Clifford gates, a quantum computer is non-universal and restricted to smaller, easier sets of tasks - and it can always be simulated by classical computers. This is like painting with a full palette of primary colors, versus only having one or two to work with. Simply put, a quantum computer that cannot implement ‘non-Clifford’ gates is not really a quantum computer.
A fault-tolerant, or error-corrected, quantum computer detects and corrects its own errors (or faults) to produce reliable results. Quantinuum has the best and brightest scientists dedicated to keeping our systems’ error rates the lowest in the world.
For a quantum computer to be fully fault-tolerant, every operation must be error-resilient, across Clifford gates and non-Clifford gates, and thus, performing “a full gate set” with error correction. While some groups have performed fully fault-tolerant gate sets in academic settings, these demonstrations were done with only a few qubits and error rates near 10%—too high for any practical use.
Today, we have published two papers that establishes Quantinuum as the first company to develop a complete solution for a universal fully fault-tolerant quantum computer with repeatable error correction, and error rates low enough for real-world applications.
This is where the magic happens
The first paper describes how scientists at Quantinuum used our System Model H1-1 to perfect magic state production, a crucial technique for achieving a fully fault-tolerant universal gate set. In doing so, they set a record magic state infidelity (7x10-5), 10x better than any previously published result.
Our simulations show that our system could reach a magic state infidelity of 10^-10, or about one error per 10 billion operations, on a larger-scale computer with our current physical error rate. We anticipate reaching 10^-14, or about one error per 100 trillion operations, as we continue to advance our hardware. This means that our roadmap is now derisked.
Setting a record magic state infidelity was just the beginning. The paper also presents the first break-even two-qubit non-Clifford gate, demonstrating a logical error rate below the physical one. In doing so, the team set another record for two-qubit non-Clifford gate infidelity (2x10-4, almost 10x better than our physical error rate). Putting everything together, the team ran the first circuit that used a fully fault-tolerant universal gate set, a critical moment for our industry.
Flipping the switch
In the second paper, co-authored with researchers at the University of California at Davis, we demonstrated an important technique for universal fault-tolerance called “code switching”.
Code switching describes switching between different error correcting codes. The team then used the technique to demonstrate the key ingredients for universal computation, this time using a code where we’ve previously demonstrated full error correction and the other ingredients for universality.
In the process, the team set a new record for magic states in a distance-3 error correcting code, over 10x better than the best previous attempt with error correction. Notably, this process only cost 28 qubits instead of hundreds. This completes, for the first time, the ingredient list for a universal gate setin a system that also has real-time and repeatable QEC.
Fully equipped for fault-tolerance
Innovations like those described in these two papers can reduce estimates for qubit requirements by an order of magnitude, or more, bringing powerful quantum applications within reach far sooner.
With all of the required pieces now, finally, in place, we are ‘fully’ equipped to become the first company to perform universal fully fault-tolerant computing—just in time for the arrival of Helios, our next generation system launching this year, and what is very likely to remain as the most powerful quantum computer on the market until the launch of its successor, Sol, arriving in 2027.
If we are to create ‘next-gen’ AI that takes full advantage of the power of quantum computers, we need to start with quantum native transformers. Today we announce yet again that Quantinuum continues to lead by demonstrating concrete progress — advancing from theoretical models to real quantum deployment.
The future of AI won't be built on yesterday’s tech. If we're serious about creating next-generation AI that unlocks the full promise of quantum computing, then we must build quantum-native models—designed for quantum, from the ground up.
Around this time last year, we introduced Quixer, a state-of-the-art quantum-native transformer. Today, we’re thrilled to announce a major milestone: one year on, Quixer is now running natively on quantum hardware.
Why this matters: Quantum AI, born native
This marks a turning point for the industry: realizing quantum-native AI opens a world of possibilities.
Classical transformers revolutionized AI. They power everything from ChatGPT to real-time translation, computer vision, drug discovery, and algorithmic trading. Now, Quixer sets the stage for a similar leap — but for quantum-native computation. Because quantum computers differ fundamentally from classical computers, we expect a whole new host of valuable applications to emerge.
Achieving that future requires models that are efficient, scalable, and actually run on today’s quantum hardware.
That’s what we’ve built.
What makes Quixer different?
Until Quixer, quantum transformers were the result of a brute force “copy-paste” approach: taking the math from a classical model and putting it onto a quantum circuit. However, this approach does not account for the considerable differences between quantum and classical architectures, leading to substantial resource requirements.
Quixer is different: it’s not a translation – it's an innovation.
With Quixer, our team introduced an explicitly quantum transformer, built from the ground up using quantum algorithmic primitives. Because Quixer is tailored for quantum circuits, it's more resource efficient than most competing approaches.
As quantum computing advances toward fault tolerance, Quixer is built to scale with it.
What’s next for Quixer?
We’ve already deployed Quixer on real-world data: genomic sequence analysis, a high-impact classification task in biotech. We're happy to report that its performance is already approaching that of classical models, even in this first implementation.
This is just the beginning.
Looking ahead, we’ll explore using Quixer anywhere classical transformers have proven to be useful; such as language modeling, image classification, quantum chemistry, and beyond. More excitingly, we expect use cases to emerge that are quantum-specific, impossible on classical hardware.
This milestone isn’t just about one model. It’s a signal that the quantum AI era has begun, and that Quantinuum is leading the charge with real results, not empty hype.
Stay tuned. The revolution is only getting started.