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.
One of the greatest privileges of working directly with the world’s most powerful quantum computer at Quantinuum is building meaningful experiments that convert theory into practice. The privilege becomes even more compelling when considering that our current quantum processor – our H2 system – will soon be enhanced by Helios, a quantum computer a stunning trillion times more powerful, and due for launch in just a few months. The moment has now arrived when we can build a timeline for applications that quantum computing professionals have anticipated for decades and which are experimentally supported.
Background
In the 1980s, in the years after Richard Feynman and David Deutsch were working on their initial thoughts around quantum computing, Nicholas Cozzarelli at the University of California, Berkeley, was grappling with a biochemical riddle – “how do enzymes called topoisomerases and recombinases untangle the DNA strands that knot themselves inside cells?”
Cozarelli teamed up with mathematicians including De Witt Sumners, who recognized that these twisted strands could be modelled using the language of knots.
Knot theory’s equations let them deduce how enzymes snipped, flipped and reattached DNA, demystifying processes essential to life. Decoding the knots in DNA proved crucial to designing better antibiotics and in advancing genetic engineering.
Cozzarelli’s team took advantage of the power of knot invariants—polynomial expressions that remain consistent markers of a knot’s identity, no matter how tangled the loops become. This is just one example of how knot theory has been used to solve real-world problems of practical value.
Today, knot theory finds practical uses in fields as diverse as chemistry, robotics, fluid dynamics, and drug design. Measuring the invariants that characterize each knot is a challenge that scales exponentially with the complexity of the knots.
This work shows how a quantum computer can cut through this exponential explosion, indicating that Quantinuum's next-generation systems will offer practical quantum advantage in solving knot theory problems.
In this article, Konstantinos Meichanetzidis, a team leader from Quantinuum’s AI group, explains intriguing and valuable new research into applying quantum computers to addressing problems in knot theory.
Quantifying quantum advantage for knot theory
Quantinuum’s applied quantum algorithms team has published a historic end-to-end algorithm for solving a famous problem in knot theory, via a preprint paper on the arXiv. The research team, led by Konstantinos Meichanetzidis, also included Quantinuum researchers Enrico Rinaldi, Chris Self, Eli Chertkov, Matthew DeCross, David Hayes, Brian Neyenhuis, Marcello Benedetti, and Tuomas Laakkonen of the Massachusetts Institute of Technology.
The project was motivated by building configurable and comprehensive algorithmic tools to pinpoint quantum advantage in practice. This was done by rigorously defining time and error budgets and quantifying both the classical and quantum resource requirements necessary to meet them. Considering realistic quantum and classical processors, they predict that Quantinuum’s forthcoming quantum computers meet those requirements.
Knot theory is a field of mathematics called ‘low-dimensional topology’, with a rich history, stemming from a wild idea proposed by lord Kelvin, who conjectured that chemical elements are different knots formed by vortices in the ether. Of course, we know today that the ether theory did not hold up under experimental scrutiny, but mathematicians have been classifying and studying knots ever since. Knot theory is intrinsically linked with many aspects of physics. For example, it naturally shows up in certain spin models in statistical mechanics. Today, physical properties of knots are important in understanding the stability of macromolecular structures, from DNA and proteins, to polymers relevant to materials design. Knots find their way into cryptography. Even the magnetohydrodynamical properties of knotted magnetic fields on the surface of the sun are an important indicator of solar activity.
Most importantly for our context, knot theory has fundamental connections to quantum computation, originally outlined by Witten’s work in topological quantum field theory, concerning spacetimes without any notion of distance but only shape. In fact, this connection formed the very motivation for attempting to build topological quantum computers, where anyons – exotic quasiparticles that live in two-dimensional materials – are braided to perform quantum gates.
Konstantinos Meichanetzidis, who led the project, said: “The relation between knot theory and quantum physics is the most beautiful and bizarre fact you have never heard of.”
