Adam Wills

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Here, the AG codes as evaluation codes are really giving you the transversality, and the transitive automorphisms are really giving you the addressability.

This improves upon our previous result which was only asymptotically good up to polylogarithmic factors. The secret in the end was a family of algebraic geomtry (AG) codes due to Stichtenoth with a transitive automorphism group.

Namely, this means that any three logical qubits, whether they’re in one, two or three blocks of the code, can be addressed with the logical CCZ gate via a depth-one circuit of physical CCZ gates.

Asymptotically Good Quantum Codes with Addressable and Transversal Non-Clifford Gates Constructing quantum codes with good parameters and useful transversal gates is a central problem in quantum error correction. In this paper, we continue our work in arXiv:2502.01864 and construct the...

New preprint out!!

scirate.com/arxiv/2507.0...

Here, we follow up our previous work by constructing the first asymptotically good quantum codes to have transversally addressable non-Clifford gates.

Hi there. I believe you may have tagged the wrong person :)

Our fifth long plenary is a merged talk featuring four presentations from winners of the "Best Student Paper" award! Details and overview below. @adamwills1.bsky.social

Those two field elements generate an additive group of size 4.

Yea have a look through Section 3 in particular the end of Section 3.1. I believe that explains it better than I can here. Essentially the “differences” between the 3 logical qudits that we want to address are described by some field elements.

“duplicate” each qubit O(1) times to get depth one - you’ll see in the paper where we do this to get down from depth 4 to depth 1. As is common, there is a tradeoff between implementation depth and code length.

Yea indeed that’s exactly the angle is to say that you don’t need to incur the overhead of these other techniques if you have a nice enough code. I should also say to be fair that while we do get depth one that’s kind of equivalent to O(1) depth here because after you have depth O(1) you can just

Yea indeed the main idea here is a specialised code construction which allows non-Clifford addressability via constant-depth circuits (in fact depth one). I definitely want to learn more about your paper too!

logical and physical qubits. Therefore I don’t think it’s unreasonable at all to consider ideas in this paper as inspiration for getting addressability on algebraic LDPC constructions. I wouldn’t say the same for more topological constructions, though.

discovered (LDPC or otherwise). One direction of work would be then to apply these addressability ideas to LDPC constructions. While our main result does use particular properties of Reed-Solomon codes, somehow the feeling is that all we needed was a nice algebraic structure on the addresses of the

Constant-Overhead Magic State Distillation Magic state distillation is a crucial yet resource-intensive process in fault-tolerant quantum computation. The protocol's overhead, defined as the number of input magic states required per output mag...

Thanks! And thanks for the question. There’s no bound on the check weights and indeed you can show that there are high weight stabilisers (linear or near-linear). The aim is, as in arxiv.org/abs/2408.07764 (and the concurrent works) to develop properties of quantum codes that have not been

While we hope this will be seen as a nice step forward, there is still a lot to do. For example, we really need LDPC versions of these codes. It does seem reasonable to attempt to obtain addressability on LDPC codes supporting transversal gates in a way similar to this work. Exciting times ahead!

We demonstrate the power of this by constructing an asymptotically good code with an addressable, transversal CCZ gate on fixed, non-overlapping triples. In another application, one can build codes with transversal, addressable T gates, up to Cliffords, although we do not provide an instantiation.

We also develop a general framework to describe transversal addressability which we call “addressable orthogonality”. This encompasses Bravyi and Haah’s original “triorthogonality” framework for T gates and all related notions.

To be explicit, given ANY triple of logical qubits in one or multiple codeblocks, you can address that triple with the logical CCZ gate via a depth-one circuit of physical CCZ operations. We discuss generalisations to other gates such as CCCZ and higher.

In fact, there are no such works for the hardest operations: the non-Clifford operations. We construct the first quantum codes with this property, and in fact we obtain such codes that are nearly asymptotically good (only a polylog away).

While this is fine for magic state distillation, we need *much* more fine-grained control for utility in general computation. There are only a small number of works studying codes supporting transversal gates that allow you to address particular logical qubits.

Last year, the first asymptotically good codes were constructed supporting non-Clifford transversal gates (and this led to the discovery of constant-overhead magic state distillation). However, this left open a big problem. The transversal gates executed the same logical gate on every logical qubit.

However, to lower the fault-tolerance overhead, we still have a long way to go to building codes with highly flexible sets of transversal gates that can adapt to a given algorithm, thus minimising the need for expensive sub-routines like magic state distillation.

The Eastin-Knill theorem prevents us from performing fault-tolerant quantum computation with transversal gates (i.e. executing logical gates on logical qubits via low-depth physical curcuits) alone.

Quantum Codes with Addressable and Transversal Non-Clifford Gates The development of quantum codes with good error correction parameters and useful sets of transversal gates is a problem of major interest in quantum error-correction. Abundant prior works have studie...

Check out our recent pre-print: arxiv.org/abs/2502.01864

In this work, we construct the first quantum codes which support transversal and addressable non-Clifford gates!

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