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.
As organizations assess the impact of quantum computing on cryptography, many focus on algorithm migration and timelines. But preparing for PQC requires a broader view—one that includes not just new algorithms, but also the quality of the inputs that support them, including randomness.
That’s why Quantinuum joined with partners Thales, Keyfactor, and IBM Consulting to form the QSafe 360 Alliance, a collaboration focused on helping organizations build crypto-agile security architectures that are ready for the quantum era. Together, we’ve released a whitepaper—Digital Trust & Cybersecurity After Quantum Computing—to offer practical guidance on post-quantum readiness, from discovery and planning to deployment.
Lessons from Past Vulnerabilities
The history of cryptography offers clear examples of what happens when randomness fail, and how long those issues can go unnoticed. The Polynonce attack, first disclosed in 2023, exploited weak randomness in Bitcoin transaction signatures and enabled the theft of at least $25 million across 773 wallets. The vulnerability persisted undetected for nine years. The Randstorm disclosure, published in 2022, revealed that biased key generation in widely used Bitcoin wallet libraries exposed millions of wallets—across a window of more than a decade (2011–2022). In both cases, cryptographic algorithms functioned as designed; it was the randomness beneath them that silently failed, leaving companies vulnerable for many years
Post-Quantum Cryptography Inherits These Risks
Post-quantum cryptography (PQC) algorithms are being designed to resist attacks from quantum computers. But they still depend on random values to generate key material. That means any implementation of PQC inherits the same reliance on randomness—but without a way to prove its quality, that layer remains a potential vulnerability.
As security teams run cryptographic inventories, develop crypto-agility plans, or build software bill-of-materials (SBOMs) for PQC migration, it’s important to include randomness in that scope. No matter how strong the algorithm, poor randomness can undermine its security from the start.
A New Approach: Proven Randomness
Quantum Origin takes a fundamentally different approach to randomness quality to deliver proven randomness which improves key generation, algorithms, and the entire security stack. It leverages strong seeded randomness extractors—mathematical algorithms that transform even weak local entropy into provably secure output. These extractors are uniquely powered by a Quantum Seed, which is generated once by Quantinuum's quantum computers using quantum processes verified through Bell tests.
This one-time quantum generation enables Quantum Origin as a software-only solution designed for maximum flexibility. It works with existing infrastructure—on cloud systems, on-premises environments, air-gapped networks, and embedded platforms—without requiring special hardware or a network connection. It's also validated to NIST SP 800-90B standards (Entropy Source Validation #E214). This approach strengthens today’s deployments of AES, RSA, ECC, and other algorithms, and lays a secure foundation for implementing the NIST PQC algorithms.
The QSafe 360 Alliance
The QSafe 360 Alliance whitepaper outlines the path to post-quantum readiness, emphasizing crypto-agility as a guiding principle: the ability to adapt cryptographic systems without major disruption, from randomness to key generation to algorithmic strength.
For security architects, CISOs, and cryptographic engineering teams building their post-quantum transition strategies, randomness is not a peripheral concern. It is a starting point.
The QSafe 360 Alliance whitepaper offers valuable guidance on structuring a comprehensive PQC journey. As you explore that framework, consider how proven randomness—available today—will help strengthen your security posture from the ground up.
Our quantum algorithms team has been hard at work exploring solutions to continually optimize our system’s performance. Recently, they’ve invented a novel technique, called the Quantum Paldus Transform (QPT), that can offer significant resource savings in future applications.
The transform takes complex representations and makes them simple, by transforming into a different “basis”. This is like looking at a cube from one angle, then rotating it and seeing just a square, instead. Transformations like this save resources because the more complex your problem looks, the more expensive it is to represent and manipulate on qubits.
You’ve changed
While it might sound like magic, transforms are a commonly used tool in science and engineering. Transforms simplify problems by reshaping them into something that is easier to deal with, or that provides a new perspective on the situation. For example, sound engineers use Fourier transforms every day to look at complex musical pieces in terms of their frequency components. Electrical engineers use Laplace transforms; people who work in image processing use the Abel transform; physicists use the Legendre transform, and so on.
In a new paper outlining the necessary tools to implement the QPT, Dr. Nathan Fitzpatrick and Mr. Jędrzej Burkat explain how the QPT will be widely applicable in quantum computing simulations, spanning areas like molecular chemistry, materials science, and semiconductor physics. The paper also describes how the algorithm can lead to significant resource savings by offering quantum programmers a more efficient way of representing problems on qubits.
Symmetry is key
The efficiency of the QPT stems from its use of one of the most profound findings in the field of physics: that symmetries drive the properties of a system.
While the average person can “appreciate” symmetry, for example in design or aesthetics, physicists understand symmetry as a much more profound element present in the fabric of reality. Symmetries are like the universe’s DNA; they lead to conservation laws, which are the most immutable truths we know.
Back in the 1920’s, when women were largely prohibited from practicing physics, one of the great mathematicians of the century, Emmy Noether, turned her attention to the field when she was tasked with helping Einstein with his work. In her attempt to solve a problem Einstein had encountered, Dr. Noether realized that all the most powerful and fundamental laws of physics, such as “energy can neither be created nor destroyed” are in fact the consequence of a deep simplicity – symmetry – hiding behind the curtains of reality. Dr. Noether’s theorem would have a profound effect on the trajectory of physics.
In addition to the many direct consequences of Noether’s theorem is a longstanding tradition amongst physicists to treat symmetry thoughtfully. Because of its role in the fabric of our universe, carefully considering the symmetries of a system often leads to invaluable insights.
Einstein, Pauli and Noether walk into a bar...