The fundamental problem in knot theory is distinguishing knots, or more generally, links. To this end, mathematicians have defined link invariants, which serve as ‘fingerprints’ of a link. As there are many equivalent representations of the same link, an invariant, by definition, is the same for all of them. If the invariant is different for two links then they are not equivalent. The specific invariant our team focused on is the Jones polynomial.
The mind-blowing fact here is that any quantum computation corresponds to evaluating the Jones polynomial of some link, as shown by the works of Freedman, Larsen, Kitaev, Wang, Shor, Arad, and Aharonov. It reveals that this abstract mathematical problem is truly quantum native. In particular, the problem our team tackled was estimating the Jones polynomial at the 5th root of unity. This is a well-studied case due to its relation to the infamous Fibonacci anyons, whose braiding is capable of universal quantum computation.
Building and improving on the work of Shor, Aharonov, Landau, Jones, and Kauffman, our team developed an efficient quantum algorithm that works end-to end. That is, given a link, it outputs a highly optimized quantum circuit that is readily executable on our processors and estimates the desired quantity. Furthermore, our team designed problem-tailored error detection and error mitigation strategies to achieve a higher accuracy.
In addition to providing a full pipeline for solving this problem, a major aspect of this work was to use the fact that the Jones polynomial is an invariant to introduce a benchmark for noisy quantum computers. Most importantly, this benchmark is efficiently verifiable, a rare property since for most applications, exponentially costly classical computations are necessary for verification. Given a link whose Jones polynomial is known, the benchmark constructs a large set of topologically equivalent links of varying sizes. In turn, these result in a set of circuits of varying numbers of qubits and gates, all of which should return the same answer. Thus, one can characterize the effect of noise present in a given quantum computer by quantifying the deviation of its output from the known result.
The benchmark introduced in this work allows one to identify the link sizes for which there is exponential quantum advantage in terms of time to solution against the state-of-the-art classical methods. These resource estimates indicate our next processor, Helios, with 96 qubits and at least 99.95% two-qubit gate-fidelity, is extremely close to meeting these requirements. Furthermore, Quantinuum’s hardware roadmap includes even more powerful machines that will come online by the end of the decade. Notably, an advantage in energy consumption emerges for even smaller link sizes. Meanwhile, our teams aim to continue reducing errors through improvements in both hardware and software, thereby moving deeper into quantum advantage territory.
The importance of this work, indeed the uniqueness of this work in the quantum computing sector, is its practical end-to-end approach. The advantage-hunting strategies introduced are transferable to other “quantum-easy classically hard” problems.
Our team’s efforts motivate shifting the focus toward specific problem instances rather than broad problem classes, promoting an engineering-oriented approach to identifying quantum advantage. This involves carefully considering how quantum advantage should be defined and quantified, thereby setting a high standard for quantum advantage in scientific and mathematical domains. And thus making sure we instill confidence in our customers and partners.
Quantinuum and NVIDIA, world leaders in their respective sectors, are combining forces to fast-track commercially scalable quantum supercomputers, further bolstering the announcement Quantinuum made earlier this year about the exciting new potential in Generative Quantum AI.
Make no mistake about it, the global quantum race is on. With over $2 billion raised by companies in 2024 alone, and over 150 new startups in the past five years, quantum computing is no longer restricted to ‘the lab’.
The United Nations proclaimed 2025 as the International Year of Quantum Science and Technology (IYQ), and as we march toward the end of the first quarter, the old maxim that quantum computing is still a decade (or two, or three) away is no longer relevant in today’s world. Governments, commercial enterprises and scientific organizations all stand to benefit from quantum computers, led by those built by Quantinuum.
That is because, amid the flurry of headlines and social media chatter filled with aspirational statements of future ambitions shared by those in the heat of this race, we at Quantinuum continue to lead by example. We demonstrate what that future looks like today, rather than relying solely on slide deck presentations.
Our quantum computers are the most powerful systems in the world. Our H2 system, the only quantum computer that cannot be classically simulated, is years ahead of any other system being developed today. In the coming months, we’ll introduce our customers to Helios, a trillion times more powerful than H2, further extending our lead beyond where the competition is still only planning to be.
