Theoretical work finds shortcut to solving the Max-Cut problem with a quantum computer
We are surrounded by optimization problems – for example, what’s the most efficient route for getting all your chores done on a Sunday? What’s the best way to pack a suitcase? Modern businesses can’t escape the importance of optimization problems, they’re critical in everything from charting shipping routes to setting prices.
To solve such real-world examples, experts build mathematical models and explore computer algorithms capable of finding the optimal path through a problem. In many cases, as they scale, problems become intractable to even the most powerful classical supercomputers. Research suggests that for some problems, quantum algorithms offer some new promise. Our researchers have explored a quantum approach to a widely applicable optimization problem called “Max-Cut”, where one cuts a graph to snip as many vertices as possible.
Finding exact solutions to the Max-Cut problem in a reasonable amount of time would have practical applications in a wide range of situations, including supply chain management, machine scheduling, image recognition, quality control, fraud detection, patient diagnostics, and electric circuit design. For a generic graph, this problem is really hard: a computer scientist would call it “NP hard”. There is no known classical algorithm to solve Max-Cut for a generic graph whose runtime is polynomial in the number of vertices L, and it is strongly believed that no such classical algorithm exists. Many other useful optimization problems have a similar problem: they may simply be too expensive to solve exactly with classical computers. Back in the real world, this explains why many aspects of daily life run sub-optimally. Consider the experience of multiple drivers delivering a succession of small goods from the same vendor, often packaged in clearly oversized boxes. The costs of this sort of inefficiency accrue in terms of time, money, and environmental impact, locally and at the full scale of the global economy.
Our team has been working on applying a quantum solution to the Max-Cut problem based on the adiabatic theorem of quantum mechanics. Using the adiabatic theorem to solve an optimization problem involves encoding the problem into the qubits (setting up the Hamiltonian), then letting the system slowly evolve some parameter, carefully keeping it in the ground state the whole time. This method is an all-purpose solver for classically hard optimization problems, but it comes at a large computational cost: the “slow” evolution means applying lots of expensive gates to perform the many time steps needed.
Our team figured out that instead of taking many expensive steps they could instead take a limited amount without destroying the convergence, as long as the optimization problem has a classical Hamiltonian. They call this “Floquet adiabatic evolution” and find that this approach reduces the required number of gates by several orders of magnitude.
Contrary to variational quantum algorithms such as Quantum Approximate Optimization Algorithm (QAOA), these low circuit depths can be achieved without classical optimization of parameters (whose sensitivity to noise and scaling behavior is not well understood).
Extrapolating their numerical simulation results, the team estimated that there may be a quantum speedup for this problem with a 2-qubit gate infidelity around 10-5 and roughly 2000 qubits. Our H1 system already boasts a world-class 2-qubit gate infidelity of 8.8 × 10-4, and we are well on our way towards even better fidelity with more qubits. You can see our roadmap here, and read the paper here.
In the meantime, the paper proposes that this method could be used as a quantum computing benchmark for application-oriented problems, making a valuable contribution to the Bench-QC project, of which Quantinuum is a founding member.
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.
Visit Quantinuum at SC26 – Booth 4838
Quantinuum is heading to SC26 in Chicago, and we'd love to see you at Booth 4838 in the Quantum Junction. Stop by during exhibit hours to catch partner theater sessions throughout the day, see what's new with Helios and Nexus, and talk with our team about how quantum computing is expanding its footprint in the HPC datacenter, including hybrid quantum-classical applications.
In our booth:
Join our experts and partners at our kiosks and for short sessions in our theater running throughout the day. Topics include:
- Next Gen Enterprise Computing Partners – how leading enterprises are bringing quantum into their computing strategy
- Error Correction: The Path to Fault Tolerance – where quantum error correction stands today and what comes next
- Develop for the Fault Tolerant Era with Nexus – building, running, and managing quantum workflows on the Nexus platfor
- Helios: The Most Accurate Quantum Computer – a closer look at our latest system and what its performance makes possible
- Startup Partners: Accelerating Quantum Ecosystem Innovation – how startups are building on Quantinuum technology
- Real Commercial Impact – quantum applications in pharma, chemicals, materials, and finance
Coffee and cookies on us
Need a break from the show floor? Our barista will be serving up coffee, and we'll have fresh cookies every afternoon. Grab a cup, pull up a seat for a theater session, and chat with the team.
