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Ä¢¹½ÊÓÆµ 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

May 9, 2023

In a meaningful advance in an important area of industrial and real-world relevance, Ä¢¹½ÊÓÆµ 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 Ä¢¹½ÊÓÆµ, explain their advances in a new paper, “â€� published on arXiv. This is one of several papers published at the launch of Ä¢¹½ÊÓÆµâ€™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 Ä¢¹½ÊÓÆµâ€™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 Ä¢¹½ÊÓÆµ 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 ²õ³ó´Ç³Ù²õ.Ìý

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.

Ä¢¹½ÊÓÆµ 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
ChartDescription automatically generated

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 Ä¢¹½ÊÓÆµâ€™s algorithm has significantly better runtime than 1-layer QAOA.

About Ä¢¹½ÊÓÆµ

Ä¢¹½ÊÓÆµ, the world’s largest integrated quantum company, pioneers powerful quantum computers and advanced software solutions. Ä¢¹½ÊÓÆµâ€™s technology drives breakthroughs in materials discovery, cybersecurity, and next-gen quantum AI. With over 500 employees, including 370+ scientists and engineers, Ä¢¹½ÊÓÆµ leads the quantum computing revolution across continents. 

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October 27, 2026
Ä¢¹½ÊÓÆµ and GE Vernova Collaborate to Advance High-Temperature Superconductivity Research

Ä¢¹½ÊÓÆµ and GE Vernova’s Advanced Research Center are launching a collaboration to apply quantum computing to one of the research community’s most consequential challenges: understanding the behavior behind high-temperature superconductivity. Advances in this field could, over the long term, transform the energy sector by enabling lighter generators, more compact and powerful motors, and electricity infrastructure that carries more power and better withstands faults.

The research will focus on Fermi–Hubbard modeling, a framework for studying how interacting electrons give rise to complex material properties. By combining Ä¢¹½ÊÓÆµâ€™s full-stack quantum computing capabilities—including access to the company’s Helios computer—with GE Vernova’s expertise in material science and engineering simulation applied to industrial applications, the collaboration will bring an industry perspective to a promising area of quantum research.

Why superconductors matter for energy

As energy systems grow, the size, weight, and performance of electrical equipment become increasingly important constraints. High-temperature superconductors offer potential ways to address those limits through their ability to carry large electrical currents without resistance under suitable operating conditions.

Potential applications span power generation, electricity grids, and industrial electrification. Superconducting generators could reduce the weight and footprint of industrial equipment. Superconducting windings could also help make utility generators and industrial or marine propulsion motors more compact and efficient. In electricity networks, superconducting cables could carry more power through constrained spaces, while fault current limiters could help protect equipment during short circuits.

Realizing those benefits more widely depends on overcoming challenges in cooling, material performance, manufacturing, and cost. Better understanding of the physics behind high-temperature superconductivity could help inform the search for materials with more practical operating characteristics.

Why quantum computing may offer new tools for understanding high-temperature superconductivity

High-temperature superconductivity involves the collective behavior of strongly interacting electrons. Accurately modeling these systems is exceptionally difficult: the interactions that make them scientifically interesting also make important aspects of their behavior computationally challenging.

The Fermi–Hubbard model captures essential features of those interactions in a simplified mathematical framework. Although it is not a complete description of a material used in  industrial applications, it provides a foundation for investigating mechanisms associated with high-temperature superconductivity.

Quantum computing offers a promising way to explore the physics. Ä¢¹½ÊÓÆµ researchers have already measured superconducting pairing correlations—including s-wave and d-wave pairing—in Fermi–Hubbard models simulated on the Helios quantum computer. These results demonstrate the ability to prepare and probe quantum states relevant to superconductivity research, establishing a foundation for further investigation.

The collaboration with GE Vernova will build on that foundation, bringing industrial expertise to the selection and interpretation of research questions.

Connecting quantum capabilities with industrial expertise

The research will be enabled through access to Ä¢¹½ÊÓÆµâ€™s full-stack capabilities, including cloud-based access to Helios, the world’s most accurate quantum computer1, and Nexus, Ä¢¹½ÊÓÆµâ€™s developer platform. Nexus connects quantum hardware with the software tools researchers need to develop and run applications in a unified environment.

GE Vernova’s Advanced Research Center brings the expertise in material science,  engineering, and industrial applications to the research and development activity.  

“High-temperature superconductors could help us overcome important limits on the size, weight, and efficiency of electrical equipment, but understanding and improving these materials remains a significant scientific challenge,â€� said Jonathan Owens, PhD, Senior Scientist, Computational Materials Physics at GE Vernova. “By combining our materials simulation and industrial expertise with Ä¢¹½ÊÓÆµâ€™s quantum computing capabilities, we can explore new approaches to these difficult problems while building the expertise to assess where quantum computing can make a meaningful contribution.â€�

The collaboration also extends GE Vernova’s exploration of quantum computing into a new area of materials research while supporting the development of its internal quantum talent. Its previous includes investigations of quantum algorithms for carbon-capture materials using simulated quantum processors.

