Quantinuum researchers are unlocking a more efficient and powerful path towards fault tolerance
We've discovered a technique based on “genon braiding” for the construction of logical gates which could be applied to “high rate” error correcting codes
“Computers are useless without error correction”
- Anonymous
If you stumble while walking, you can regain your balance, recover, and keep walking. The ability to function when mistakes happen is essential for daily life, and it permeates everything we do. For example, a windshield can protect a driver even when it’s cracked, and most cars can still drive on a highway if one of the tires is punctured. In fact, most commercially operated planes can still fly with only one engine. All of these things are examples of what engineers call “fault-tolerance”, which just describes a system’s ability to tolerate faults while still functioning.
When building a computer, this is obviously essential. It is a truism that errors will occur (however rarely) in all computers, and a computer that can’t operate effectively and correctly in the presence of faults (or errors) is not very useful. In fact, it will often be wrong - because errors won’t be corrected.
In a new paper from Quantinuum’s world class quantum error correction team, we have made a hugely significant step towards one of the key issues faced in quantum error correction – that of executing fault-tolerant gates with efficient codes.
This work explores the use of “genon braiding” – a cutting-edge concept in the study of topological phases of matter, motivated by the mathematics of category theory, and both related to and inspired by our prior groundbreaking work on non-Abelian anyons.
The native fault tolerant properties of braided toric codes have been theoretically known for some time, and in this newly published work, our team shares how they have discovered a technique based on “genon braiding” for the construction of logical gates which could be applied to “high rate” error correcting codes – meaning codes that require fewer physical qubits per logical qubit, which can have a huge impact on scaling.
Stepping along the path to fault-tolerance
In classical computing, building in fault-tolerance is relatively easy. For starters, the hardware itself is incredibly robust and native error rates are very low. Critically, one can simply copy each bit, so errors are easy to detect and correct.
Quantum computing is, of course, much trickier with challenges that typically don’t exist in classical computing. First off, the hardware itself is incredibly delicate. Getting a quantum computer to work requires us to control the precise quantum states of single atoms. On top of that, there’s a law of physics called the no cloning theorem, which says that you can’t copy qubits. There are also other issues that arise from the properties that make quantum computing so powerful, such as measurement collapse, that must be considered.
Some very distinguished scientists and researchers have thought about quantum error correcting including Steane, Shor, Calderbank, and Kitaev [9601029.pdf (arxiv.org), 9512032.pdf (arxiv.org), arXiv:quant-ph/9707021v1 9 Jul 1997]. They realized that you can entangle groups of physical qubits, store the relevant quantum information in the entangled state (called a “logical qubit”), and, with a lot of very clever tricks, perform computations with error correction.
There are many different ways to entangle groups of physical qubits, but only some of them allow for useful error detection and correction. This special set of entangling protocols is called a “code” (note that this word is used in a different sense than most readers might think of when they hear “code” - this isn’t “Hello World”).
A huge amount of effort today goes into “code discovery” in companies, universities, and research labs, and a great deal of that research is quite bleeding-edge. However, discovering codes is only one piece of the puzzle: once a code is discovered, one must still figure out how to compute with it. With any specific way of entangling physical qubits into a logical qubit you need to figure out how to perform gates, how to infer faults, how to correct them, and so on. It’s not easy!
Quantinuum has one of the world’s leading teams working on error correction and has broken new ground many times in recent years, often with industrial or scientific research partners. Among many firsts, we were the first to demonstrate real-time error correction (meaning a fully-fault tolerant QEC protocol). This included many milestones: repeated real-time error correction, the ability to perform quantum "loops" (repeat-until-success protocols), and real-time decoding to determine the corrections during the computation. We were also the first to perform a logical two-qubit gate on a commercial system. In one of our most recent demonstrations, in partnership with Microsoft, we supported the use of error correcting techniques to achieve the first demonstration of highly reliable logical qubits, confirming our place at the forefront of this research – and indeed confirming that Quantinuum’s H2-1 quantum computer was the first – and at present only – device in the world capable of what Microsoft characterizes as Level 2 Resilient quantum computing.
Introducing new, exotic error correction codes
While codes like the Steane code are well-studied and effective, our team is motivated to investigate new codes with attractive qualities. For example, some codes are “high-rate”, meaning that you get more logical qubits per physical qubit (among other things), which can have a big impact on outlooks for scaling – you might ultimately need 10x fewer physical qubits to perform advanced algorithms like Shor’s.
Implementing high-rate codes is seductive, but as we mentioned earlier we don’t always know how to compute with them. A particular difficulty with high-rate codes is that you end up sharing physical qubits between logical qubits, so addressing individual logical qubits becomes tricky. There are other difficulties that come from sharing physical qubits between logical qubits, such as performing gates between different logical qubits (scientists call this an “inter-block” gate).
One well-studied method for computing with QEC codes is known as “braiding”. The reason it is called braiding is because you move particles, or “braid” them, around each other, which manipulates logical quantum information. In our new paper, we crack open computing with exotic codes by implementing “genon” braiding. With this, we realize a paradigm for constructing logical gates which we believe could be applied to high-rate codes (i.e. inter-block gates).
What exactly “genons” are, and how they are braided, is beautiful and complex mathematics - but the implementation is surprisingly simple. Inter-block logical gates can be realized through simple relabeling and physical operations. “Relabeling”, i.e. renaming qubit 1 to qubit 2, is very easy in Quantinuum’s QCCD architecture, meaning that this approach to gates will be less noisy, faster, and have less overhead. This is all due to our architectures’ native ability to move qubits around in space, which most other architectures can’t do.
Using this framework, our team delivered a number of proof-of-principle experiments on the H1-1 system, demonstrating all single qubit Clifford operations using genon braiding. They then performed two kinds of two-qubit logical gates equivalent to CNOTs, proving that genon braiding works in practice and is comparable to other well-researched codes such as the Steane code.
What does this all mean? This work is a great example of co-design – tailoring codes for our specific and unique hardware capabilities. This is part of a larger effort to find fault-tolerant architectures tailored to Quantinuum's hardware. Quantinuum scientist and pioneer of this work, Simon Burton, put it quite succinctly: “Braiding genons is very powerful. Applying these techniques might prove very useful for realizing high-rate codes, translating to a huge impact on how our computers will scale.”
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.