Catch Quantinuum in the SC26 program
Our experts are also speaking in the SC26 technical program. Add these sessions to your schedule (all times CST):
Speaking Sessions
November 15th
9:45 – 10:00am | Room: W178a
Quantum-HPC Workflows Across Multiple Quantum Computing Platforms: Two Case Studies – part of the 2nd International Workshop for Software Frameworks and Workload Management on Quantum-HPC Ecosystems
Presenting: Philipp Seitz
November 16th
3:30 – 4:00pm | Room: W179a
Software for Large Scale Application – part of the 2nd Annual Workshop on Large-Scale Quantum-Classical Computing (LSQCC)
Presenting: Juan Pederson
November 19th
3:30 – 4:00pm | Room: W181abc
Bringing Quantum Computing to the HPC Datacenter
Presenting: Kentaro Yamamoto
Theater Schedule
Note: Schedule subject to changes.
See you in Chicago
Whether you're exploring quantum for the first time or planning how to integrate it with your HPC environment, our team is ready to talk. Find us at Booth 4838 in the Quantum Junction, November 16–19.
Quantinuum has been recognized as a “Market Shaper” in Gartner’s first Emerging Market Quadrant for Quantum Computing. According to Gartner, Market Shapers combine a high potential to transform the market with strong execution capabilities.
You can access the report here.
While this recognition is welcome and validates much of what we have contributed to the quantum computing space, we believe there is compelling evidence that supports an even stronger leadership position.
The distinction matters for customers deciding where to strategically invest their time, expertise and resources. Quantum leadership requires reliable computation at useful speed, software that enables application development across hardware generations, and the capacity to deliver at scale. Across these measures, our proven results, growing adoption and long-term customer commitments demonstrate Quantinuum’s leadership.
Quantinuum’s position has been repeatedly recognized by others in the industry as well, including experts like André M. König, CEO of Global Quantum Intelligence (GQI).
According to André: “Traditional IT analyst frameworks often struggle with quantum because they weigh near-term service wrappers on the same scale as deep-tech physics. Most of what this industry publishes is a slideware roadmap. Quantinuum’s recent error-correction milestones - reaching 99.9995% logical memory fidelity on Helios - were demonstrated on a commercially deployed system with the data open to inspection. For enterprise buyers and sovereign programs trying to separate engineering reality from marketing ambition, demonstrated logical performance is the only metric that matters today.”
Advancing a Credible Path to Fault Tolerance
Quantinuum’s progress places us at the forefront of scalable, fault-tolerant computing. We bring together the three capabilities essential to achieving it: accurate hardware, an architecture that scales efficiently, and error correction that improves reliability while managing resource requirements.
In the third quarter, we introduced an end-to-end logical architecture on Helios that combines tailored AI decoders, all-to-all qubit connectivity, high-fidelity physical operations and hardware-level error correction. Two different error-correcting codes running within that architecture on the same hardware delivered back-to-back world records in September and October, reinforcing what we believe is the industry’s most credible path to universal, fully fault-tolerant quantum computing.
October’s result reached 99.9995% logical memory fidelity, equivalent to five errors in one million operations. That error rate was ten times lower than our September record and 100 times lower than the previous best published result across other hardware modalities, achieved by Google.
The results also validated the scalability of our architecture. Each two-step increase in error-correction code distance reduced logical memory errors by approximately twelvefold, compared with roughly twofold in Google’s published superconducting result. We estimate this stronger suppression points to roughly 30 times fewer physical qubits needed to reach target logical error rates in that comparison—a significant advantage for scaling.
These results build on years of advancing our architecture and delivering successive systems, from H1 through Helios. That record gives customers a concrete basis for confidence in our roadmap toward Sol and Apollo.
Leadership also means helping customers understand which performance measures matter. As our Chief Scientist, Harry Buhrman, explains in Fidelity First in the Quantum Race, faster gates do not necessarily produce faster useful answers. Higher fidelity can reduce the additional qubits and operations needed for error correction, shortening the time to a reliable result.
QUOPS, developed by Sandia National Laboratories with input from Quantinuum and NVIDIA, helps customers evaluate both computational capability and speed. In the first published study, Helios achieved the highest computational capability score of the four systems assessed—a measure of circuit size—at 1,504, or 1,824 with leakage post-selection. Other systems achieved higher computational rates, but on smaller circuits.