Building toward industrial value

Translating insights from simplified models into practical materials requires sustained scientific and engineering work. Industrial expertise helps connect that effort to the properties, operating conditions, and manufacturing considerations that ultimately determine a material’s usefulness.

For Ä¢¹½ÊÓÆµ, this collaboration is an opportunity to advance quantum simulation with an industrial collaborator that understands both the potential applications and the barriers to adoption. It brings together demonstrated computing capabilities, a challenging materials problem, and the expertise needed to connect scientific progress with industrial requirements.

The research collaboration aims to deepen understanding of this field and explore how quantum computing may contribute to future energy technologies.

1 Based on two-qubit gate fidelity as of December 31, 2025.

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October 22, 2026
Ä¢¹½ÊÓÆµ and Oracle Advance Hybrid Quantum-AI Computing with Early Access to Helios

From Oracle's Quantum AI Compute beta program to upcoming Helios installation milestones and Oracle AI World, our partnership continues to gain momentum.

When Ä¢¹½ÊÓÆµ and Oracle announced a strategic partnership earlier this year, the goal was not simply to deploy a quantum computer in the cloud. It was to create a practical path for bringing quantum computing into the enterprise environments where AI, data, and high-performance computing (HPC) already come together.  

By combining Oracle Cloud Infrastructure (OCI)'s AI, data, and cloud capabilities with Helios, Ä¢¹½ÊÓÆµ's most advanced quantum computer, we're helping lay the foundation for hybrid quantum AI computing at enterprise scale. The partnership reflects our belief that some of the most valuable future applications will emerge when quantum computing, AI and classical HPC work together to tackle problems that remain difficult to solve today.  

Oracle Opens Early Access for Quantum AI Compute

That vision is now being put into practice. This month, Oracle launched the , giving select organizations an opportunity to begin evaluating how quantum computing fits into existing workflows and computational challenges.

Through the program, approved participants will gain cloud-based access to Helios, the world's most accurate commercial quantum computer, alongside OCI's GPU and HPC infrastructure. For organizations exploring quantum computing, this creates a practical starting point: access to industry-leading hardware within an enterprise cloud environment, without the need to build specialized infrastructure of their own.

The goal is to help organizations understand where hybrid quantum AI workflows may create value across areas such as drug discovery, materials science, energy, financial modeling, and optimization.

For many organizations, the starting point is not quantum technology itself. It's a business or research problem. Where are today's approaches reaching meaningful limits? Which workloads consume disproportionate resources? And where could a new computational capability create an advantage?

Organizations interested in participating can apply through Oracle's OCI Preview Programs . Oracle will review applications and select participants based on eligibility, capacity and program requirements.

Ä¢¹½ÊÓÆµ and Oracle Leadership Takes the Stage at Oracle AI World

The opportunity for hybrid quantum-AI computing will be a major topic at .  

In a main stage session, "," Larry Stack, Chief Commercial Officer at Ä¢¹½ÊÓÆµ, will join Mahesh Thiagarajan, Executive Vice President and Head of Oracle Cloud Infrastructure, to discuss how quantum computing, AI and classical HPC can work together to address some of the world's most computationally demanding challenges.

The discussion will focus on a core question many organizations are asking: where should they start? Rather than leading with technology, the conversation will explore how organizations can identify high-value problems, establish today's performance baseline, and evaluate where quantum computing ultimately provides an advantage.

Later in the day, Ä¢¹½ÊÓÆµ and Oracle experts will at how bringing Helios into OCI provides managed access to quantum computing natively within an enterprise cloud environment to support hybrid quantum-AI workflows.

Building Momentum Toward Hybrid Quantum-AI Computing

The collaboration between Ä¢¹½ÊÓÆµ and Oracle continues to progress from vision to execution.

With Helios advancing toward installation, Oracle's Quantum AI Compute program now open for early access, and enterprise interest growing around hybrid computing, the pieces are coming together. Organizations now have a practical way to begin exploring quantum computing through cloud-based access to Helios alongside AI, HPC, and existing enterprise workflows.

We look forward to continuing the conversation at Oracle AI World 2026 and working with customers who want to better understand where hybrid quantum-AI computing can create real-world value.

We're excited to continue that conversation at Oracle AI World 2026 and to help customers begin exploring what's possible through the OCI Quantum AI Compute Beta Program.

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October 21, 2026
Ä¢¹½ÊÓÆµ and Google: Two Fault-Tolerance Results, Two Different Measures of Progress

By: David Hayes, Sr. Director of Computational Design and Integrated Software

Two recent announcements from Ä¢¹½ÊÓÆµ and Google mark important progress toward fault-tolerant quantum computing.

Because both announcements focus on reducing errors, it may be tempting to compare the numbers directly. But these results are not the same. They measure different parts of the fault-tolerance challenge and answer fundamentally different technical questions.

