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.
- Mitsui & Co. and Mitsubishi Electric demonstrated one of the world’s largest approximate Quantum Fourier Transforms (QFT) on Quantinuum Helios, scaling from prior records to 98 physical qubits.
- The collaboration also implemented a logical QFT using a QEC (Quantum Error Correction) code with up to 12 logical qubits.
- The work highlights Quantinuum’s accuracy and flexible architecture.
While there is ongoing debate around the pace of quantum computing’s development, a more grounded way to assess progress is through concrete demonstrations of foundational algorithms at meaningful scale. In this context, Mitsui & Co. and Mitsubishi Electric are taking a pragmatic view of quantum progress—focusing on how close the field is to executing core algorithmic primitives that underpin many potential industrial applications, rather than relying on abstract milestones or timelines.
In a new white paper, the industrial giants teamed up with Quantinuum to measure how close we are to running the Quantum Fourier Transform (QFT), a widely-used algorithmic primitive, at scales necessary for industrial applications. In the process, the team successfully ran one of the largest instances of the approximate QFT ever demonstrated. This achievement matters because the QFT is an essential primitive that underpins many of the quantum algorithms expected to deliver practical advantages.
You may have heard of the (classical) Fourier transform (FT), due to its ubiquity throughout modern computing. The FT is essential in everything from image analysis to data compression, with almost limitless applications in between. The quantum Fourier transform (QFT) is similar; it’s used in everything from chemistry to finance.
Because the QFT is a foundational primitive underpinning many quantum algorithms, demonstrating it at larger scales and higher fidelity is a practical way to measure quantum computing readiness. This is exactly the type of benchmarking that organizations should consider to understand where today’s systems are useful, and to see how fault-tolerant approaches are progressing. Ultimately, algorithm-level benchmarking like this is one of the most useful ways to understand not just where we are, but where we are going.
A Transformative Approach
Primitives like Fourier Transform are so widespread because they simplify problems by transforming them into something that is easier to deal with. At Quantinuum, we are very interested in transforms: not only are they crucial for industrial applications but they can also simplify algorithms, making them possible to run now instead of later. This ‘transformational’ approach extends beyond the QFT - other transforms exist, and we have even invented our own quantum-native transforms.
Using our Helios quantum computer and Guppy language, the joint team explored running the QFT on both physical qubits and on logical qubits, showing that fault tolerance is progressing quickly. Running the QFT on 98 physical qubits; the paper shows a clear progression from previous results.
Then, using the Steane code, one of the best-studied quantum error correcting codes, the team used Helios’ 98 physical qubits to form 12 logical qubits, successfully running the QFT with the mechanisms of quantum error correction interwoven into the algorithm. This marks a crucial step forward for the field.
Foundational Progress
Taken together, these results provide a more concrete lens through which to view progress in quantum computing: not as abstract projections, but as measurable advances in the execution of foundational algorithms at increasing scale. By benchmarking the Quantum Fourier Transform on both physical and logical qubits, Mitsui & Co. and Mitsubishi Electric are helping to clarify what today’s hardware can already achieve, and where fault-tolerant approaches begin to extend those limits.
More broadly, the organizations best positioned to benefit from quantum computing will be those that focus on these foundational capabilities early, and use them to build a clear, evidence-based understanding of how the technology fits into their business goals.
It is believed that unlocking answers to some of the most complex scientific and industrial problems will require the seamless integration of high-performance computing (HPC), generative AI (GenAI), and quantum computing. Toward this goal, Quantinuum, NVIDIA, and a major pharmaceutical company have successfully demonstrated the first step in a proof-of-principle framework designed to connect these three distinct computing paradigms for industrially relevant computational chemistry.
This milestone, enabled by three industry leaders and experts in their respective domains, serves as a foundational capability that could support the development of future hybrid quantum-AI workflows to help optimize industrial research and development (R&D).
The potential value is a path toward more automated, repeatable, and scalable workflows for translating chemistry problems into executable quantum programs—capabilities that could eventually make hybrid computing easier to deploy in industrial R&D.
The GenQAI Framework
The framework, termed Generative Quantum AI (GenQAI), involved a quantum computer simulating a pharmaceutical compound using programming instructions generated by an AI model, which itself was trained on quantum data that was simulated using HPC.
While the vision for GenQAI explores how future industrial simulation workflows might be optimized by training AI models using quantum data derived directly from a quantum computer, the framework currently consists of four main technical steps:
- Simulating quantum data: The process began by simulating quantum data with NVIDIA accelerated computing using NVIDIA CUDA-Q.
- Fine-tuning the AI: This simulated quantum data was used to fine-tune a pre-trained AI model from the open NVIDIA Nemotron family.
- Generating instructions: The AI model then generated quantum circuits, which are the programming instructions required for the quantum simulation.
- Validating accuracy: To validate the results, the circuits were run on Quantinuum’s Helios quantum computer using its InQuanto quantum chemistry platform.
The core novelty of this development lies within the process of the framework itself. In this proof-of-principle experiment, an AI model fine-tuned on simulated quantum data generated circuits that were successfully executed and validated on Quantinuum’s Helios system. Rather than delivering an immediate commercial advantage, this achievement establishes a credible, verifiable baseline for how HPC, AI, and quantum computing can function in tandem.
The Case Study
The validation of the framework represents an early step toward the goal of developing scalable architectures for the pharmaceutical industry.
With a shared view toward eventually scaling the framework for pharmaceutical R&D applications, the researchers simulated a pharmaceutical compound: imipramine. This anti-depressant was chosen because it serves as a model compound for drug degradation and shelf-life studies, which are standard components of the pharmaceutical R&D lifecycle.
Developing hybrid infrastructure that enterprises may adopt requires a deep, coordinated effort among domain experts. As such, this successful test highlights the value of combining the strengths of a quantum computing hardware and software leader (Quantinuum), with a hybrid-quantum classical platform (NVIDIA), and a leading enterprise end-user to build and test future computing capabilities for industrial chemistry.
Scaling the Framework
Although demonstrated on a pharmaceutical compound, the architecture could eventually inform similar molecular-simulation workflows in sectors such as energy, agriculture, advanced materials, and electronics. At this stage, it provides a reference for further testing and development.
Engage Further
Access the paper here to explore the full technical details of this demonstration and contact our team to learn more about joining Quantinuum’s enterprise partner network.
Quantinuum is pleased to announce that applications are now open for the Quantinuum SG Grand Challenge 2026, a global innovation challenge designed to bring together researchers, developers, scientists and innovators to explore practical applications of quantum computing.
Organized by Quantinuum and supported by Singapore's National Quantum Office and Aqora, the three-month program aims to foster collaboration across academia, industry and the quantum developer community while supporting the continued growth of Singapore's quantum ecosystem.
A Platform for Quantum Computing Innovation
Participants will work in teams to develop solutions across a range of challenge areas, including chemistry and molecular simulation, optimization, AI for quantum systems, quantum error correction, condensed matter and materials science, and open innovation. Throughout the program, participants will have access to mentoring, technical enablement and Quantinuum quantum computing resources.
Singapore Grand Finale
Selected finalist teams will be invited to present their work at the Grand Finale hosted in Singapore before representatives from academia, and industry. The event will celebrate innovative applications of quantum computing while providing an opportunity for participants to engage with Singapore's growing quantum community.
Join the Challenge
The Quantinuum SG Grand Challenge welcomes participants from around the world. Whether you are an experienced quantum researcher or beginning your quantum computing journey, the program offers an opportunity to collaborate, learn and contribute to the development of practical quantum applications.
Applications are now open. Spaces are limited and subject to review and approval.