These dimensions must be considered together to understand what a system can reliably deliver. We are working toward an industry standard around QUOPS so customers can compare systems and make better-informed purchasing decisions.
Giving Developers a Path from Today’s Systems to Fault Tolerance
Our leadership extends to the software customers need to put increasingly capable hardware to work.
Quantinuum Nexus brings quantum application development and deployment into one environment, enabling developers and error-correction experts to advance their work together. Its multigenerational roadmap aligns software capabilities with successive hardware generations through Apollo and beyond, helping customers carry forward the applications, workflows and expertise they build today.
We are already delivering against that roadmap. The September release extended our Guppy programming language with tools for programming logical qubits and applying supported error-correction codes, reducing the need to rewrite application logic for each code. The planned December release will expand hybrid workflows, allowing applications to respond to quantum results as they become available, alongside additional codes and execution analytics.
Adoption provides another measure of progress. In the third quarter, 215 organizations were building on Nexus, up nearly 20% from the previous quarter. Total job submissions increased tenfold in the twelve months through August 2026 compared with the preceding twelve-month period.
Our approach also connects quantum computing with high-performance computing and AI. At RIKEN in Japan, Quantinuum’s Reimei quantum computer works alongside the Fugaku supercomputer and ROQUO GPU supercomputer. Researchers are exploring materials and biomolecular chemistry through workflows combining quantum calculations, classical simulation and AI.
Converting Progress into Customer Value
Customer adoption and commitments provide another concrete measure of our leadership.
Our collaborations span financial services, drug development, materials science and logistics, focusing research on specific customer problems. With Johnson & Johnson, we are applying quantum computing and AI to the creation of new cancer-therapy materials. With GE Vernova, we are advancing research into superconducting materials for smaller, lighter and more efficient electrical infrastructure. Our collaboration with Abu Dhabi Maritime Academy and Quincus explores quantum, AI and high-performance computing for maritime and logistics applications.
Customers are also committing across hardware generations. In the third quarter, Quantinuum secured its largest cloud agreement: a multiyear extension with a leading global financial institution that includes committed access to our systems through Apollo using Nexus, supporting fault-tolerant application development and deployment across multiple core business functions.
This is in addition to our Oracle partnership. Plans to deploy Helios within an Oracle Cloud Infrastructure AI data center will place quantum alongside GPU and high-performance computing resources. Through Oracle’s Quantum AI Compute beta program, selected organizations can already explore hybrid quantum and AI applications.
In the third quarter, we also signed an agreement with another leading hyperscaler serving millions of developers and enterprises worldwide, further expanding access to our hardware and software.
Quantinuum is also building and scaling manufacturing partnerships.
Our longstanding partnerships with GlobalFoundries, Infineon, Honeywell Aerospace and Monarch Quantum bring manufacturing expertise into critical-component design early, helping reduce complexity, improve reliability and make production more repeatable. Our finalized CHIPS R&D award further supports these efforts; Quantinuum was the only trapped-ion company selected for the award.
The Future of Quantum Leadership
We believe Quantinuum’s demonstrated performance, software capabilities and customer commitments establish the quantum computing industry’s strongest leadership position.
Our focus is on extending that lead through execution: advancing toward Sol and Apollo, expanding adoption of Nexus, and delivering the capabilities customers need to put quantum computing to work.
Forward-Looking Statements
This post contains forward-looking statements, including statements about Quantinuum's technology and product roadmap (including Sol and Apollo), planned software releases and platform expansion, the scalability and performance of our architecture, and anticipated customer adoption. Words such as "will," "plan," "expect," "believe," "roadmap" and similar expressions identify forward-looking statements. These statements reflect our current expectations and assumptions and are subject to risks and uncertainties, including technical, development, manufacturing, supply chain, partner and market risks, that could cause actual results to differ materially. Forward-looking statements speak only as of the date of this post, and Quantinuum undertakes no obligation to update them, except as required by law.
- RIKEN and Quantinuum have upgraded Reimei to System Model H2, bringing quantum advantage into sight with their hybrid supercomputing platform.
