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ҹɫֱ 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

June 17, 2024
“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 from ҹɫֱ’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 .

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 [ ]. 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!

ҹɫֱ 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, . 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. In one of our most recent demonstrations, in partnership with Microsoft, we supported the use of error correcting techniques to achieve , confirming our place at the forefront of this research – and indeed confirming that ҹɫֱ’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 , 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 ҹɫֱ’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 ҹɫֱ's hardware. ҹɫֱ 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 ҹɫֱ

ҹɫֱ, the world’s largest integrated quantum company, pioneers powerful quantum computers and advanced software solutions. ҹɫֱ’s technology drives breakthroughs in materials discovery, cybersecurity, and next-gen quantum AI. With over 500 employees, including 370+ scientists and engineers, ҹɫֱ leads the quantum computing revolution across continents.

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March 28, 2025
Being Useful Now – Quantum Computers and Scientific Discovery

The most common question in the public discourse around quantum computers has been, “When will they be useful?” We have an answer.

Very recently in Nature we a successful demonstration of a quantum computer generating certifiable randomness, a critical underpinning of our modern digital infrastructure. We explained how we will be taking a product to market this year, based on that advance – one that could only be achieved because we have the world’s most powerful quantum computer.

Today, we have made another huge leap in a different domain, providing fresh evidence that our quantum computers are the best in the world. In this case, we have shown that our quantum computers can be a useful tool for advancing scientific discovery.

Understanding magnetism

Our latest shows how our quantum computer rivals the best classical approaches in expanding our understanding of magnetism. This provides an entry point that could lead directly to innovations in fields from biochemistry, to defense, to new materials. These are tangible and meaningful advances that will deliver real world impact.

To achieve this, we partnered with researchers from Caltech, Fermioniq, EPFL, and the Technical University of Munich. The team used ҹɫֱ’s System Model H2 to simulate quantum magnetism at a scale and level of accuracy that pushes the boundaries of what we know to be possible.

As the authors of the paper state:

“We believe the quantum data provided by System Model H2 should be regarded as complementary to classical numerical methods, and is arguably the most convincing standard to which they should be compared.”

Our computer simulated the quantum Ising model, a model for quantum magnetism that describes a set of magnets (physicists call them ‘spins’) on a lattice that can point up or down, and prefer to point the same way as their neighbors. The model is inherently “quantum” because the spins can move between up and down configurations by a process known as “quantum tunneling”.  

Gaining material insights

Researchers have struggled to simulate the dynamics of the Ising model at larger scales due to the enormous computational cost of doing so. Nobel laureate physicist Richard Feynman, who is widely considered to be the progenitor of quantum computing, once said, “.” When attempting to simulate quantum systems at comparable scales on classical computers, the computational demands can quickly become overwhelming. It is the inherent ‘quantumness’ of these problems that makes them so hard classically, and conversely, so well-suited for quantum computing.

These inherently quantum problems also lie at the heart of many complex and useful material properties. The quantum Ising model is an entry point to confront some of the deepest mysteries in the study of interacting quantum magnets. While rooted in fundamental physics, its relevance extends to wide-ranging commercial and defense applications, including medical test equipment, quantum sensors, and the study of exotic states of matter like superconductivity.  

Instead of tailored demonstrations that claim ‘quantum advantage’ in contrived scenarios, our breakthroughs announced this week prove that we can tackle complex, meaningful scientific questions difficult for classical methods to address. In the work described in this paper, we have proved that quantum computing could be the gold standard for materials simulations. These developments are critical steps toward realizing the potential of quantum computers.

With only 56 qubits in our commercially available System Model H2, the most powerful quantum system in the world today, we are already testing the limits of classical methods, and in some cases, exceeding them. Later this year, we will introduce our massively more powerful 96-qubit Helios system - breaching the boundaries of what until recently was deemed possible.

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March 27, 2025
ҹɫֱ and Google DeepMind Unveil the Reality of the Symbiotic Relationship Between Quantum and AI

The marriage of AI and quantum computing is going to have a widespread and meaningful impact in many aspects of our lives, combining the strengths of both fields to tackle complex problems.

Quantum and AI are the ideal partners. At ҹɫֱ, we are developing tools to accelerate AI with quantum computers, and quantum computers with AI. According to recent independent analysis, our quantum computers are the world’s most powerful, enabling state-of-the-art approaches like Generative Quantum AI (Gen QAI), where we train classical AI models with data generated from a quantum computer.

We harness AI methods to accelerate the development and performance of our full quantum computing stack as opposed to simply theorizing from the sidelines. A paper in Nature Machine Intelligence reveals the results of a recent collaboration between ҹɫֱ and Google DeepMind to tackle the hard problem of quantum compilation.