At Quantinuum, we have been convinced for years that the impact of quantum computers on the real world will happen earlier than anticipated. However, we have known that impact will be when powerful quantum computers and powerful classical systems work together.
This sort of hybrid ‘supercomputer’ has been referenced a few times in the past few months, and there is, rightly, a sense of excitement about what such an accelerated quantum supercomputer could achieve.
The Power of Hybrid Quantum and Classical Compute
In a revolutionary move on March 18th, 2025, at the GTC AI conference, NVIDIA announced the opening of a world-class accelerated quantum research center with Quantinuum selected as a key founding collaborator to work on projects with NVIDIA at the center.
With details shared in an accompanying press statement and blog post, the NVIDIA Accelerated Quantum Research Center (NVAQC) being built in Boston, Massachusetts, will integrate quantum computers with AI supercomputers to ultimately explore how to build accelerated quantum supercomputers capable of solving some of the world’s most challenging problems. The center will begin operations later this year.
As shared in Quantinuum’s accompanying statement, the center will draw on the NVIDIA CUDA-Q platform, alongside a NVIDIA GB200 NVL72 system containing 576 NVIDIA Blackwell GPUs dedicated to quantum research.
The Role of CUDA-Q in Quantum-Classical Integration
Integrating quantum and classical hardware relies on a platform that can allow researchers and developers to quickly shift context between these two disparate computing paradigms within a single application. NVIDIA CUDA-Q platform will be the entry-point for researchers to exploit the NVAQC quantum-classical integration.
In 2022, Quantinuum became the first company to bring CUDA-Q to its quantum systems, establishing a pioneering collaboration that continues to today. Users of CUDA-Q are currently offered access to Quantinuum’s System H1 QPU and emulator for 90 days.
Quantinuum’s future systems will continue to support the CUDA-Q platform. Furthermore, Quantinuum and NVIDIA are committed to evolving and improving tools for quantum classical integration to take advantage of the latest hardware features, for example, on our upcoming Helios generation.
The Gen-Q-AI Moment
A few weeks ago, we disclosed high level details about an AI system that we refer to as Generative Quantum AI, or GenQAI. We highlighted a timeline between now and the end of this year when the first commercial systems that can accelerate both existing AI and quantum computers.
At a high level, an AI system such as GenQAI will be enhanced by access to information that has not previously been accessible. Information that is generated from a quantum computer that cannot be simulated. This information and its effect can be likened to a powerful microscope that brings accuracy and detail to already powerful LLM’s, bridging the gap from today’s impressive accomplishments towards truly impactful outcomes in areas such as biology and healthcare, material discovery and optimization.
Through the integration of the most powerful in quantum and classical systems, and by enabling tighter integration of AI with quantum computing, the NVAQC will be an enabler for the realization of the accelerated quantum supercomputer needed for GenQAI products and their rapid deployment and exploitation.
Innovating our Roadmap
The NVAQC will foster the tools and innovations needed for fully fault-tolerant quantum computing and will be enabler to the roadmap Quantinuum released last year.
With each new generation of our quantum computing hardware and accompanying stack, we continue to scale compute capabilities through more powerful hardware and advanced features, accelerating the timeline for practical applications. To achieve these advances, we integrate the best CPU and GPU technologies alongside our quantum innovations. Our long-standing collaboration with NVIDIA drives these advancements forward and will be further enriched by the NVAQC.
Here are a couple of examples:
In quantum error correction, error syndromes detected by measuring "ancilla" qubits are sent to a "decoder." The decoder analyzes this information to determine if any corrections are needed. These complex algorithms must be processed quickly and with low latency, requiring advanced CPU and GPU power to calculate and apply corrections keeping logical qubits error-free. Quantinuum has been collaborating with NVIDIA on the development of customized GPU-based decoders which can be coupled with our upcoming Helios system.
In our application space, we recently announced the integration of InQuanto v4.0, the latest version of Quantinuum’s cutting edge computational chemistry platform, with NVIDIA cuQuantum SDK to enable previously inaccessible tensor-network-based methods for large-scale and high-precision quantum chemistry simulations.