- Using the new quantum processor, a Quantinuum-led frontier project team is combining quantum and classical data to map complex material behavior, using Reimei for classically challenging regimes, the JHPC-quantum GPU supercomputer ROQUO and the supercomputer Fugaku for large-scale simulation and AI, and generative models to predict unexplored conditions.
- A second frontier project is focused on creating a scalable hybrid workflow for biomolecular chemistry, combining quantum computing, supercomputing, and AI to simulate the excited-state properties of complex molecules—with potential applications in drug discovery, advanced materials, and solar energy. Once these projects conclude, Reimei will start regular operations under the Test User Program.
The future of supercomputing just got an upgrade in Japan.
RIKEN and Quantinuum have upgraded the Reimei quantum computer to Quantinuum’s System Model H2, bringing quantum advantage into sight with their hybrid supercomputing platform. Their combination of Reimei, the supercomputer Fugaku, and the ROQUO GPU supercomputer is a world-leading platform that reaches far beyond what any modality can currently offer on its own.
With 56 fully-connected high-fidelity qubits, Reimei is already supporting two frontier projects in quantum materials and biomolecular chemistry. Both are designed to move hybrid computing beyond infrastructure demonstrations and toward high-value scientific applications.
Expanding the landscape of supercomputing
Many scientific problems contain both classically ‘accessible’ and classically ‘inaccessible’ regions.
For example, a classical supercomputer may efficiently explore broad areas of a model’s parameter space but struggle near a phase transition, where correlations grow and the required computational resources increase sharply. In chemistry, classical methods can model much of a molecule accurately but encounter difficulties in small, strongly correlated regions that determine its most important properties. In contrast, quantum computers can often handle these problems deftly, thanks to their native “quantumness”.
We have been working to bring quantum computers together with classical computers, using them as specialized accelerators inside broader heterogeneous computing environments.
RIKEN’s platform is our first instantiation of that vision, bringing together three complementary resources:
- Fugaku, RIKEN’s classical supercomputer, provides large-scale classical modeling, data processing, and established scientific computing methods.
- ROQUO, RIKEN’s GPU supercomputer, supports tensor-network simulation, AI training, and massively parallel computation.
- Reimei, RIKEN’s quantum computer, performs selected calculations involving quantum states and correlations that become prohibitively expensive to represent classically.
Quantinuum Nexus’s hybrid workflow management system coordinates these resources, allowing jobs running on classical infrastructure to submit quantum tasks to Reimei and incorporate the results into a larger calculation.
This foundation has been operational for some time now. A major result from earlier this year used Reimei and Fugaku together to investigate chemical reactions inside biomolecules. Recently, we expanded our work using Fugaku and QPUs: coordinating Reimei and ibm_kobe in a combined VQE–QPE workflow to calculate a simple system’s ground-state energy. In all these cases, quantum hardware augmented the classical supercomputer, with each processor assigned the part of the calculation best suited to its strengths.
The addition of ROQUO now extends this architecture with GPU-accelerated simulation, optimization, and AI. Combined with the upgrade of Reimei to System Model H2, we have launched two frontier projects to push the forefront of scientific computing and prove out Reimei’s capability.
Project 1: GenQAI for materials discovery
The first frontier project brings together quantum simulation, classical tensor networks, and generative AI to investigate many-body physics.
The goal is to discover a sort of ‘treasure map’ for a material: the phase diagram. A phase diagram is a multidimensional map that shows how a material’s properties change when variables like temperature, pressure, or magnetic field are changed. Phase diagrams can hold the secret to exotic properties like superconductivity; can point the way to novel materials for memory devices and energy transfer, or can help to elucidate new medical imaging techniques.
Phase diagrams are extremely valuable, but they can be difficult to calculate or measure. To measure one, you would need a laboratory that could detect material properties at hundreds of points while also generating repeatable parameter changes. Computationally, the problem is similar, but (as mentioned above) one often encounters regions where correlations extend across larger portions of the system, making it incredibly difficult to compute. On top of this, during pre-thermal dynamics or phase transitions, entanglement can grow rapidly, further stretching classical computing capacity.
Reimei is well suited to probing these difficult regimes. We have already used System Model H2 to explore quantum magnetism at scales that frustrate classical approaches. Its high-fidelity operations and flexible qubit connectivity enable the execution of demanding quantum many-body circuits at a scale where matched-accuracy classical simulation can become impractical. But this quantum data is also expensive to generate. The goal is therefore to use it selectively.
