Please feel free to contact me and/or my coauthors (emails in the paper) for discussions and/or questions.

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.

In another application, one can build codes with transversal, addressable T gates, up to Cliffords, although we do not provide an instantiation.

We demonstrate the power of this by constructing an asymptotically good code with an addressable, transversal CCZ gate on fixed, non-overlapping triples.

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 (this led to 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-tolerant 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 circuits) alone.

Check out our recent pre-print: . In this work, we construct the first quantum codes which support transversal and addressable non-Clifford gates!.

Or even what we should call such a conjecture!.

state distillation (\gamma=0) but these codes are not LDPC. Given these recently discovered facts, it might be reasonable to conjecture that there exist asymptotically good qLDPC codes with non-Clifford transversal gates - but who knows how to prove such a thing -.

the magic state distillation exponent \gamma \to 0 for qubits (since they have constant rate and a growing distance) and they’re LDPC!!! In contrast, the recent discovery of asymptotically good qubit codes with non-Clifford transversal gates gives constant-overhead magic.

This is super exciting - - congratulations to the authors @artix41, Thomas and Mark (who I don’t believe are on Twitter). They construct non-asymptotically good codes with non-Clifford transversal gates on qubits, but the parameters are good enough to get.

Director of Studies during my Bachelor’s and Master’s). Please share if you find this interesting, I look forward to engaging discussions!.

@quantum_minhsiu once again. In fact, @quantum_minhsiu will speak on this work later today at the symposium happening in Cambridge unofficially known as “Datta Fest” in honour of the amazing Nilanjana Datta (who I was lucky enough to have as my….

The work also contains a number of very interesting open problems that we hope people will engage with. It was great to coauthor with @HayataYamasaki for the first time - and am very grateful that he funded my first ever visit to Japan - and wonderful to work with….

in this work - we only show that they exist - there is quite a large amount of room for optimisation. In such a future optimisation, we intend to use both the algebraic geometry codes and Reed-Solomon codes within our prime-power qudit framework to tackle this problem.