Many of the systems we are interested in simulating with quantum computers are, at their heart, systems of electrons. Whether we are looking at how electrons move in a paired dance inside superconductors, or how they form orbitals and bonds in a chemical system, the motion of electrons are at the core.
Seven years after Noether published her blockbuster results, Wolfgang Pauli made waves when he published the work describing his Pauli exclusion principle, which relies heavily on symmetry to explain basic tenets of quantum theory. Pauli’s principle has enormous consequences; for starters, describing how the objects we interact with every day are solid even though atoms are mostly empty space, and outlining the rules of bonds, orbitals, and all of chemistry, among other things.
Symmetry in motion
It is Pauli's symmetry, coupled with a deep respect for the impact of symmetry, that led our team at Quantinuum to the discovery published today.
In their work, they considered the act of designing quantum algorithms, and how one’s design choices may lead to efficiency or inefficiency.
When you design quantum algorithms, there are many choices you can make that affect the final result. Extensive work goes into optimizing each individual step in an algorithm, requiring a cyclical process of determining subroutine improvements, and finally, bringing it all together. The significant cost and time required is a limiting factor in optimizing many algorithms of interest.
This is again where symmetry comes into play. The authors realized that by better exploiting the deepest symmetries of the problem, they could make the entire edifice more efficient, from state preparation to readout. Over the course of a few years, a team lead Dr. Fitzpatrick and his colleague Jędrzej Burkat slowly polished their approach into a full algorithm for performing the QPT.
The QPT functions by using Pauli’s symmetry to discard unimportant details and strip the problem down to its bare essentials. Starting with a Paldus transform allows the algorithm designer to enjoy knock-on effects throughout the entire structure, making it overall more efficient to run.
“It’s amazing to think how something we discovered one hundred years ago is making quantum computing easier and more efficient,” said Dr. Nathan Fitzpatrick.
Ultimately, this innovation will lead to more efficient quantum simulation. Projects we believed to still be many years out can now be realized in the near term.
Transforming the future
The discovery of the Quantum Paldus Transform is a powerful reminder that enduring ideas—like symmetry—continue to shape the frontiers of science. By reaching back into the fundamental principles laid down by pioneers like Noether and Pauli, and combining them with modern quantum algorithm design, Dr. Fitzpatrick and Mr. Burkat have uncovered a tool with the potential to reshape how we approach quantum computation.
As quantum technologies continue their crossover from theoretical promise to practical implementation, innovations like this will be key in unlocking their full potential.
In a new paper in Nature Physics, we've made a major breakthrough in one of quantum computing’s most elusive promises: simulating the physics of superconductors. A deeper understanding of superconductivity would have an enormous impact: greater insight could pave the way to real-world advances, like phone batteries that last for months, “lossless” power grids that drastically reduce your bills, or MRI machines that are widely available and cheap to use. The development of room-temperature superconductors would transform the global economy.
A key promise of quantum computing is that it has a natural advantage when studying inherently quantum systems, like superconductors. In many ways, it is precisely the deeply ‘quantum’ nature of superconductivity that makes it both so transformative and so notoriously difficult to study.
Now, we are pleased to report that we just got a lot closer to that ultimate dream.
Making the impossible possible
To study something like a superconductor with a quantum computer, you need to first “encode” the elements of the system you want to study onto the qubits – in other words, you want to translate the essential features of your material onto the states and gates you will run on the computer.
For superconductors in particular, you want to encode the behavior of particles known as “fermions” (like the familiar electron). Naively simulating fermions using qubits will result in garbage data, because qubits alone lack the key properties that make a fermion so unique.
Until recently, scientists used something called the “Jordan-Wigner” encoding to properly map fermions onto qubits. People have argued that the Jordan-Wigner encoding is one of the main reasons fermionic simulations have not progressed beyond simple one-dimensional chain geometries: it requires too many gates as the system size grows.
Even worse, the Jordan-Wigner encoding has the nasty property that it is, in a sense, maximally non-fault-tolerant: one error occurring anywhere in the system affects the whole state, which generally leads to an exponential overhead in the number of shots required. Due to this, until now, simulating relevant systems at scale – one of the big promises of quantum computing – has remained a daunting challenge.
Theorists have addressed the issues of the Jordan-Wigner encoding and have suggested alternative fermionic encodings. In practice, however, the circuits created from these alternative encodings come with large overheads and have so far not been practically useful.
We are happy to report that our team developed a new way to compile one of the new, alternative, encodings that dramatically improves both efficiency and accuracy, overcoming the limitations of older approaches. Their new compilation scheme is the most efficient yet, slashing the cost of simulating fermionic hopping by an impressive 42%. On top of that, the team also introduced new, targeted error mitigation techniques that ensure even larger systems can be simulated with far fewer computational "shots"—a critical advantage in quantum computing.
Using their innovative methods, the team was able to simulate the Fermi-Hubbard model—a cornerstone of condensed matter physics— at a previously unattainable scale. By encoding 36 fermionic modes into 48 physical qubits on System Model H2, they achieved the largest quantum simulation of this model to date.
This marks an important milestone in quantum computing: it demonstrates that large-scale simulations of complex quantum systems, like superconductors, are now within reach.
Unlocking the Quantum Age, One Breakthrough at a Time
This breakthrough doesn’t just show how we can push the boundaries of what quantum computers can do; it brings one of the most exciting use cases of quantum computing much closer to reality. With this new approach, scientists can soon begin to simulate materials and systems that were once thought too complex for the most powerful classical computers alone. And in doing so, they’ve unlocked a path to potentially solving one of the most exciting and valuable problems in science and technology: understanding and harnessing the power of superconductivity.
The future of quantum computing—and with it, the future of energy, electronics, and beyond—just got a lot more exciting.