Our work with NVIDIA underscores the partnership between quantum computers and classical processors to maximize the speed toward scaled quantum computers. These systems offer error-corrected qubits for operations that accelerate scientific discovery across a wide range of fields, including drug discovery and delivery, financial market applications, and essential condensed matter physics, such as high-temperature superconductivity.
We look forward to sharing details with our partners and bringing meaningful scientific discovery to generate economic growth and sustainable development for all of humankind.
In the rapidly advancing world of quantum computing, to be a leader means not just keeping pace with innovation but driving it forward. It means setting new standards that shape the future of quantum computing performance. A recent independent study comparing 19 quantum processing units (QPUs) on the market today has validated what we’ve long known to be true: Quantinuum’s systems are the undisputed leaders in performance.
The Benchmarking Study
A comprehensive study conducted by a joint team from the Jülich Supercomputing Centre, AIDAS, RWTH Aachen University, and Purdue University compared QPUs from leading companies like IBM, Rigetti, and IonQ, evaluating how well each executed the Quantum Approximate Optimization Algorithm (QAOA), a widely used algorithm that provides a system level measure of performance. After thorough examination, the study concluded that:
“...the performance of quantinuum H1-1 and H2-1 is superior to that of the other QPUs.”
Quantinuum emerged as the clear leader, particularly in full connectivity, the most critical category for solving real-world optimization problems. Full connectivity is a huge comparative advantage, offering more computational power and more flexibility in both error correction and algorithmic design. Our dominance in full connectivity—unattainable for platforms with natively limited connectivity—underscores why we are the partner of choice in quantum computing.
Leading Across the Board
We take benchmarking seriously at Quantinuum. We lead in nearly every industry benchmark, from best-in-class gate fidelities to a 4000x lead in quantum volume, delivering top performance to our customers.
Our Quantum Charged-coupled Device (QCCD) architecture has been the foundation of our success, delivering consistent performance gains year-over-year. Unlike other architectures, QCCD offers all-to-all connectivity, world-record fidelities, and advanced features like real-time decoding. Altogether, it’s clear we have superior performance metrics across the board.
While many claim to be the best, we have the data to prove it. This table breaks down industry benchmarks, using the leading commercial spec for each quantum computing architecture.
These metrics are the key to our success. They demonstrate why Quantinuum is the only company delivering meaningful results to customers at a scale beyond classical simulation limits.
Our progress builds upon a series of Quantinuum’s technology breakthroughs, including the creation of the most reliable and highest-quality logical qubits, as well as solving the key scalability challenge associated with ion-trap quantum computers — culminating in a commercial system with greater than 99.9% two-qubit gate fidelity.
From our groundbreaking progress with System Model H2 to advances in quantum teleportation and solving the wiring problem, we’re taking major steps to tackle the challenges our whole industry faces, like execution speed and circuit depth. Advancements in parallel gate execution, faster ion transport, and high-rate quantum error correction (QEC) are just a few ways we’re maintaining our lead far ahead of the competition.
This commitment to excellence ensures that we not only meet but exceed expectations, setting the bar for reliability, innovation, and transformative quantum solutions.
Onward and Upward
To bring it back to the opening message: to be a leader means not just keeping pace with innovation but driving it forward. It means setting new standards that shape the future of quantum computing performance.
We are just months away from launching Quantinuum’s next generation system, Helios, which will be one trillion times more powerful than H2. By 2027, Quantinuum will launch the industry’s first 100-logical-qubit system, featuring best-in-class error rates, and we are on track to deliver fault-tolerant computation on hundreds of logical qubits by the end of the decade.
The evidence speaks for itself: Quantinuum is setting the standard in quantum computing. Our unrivaled specs, proven performance, and commitment to innovation make us the partner of choice for those serious about unlocking value with quantum computing. Quantinuum is committed to doing the hard work required to continue setting the standard and delivering on our promises. This is Quantinuum. This is leadership.
Dr. Chris Langer is a Fellow, a key inventor and architect for the Quantinuum hardware, and serves as an advisor to the CEO.
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