This week, we a world-record error-correction result, using our error-correction architecture on Helios to deliver a logical fidelity of 99.9995%, equivalent to just five errors per million operations and representing a 100x reduction in errors compared to the best published result across any other modality—reported by .  

Last week, Google a 99.99% magic-state fidelity result using a new cultivation technique, citing a 40x reduction in errors.

As fault-tolerant quantum computing matures, understanding what is being measured becomes just as important as understanding the headline number itself. Google's work measured the fidelity of a resource used in certain fault-tolerant operations. Our work measured the fidelity of the logical computation that consumes those resources.

Across the published results, Ä¢¹½ÊÓÆµ demonstrates state-of-the-art performance in fault-tolerance, combining record logical computational fidelity with substantial advantages in resource efficiency. Understanding starts with examining what each study measured, what it achieved, and the resources it required.

Ä¢¹½ÊÓÆµ's World-Record Result: Measuring the Accuracy of a Logical Computation

This week’s result measured how accurately an error-corrected logical quantum system can execute a computation.

To achieve the result, we used a well-known “color codeâ€� within our error-correction architecture. The error rate is 10 times lower than Ä¢¹½ÊÓÆµâ€™s own world record achieved last month and 100 times lower than the best published result across all other hardware modalities—the 2024 Google result.

The study also demonstrated that logical errors fell exponentially as code distance increased. Code distance is a key measure of how quantum information can be protected as an error-correction system scales.

Each increase tested in the study reduced the remaining logical error rate by a record factor of 12, demonstrating exponentially effective error suppression as the code grows, a critical capability for scalable fault-tolerant quantum computing.

Together, these results demonstrate how Ä¢¹½ÊÓÆµ's highly accurate trapped-ion hardware and flexible logical architecture can drive rapid gains in computational accuracy. They also show that fault-tolerant performance can be achieved with substantially fewer physical qubits than competing modalities.

The result places Ä¢¹½ÊÓÆµ within the target logical-performance range required for Apollo, our planned universal fault-tolerant quantum computer targeted for 2029.

Google's Result: Advancing Magic-State Preparation

Google's latest paper focused on a different aspect of fault tolerance: the preparation of high-fidelity magic states.

Magic states are an important resource required for certain operations in a fault-tolerant quantum computer. Generating them efficiently is widely recognized as one of the key engineering challenges facing large-scale fault-tolerant systems, particularly for certain modalities.

Google's work introduced a new approach known as cultivation, designed to improve the fidelity of magic-state preparation while reducing the resources required to produce those states. The study demonstrated a magic-state fidelity of 99.99% using a protocol that retained approximately 8% of attempts while discarding the remainder. This post-selection process was a key contributor to the reported 40x reduction in error rate.

The study did not measure the fidelity of a larger logical computation that incorporates those magic states into an end-to-end algorithm. Instead, it focused specifically on the creation and refinement of the resource itself.

That distinction is important because preparing a high-fidelity resource and demonstrating the performance of a logical computation are different milestones on the path to fault tolerance.

Directly Comparing Ä¢¹½ÊÓÆµ and Google’s Magic-State Results

Ä¢¹½ÊÓÆµ's latest logical computation result should not be compared directly with Google's latest magic-state result. It should be compared against the distance scaling result published by Google in 2024.

That said, we have published studies measuring an analogous magic-state capability examined in Google’s latest work.

, we achieved 99.993% magic-state fidelity with an 85% retention rate, compared with the 99.99% fidelity and approximately 8% retention reported in Google’s latest work. Our result also required fewer physical qubits and fewer operational steps, resulting in significantly lower space-time overhead.

That combination of smaller qubit and operational steps footprint, along with substantially higher retention means fewer resources are consumed preparing each usable magic state.

As fault-tolerant systems scale, those efficiency advantages become increasingly important because they directly affect the amount of hardware required to perform useful computations.

The Bigger Picture

Taken together, these results establish Ä¢¹½ÊÓÆµâ€™s leadership in demonstrated fault-tolerant performance: record logical computation fidelity, alongside a directly comparable magic-state result that achieves higher fidelity with substantially lower resource overhead.

That combination—computational accuracy and the efficiency with which it is achieved—is critical to delivering reliable answers to useful problems at a practical scale.

Ultimately, customers do not buy two-qubit gate fidelities or magic states. They buy answers.

Forward-Looking Statements

This blog post contains forward-looking statements within the meaning of the Private Securities Litigation Reform Act of 1995. These include statements about our technology roadmap, our expected logical performance, and the planned timing and capabilities of future systems, including Apollo. Words such as "target," "expect," "plan," and similar expressions identify forward-looking statements. These statements are based on our current expectations and involve risks and uncertainties that could cause actual results to differ materially. Those risks include challenges in developing, manufacturing, and scaling our quantum computing systems. For a discussion of these and other risks, see the "Risk Factors" section of our most recent Quarterly Report on Form 10-Q and our other filings with the SEC, available at ir.quantinuum.com. Forward-looking statements speak only as of the date of this post, and we undertake no obligation to update them except as required by law.

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