Quantinuum researchers are unlocking a more efficient and powerful path towards fault tolerance

“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.”