The work shows a classical AI model supporting quantum computing by demonstrating its potential for quantum circuit optimization. An AI approach like this has the potential to lead to more effective control at the hardware level, to a richer suite of middleware tools for quantum circuit compilation, error mitigation and correction, even to novel high-level quantum software primitives and quantum algorithms.

An AI power-up for circuit optimization

The joint ҹɫֱ-Google DeepMind team of researchers tackled one of quantum computing’s most pressing challenges: minimizing the number of highly expensive but essential T-gates required for universal quantum computation. This is important specifically for the fault-tolerant regime, which is becoming increasingly relevant as quantum error correction protocols are being explored on rapidly developing quantum hardware. The joint team of researchers adapted AlphaTensor, Google DeepMind’s reinforcement learning AI system for algorithm discovery, which was introduced to improve the efficiency of linear algebra computations. The team introduced AlphaTensor-Quantum, which takes as input a quantum circuit and returns a new, more efficient one in terms of number of T-gates, with exactly the same functionality!

AlphaTensor-Quantum outperformed current state-of-the art optimization methods and matched the best human-designed solutions across multiple circuits in a thoroughly curated set of circuits, chosen for their prevalence in many applications, from quantum arithmetic to quantum chemistry. This breakthrough shows the potential for AI to automate the process of finding the most efficient quantum circuit. This is the first time that such an AI model has been put to the problem of T-count reduction at such a large scale.

A quantum power-up for machine learning

The symbiotic relationship between quantum and AI works both ways. When AI and quantum computing work together, quantum computers could dramatically accelerate machine learning algorithms, whether by the development and application of natively quantum algorithms, or by offering quantum-generated training data that can be used to train a classical AI model.

Our recent announcement about Generative Quantum AI (Gen QAI) spells out our commitment to unlocking the value of the data generated by our H2 quantum computer. This value arises from the world’s leading fidelity and computational power of our System Model H2, making it impossible to exactly simulate on any classical computer, and therefore the data it generates – that we can use to train AI – is inaccessible by any other means. ҹɫֱ’s Chief Scientist for Algorithms and Innovation, Prof. Harry Buhrman, has likened accessing the first truly quantum-generated training data to the invention of the modern microscope in the seventeenth century, which revealed an entirely new world of tiny organisms thriving unseen within a single drop of water.

Recently, we announced a wide-ranging partnership with NVIDIA. It charts a course to commercial scale applications arising from the partnership between high-performance classical computers, powerful AI systems, and quantum computers that breach the boundaries of what previously could and could not be done. Our President & CEO, Dr. Raj Hazra spoke to CNBC recently about our partnership. Watch the video here.

As we prepare for the next stage of quantum processor development, with the launch of our Helios system in 2025, we’re excited to see how AI can help write more efficient code for quantum computers – and how our quantum processors, the most powerful in the world, can provide a backend for AI computations.

As in any truly symbiotic relationship, the addition of AI to quantum computing equally benefits both sides of the equation.

To read more about ҹɫֱ and Google DeepMind’s collaboration, please read the scientific paper .

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March 26, 2025
ҹɫֱ Introduces First Commercial Application for Quantum Computers

Few things are more important to the smooth functioning of our digital economies than trustworthy security. From finance to healthcare, from government to defense, quantum computers provide a means of building trust in a secure future.

ҹɫֱ and its partners JPMorganChase, Oak Ridge National Laboratory, Argonne National Laboratory and the University of Texas used quantum computers to solve a known industry challenge, generating the “random seeds” that are essential for the cryptography behind all types of secure communication. As our partner and collaborator, JPMorganChase explain in this that true randomness is a scarce and valuable commodity.

This year, ҹɫֱ will introduce a new product based on this development that has long been anticipated, but until now thought to be some years away from reality.

It represents a major milestone for quantum computing that will reshape commercial technology and cybersecurity: Solving a critical industry challenge by successfully generating certifiable randomness.

Building on the extraordinary computational capabilities of ҹɫֱ’s H2 System – the highest-performing quantum computer in the world – our team has implemented a groundbreaking approach that is ready-made for industrial adoption. of a proof of concept with JPMorganChase, Oak Ridge National Laboratory, Argonne National Laboratory, and the University of Texas alongside ҹɫֱ. It lays out a new quantum path to enhanced security that can provide early benefits for applications in cryptography, fairness, and privacy.

By harnessing the powerful properties of quantum mechanics, we’ve shown how to generate the truly random seeds critical to secure electronic communication, establishing a practical use-case that was unattainable before the fidelity and scalability of the H2 quantum computer made it reliable. So reliable, in fact, that it is now possible to turn this into a commercial product.

ҹɫֱ will integrate quantum-generated certifiable randomness into our commercial portfolio later this year. Alongside Generative Quantum AI and our upcoming Helios system – capable of tackling problems a trillion times more computationally complex than H2 – ҹɫֱ is further cementing its leadership in the rapidly-advancing quantum computing industry.