ROQUO can perform dense tensor-network simulations across classically tractable regions, parallelizing calculations over model parameters and bond dimensions. This allows Reimei to focus on regimes requiring deep time evolution circuits, where long-range correlations and growing entanglement can sharply increase the cost of classical simulation. Classical data alone is not enough to train a robust generative model across the phase diagram, and that is why quantum data becomes essential.
The team has already collected hardware data for a 6 × 6 two-dimensional spin model, trained a Transformer model for zero-noise extrapolation across the parameter space, and applied active learning to prioritize additional quantum data collection.
Using these results, the team trained a generative AI model capable of learning a parametric representation of the fluctuations and many-body correlations across the combined dataset: the classically reachable and the classically hard regions are both well described by our trained generative model.
Once trained, the generative model is used at inference time on ROQUO to sample the phase diagram at conditions that have not yet been simulated and obtain results for material properties with good accuracy. Step by step, the phase diagram for a material is filled out, generating a ‘treasure map’ of its key behaviors.
For materials researchers, this ‘map’ can add up to a lot. Quantum computers, such as Reimei, could contribute to more accurate predictions of phase diagrams and response functions, helping researchers understand how materials respond to external conditions, a key determinant in electronics, sensing, medical imaging, energy infrastructure, and more.
Project 2: A hybrid blueprint for biomolecular chemistry
The second frontier project applies the same hybrid philosophy to one of quantum computing’s most anticipated applications: the accurate simulation of complex molecules.
Researchers from RIKEN, NVIDIA, and Quantinuum are working together to develop a scalable QPU–GPU–HPC workflow for predicting realistic chemical properties of biomolecular systems. Our initial target is zinc porphyrin, a light-absorbing molecule whose response to light is influenced by its surrounding environment.
While many current projects in quantum computational chemistry are focused on ground state searches, this project focuses on excited states—the electronically energized states involved in processes such as light absorption. These states are typically more complicated to calculate than a molecule’s ground state, but they are essential to understanding how photoactive molecules function in the real world.
As before, the hybrid workflow assigns each part of the calculation to the most appropriate processor:
- Fugaku and conventional HPC methods represent the chromophore’s larger molecular environment and perform the broader chemistry workflow.
- ROQUO’s NVIDIA GPUs support optimization, configuration-interaction calculations, AI-assisted circuit design, and spectral reconstruction.
- Reimei concentrates on strongly correlated electronic regions and searches for important electron configurations that classical methods may miss.
This gives the QPU a focused role: discovering important determinants (candidate electronic configurations) that can enrich the classical calculation. The HPC systems then use those configurations to calculate energies and reconstruct experimentally meaningful properties, including the molecule’s absorption spectrum.
This separation of responsibilities makes the workflow scalable. The QPU is not asked to represent the entire biomolecular environment. Instead, it targets the part of the electronic structure problem where quantum sampling could add information that is difficult to obtain through classical methods alone. To help tackle this, we developed a new hybrid method to solve complicated electronic structure problems.
This approach could provide a blueprint for studying functional biomolecules at the accuracy needed for industrial research. Applications could eventually span drug discovery, biomolecular engineering, advanced materials, and the design of more efficient light-harvesting systems such as solar cells.
A platform for the next era of discovery
Hybrid computing is sometimes described as a future architecture. At RIKEN, these foundations have been operational since 2025 – and they just got a massive upgrade.
Reimei supplies high-fidelity quantum computation. Fugaku provides the scale of a world-leading supercomputer. ROQUO adds accelerated computing and AI. The Nexus workflow management system brings the systems together into coordinated scientific workflows.
Together, they demonstrate a broader principle: the value of quantum computing will not be measured by what a QPU can do in isolation, but by what becomes possible when quantum computers are integrated into the world’s most advanced computing environments.
With Reimei, RIKEN and Quantinuum are building that future now—and building it with Japan.
*Reimei deployment is supported by the New Energy and Industrial Technology Development Organization (NEDO), an organization under the jurisdiction of Japan's Ministry of Economy, Trade and Industry (METI)'s "Development of Integrated Utilization Technology for Quantum and Supercomputers" as part of the "Project for Research and Development of Enhanced Infrastructures for Post 5G Information and Communications Systems."