This Matters Because Cybersecurity Matters

Cryptographic security, a bedrock of the modern economy, relies on two essential ingredients: standardized algorithms and reliable sources of randomness – the stronger the better. Non-deterministic physical processes, such as those governed by quantum mechanics, are ideal sources of randomness, offering near-total unpredictability and therefore, the highest cryptographic protection. Google, when it originally announced , speculated on the possibility of using the random circuit sampling (RCS) protocol for the commercial production of certifiable random numbers. RCS has been used ever since to demonstrate the performance of quantum computers, including a milestone achievement in June 2024 by ҹɫֱ and JPMorganChase, demonstrating their first quantum computer to defy classical simulation. More recently RCS was used again by Google for the launch of its Willow processor.

In today’s , our joint team used the world’s highest-performing quantum and classical computers to generate certified randomness via RCS. The work was based on advanced research by Shih-Han Hung and Scott Aaronson of the University of Texas at Austin, who are co-authors on today’s paper.

Following a string of major advances in 2024 – solving the scaling challenge, breaking new records for reliability in partnership with Microsoft, and unveiling a hardware roadmap, today proves how quantum technology is capable of creating tangible business value beyond what is available with classical supercomputers alone.

What follows is intended as a non-technical explainer of the results in today’s Nature paper.

Certified Randomness: The First Commercial Application for Quantum Computers

For security sensitive applications, classical random number generation is unsuitable because it is not fundamentally random and there is a risk it can be “cracked”. The holy grail is randomness whose source is truly unpredictable, and Nature provides just the solution: quantum mechanics. Randomness is built into the bones of quantum mechanics, where determinism is thrown out the door and outcomes can be true coin flips.

At ҹɫֱ, we have a strong track record in developing methods for generating certifiable randomness using a quantum computer. In 2021, we introduced Quantum Origin to the market, as a quantum-generated source of entropy targeted at hardening classically-generated encryption keys, using well known quantum technologies that prior to that it had not been possible to use.

In their theory paper, , Hung and Aaronson ask the question: is it possible to repurpose RCS, and use it to build an application that moves beyond quantum technologies and takes advantage of the power of a quantum computer running quantum circuits?

This was the inspiration for the collaboration team led by JPMorganChase and ҹɫֱ to draw up plans to execute the proposal using real-world technology. Here’s how it worked:

  • The team sent random circuits to ҹɫֱ’s H2, the world’s highest performing commercially available quantum computer.
  • The quantum computer executed each circuit and returned the corresponding sample. The response times were remarkably short, and it could be proven that the circuits could not have been simulated classically within those times, even using the best-known techniques on computing resources greater than those available in the world’s most powerful classical supercomputer.
  • The randomness of the returned sample was mathematically certified using Frontier, the world’s most powerful classical supercomputer, establishing it achieved a “passing threshold” on a measure known as the “cross-entropy benchmark”. The better your quantum computer, the higher you can set the “passing threshold”. When the threshold is sufficiently high, "spoofing" the cross-entropy benchmark using only classical methods becomes inefficient.
  • Therefore, if the samples are returned quickly and meet the high threshold, the team could be confident that they were generated by a quantum computer – and thus be truly random.

This confirmed that ҹɫֱ’s quantum computer is not only incapable of being matched by classical computers but can also be used reliably to produce a certifiably random seed from a quantum computer without the need to build your own device, or even trust the device you are accessing.

Looking ahead

The use of randomness in critical cybersecurity environments will gravitate towards quantum resources, as the security demands of end users grows in the face of ongoing cyber threats.

The era of quantum utility offers the promise of radical new approaches to solving substantial and hard problems for businesses and governments.

ҹɫֱ’s H2 has now demonstrated practical value for cybersecurity vendors and customers alike, where non-deterministic sources of encryption may in time be overtaken by nature’s own source of randomness.

In 2025, we will launch our Helios device, capable of supporting at least 50 high-fidelity logical qubits – and further extending our lead in the quantum computing sector. We thus continue our track record of disclosing our objectives and then meeting or surpassing them. This commitment is essential, as it generates faith and conviction among our partners and collaborators, that empirical results such as those reported today can lead to successful commercial applications.

Helios, which is already in its late testing phase, ahead of being commercially available later this year, brings higher fidelity, greater scale, and greater reliability. It promises to bring a wider set of hybrid quantum-supercomputing opportunities to our customers – making quantum computing more valuable and more accessible than ever before.

And in 2025 we look forward to adding yet another product, building out our cybersecurity portfolio with a quantum source of certifiably random seeds for a wide range of customers who require this foundational element to protect their businesses and organizations.

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