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Regarding the aforementioned follow-up research, I have now recorded and published a video on the subject.
https://youtu.be/kLWgero0a0w
As for the write-up, I hope to finish it in the couple of next months.

This is a very nice paper, and I congratulate the authors on that. However, there seems to be a significant issue with the proof, and as of now we believe it to be significant enough to undermine the main result. Here I'll be relaying the discussion on Twitter (= X): https://x.com/marcotomamichel/st

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Thanks a lot!

For (1): yes, I generalized it to work beyond just the triangular lattice, by using tour dragging to lift the solution. It should be able to decode things like holes being braided. I wouldn't say it works for all color codes (e.g. it can't decode color code circuits that cycle between measuring X th

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Congratulations on your great work! May I ask two small questions?

1. The previous Möbius decoder in [SB22] was applicable only to triangular color codes with three boundaries. It seems that your decoder doesn't have this limitation. Is it correct? Is it applicable to arbitrary color code lattice

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Thanks Pedro, thanks Ryan!

It sounds like this outperforms QSVT in some regimes? Are there other regimes where QSVT is the right choice?

I'd love to hear more about when I should choose to use each technique.

Indeed, thanks for this discussion. We would not have written the paper posted last night without it.

Dear Matteo,

The numerical results that Ryan mentioned previously are disclosed now at https://arxiv.org/abs/2312.07690. Notice that we do not even consider the simulation of the randomized method in some discrete framework, like queries of the block-encoding. Thus, we expected an even worse comple

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Hi Josu,

Thanks a lot for the pointers! We have updated the arxiv to include and discuss the papers you mentioned.

If correct, it is one of the best results I have seen in several years. :) Congrats!

"All cluster states are local-Clifford equivalent to a stabilizer state" Did you mean the reverse: all stabilizer states are local-Clifford equivalent to a cluster state? Cluster states are already stabilizer states; the more interesting fact is that (as your GHZ example illustrates) an arbitrary st

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Exciting!

FYI, definitions 5 and 7 in the paper do not work properly with topologically ordered states.

Very interesting article. I see that you are considering scenarios where the noise fluctuates. I add you a couple of articles where we construct time-varying noise models due to the fluctuations of coherence times in superconducting qubits:

- https://www.nature.com/articles/s41534-021-00448-5

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A few comments:

1. Your conditions for any scientific theory (NCT) does not seem to be required in lewisian sense, i.e. when the theory in question is treated as a ,,best system'' encapsulating (perhaps compressing in some algorithmic sense) our perceptions. MWI can be such a (meta)theory.

2

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Ah, the distinction might be rotated vs unrotated surface code. I just assumed you were using rotated since it's more efficient.

The claim that Y basis measurement along an entire row or column is survivable is correct. But I think it's underselling it. I think the claim that measuring Y along an entire diagonal will break the logical qubit is actually wrong. You can measure every single data qubit except for one and have the

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> Table 1: it'd take 30 million years of supercomputer time to do d=9 surface codes

> Conclusion: it's feasible to apply this technique to d=9 surface codes

...What?

Checks out! I very much like how the paper is written, by the way :)

Misremembering the term would definitely explain why I wasn't able to find where I read about it.

Isn't the concept of boosting usually known as pumping? Or am I misunderstanding something?

Thanks for the reach out, and we enjoy reading your work with Prof. Dakic. Actually, we have cited it around Eq (16) (very nice formula). And we will also cite your work in Sec. V in the revised version.
In my opinion, it is very unfair to say “shows a strong degree of overlap”, and our work is dis

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Very similar to the recent publication Phys. Rev. Lett. 131, 083601 (2023)

Thank you! Yes, in Proposition V.2 we explain how the spacetime graph for the overlapping window decoder can be constructed by taking the hypergraph product of the QLDPC code with a repetition code. Our understanding is that your result from Ref. [93] implies that all circuits constructed using this

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Enjoyed looking through this paper! I had a basic question about 3D surface codes, as they relate to my work on distance-preserving stabilizer circuits. You write "recent work suggests that the ordering of operations in the syndrome extraction circuit does not affect the
effective distance of the c

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Hello, I believe this result shows a strong degree of overlap with [a previous work][1] of my group, particularly the estimation of off diagonal elements (one of the main results given in the latter half of the paper).

Best,
Joshua Morris

[1]: https://arxiv.org/abs/1909.05880

In a follow-up research, I found out that even if just a single known qubit of query registers is affected by the depolarizing noise of rate p, quantum search among n elements cannot be done any faster than in O(np) queries. This holds both when the affected qubit is one of the log(n) index qubits a

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I see. Thanks for mentioning this point and your paper to us!

This isn't really core to the paper or anything, but the CX*H*CX*H circuit in fig 16 can be optimized into CX*H*CX*Z because Z has the same action as H on the |Y> state ( as in https://arxiv.org/abs/1708.00054 ). Z is cheaper than H because it can be done in the classical tracking instead of on the

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This is a well presented, innovative algorithm.

Agreed - really informative and well organized. A maintained version of this would be a very welcome resource for the community

A really impressive work. It would be better if this is uploaded to a website so that the information can be updated.

Thank you very much, Eric! Our model (depicted in Fig.2c) is defined by coupling Alice's input signals to environmental systems through unitary interactions. Consequently, this model is consistent with quantum mechanics and, in particular, it does not violate the quantum no-cloning theorem. Once inf

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Hi Francesco, this is excellent work! I'm always excited to see more ways to carry out QI transport. I have one conceptual question that may be answered in your paper in a way I did not fully understand. By thermal noise, one usually means phonon interactions. If a photon's QI is lost to the system

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Very interesting paper and good comment by Jason. I agree that such insights should be clearly written up and simple to find in the literature!

I want to add that the fact that the Pauli group is not complemented within the Clifford group (i.e. there's no group $G$ in Jason's comment) is known from

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This is very interesting! I am sure the explicit character tables will be helpful in the future.

I just wanted to point out that Conjectures 5.4 and 5.5 are known (or follow directly from known results). In the below, always take $n\geq 3$. The main facts being used are the observation that $\ma

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Is it clear if this protocol works for noise models where different Pauli errors occur with different probabilities? My understanding right now is that you have to assume each fault occurs with the same probability *p*, but maybe there is some way around that?

Ah, true, the hermitian conjugate is only equivalent to the inverse for unitaries, simple mistake. Thanks!

Yes the EM3 distance does usually match the embedded distance, although we found one case where they differed (for n=320, k=18 with EM3 noise the minimum-weight error included Pauli errors that caused time-separated detection events). Thank you for pointing me to your updated GitHub repo, and I agre

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The spectral decomposition you use in Lemma 1 is only valid for normal matrices, not all diagonalizable matrices. Of course, the lemma (trace = sum of eigenvalues) is true for all diagonalizable matrices, but for diagonal matrices that are not normal, the proof of that fact requires more than just a

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Thanks for your comment, Oscar! Yes, the DP1 distance the way you defined (and is equivalent to the code distance defined in our paper) equals to the lesser of "the embedded distance of the superlattice" and "twice the embedded distance of the dual of the superlattice". It is still interesting to me

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Thanks a lot for the hints! I'm now surprised I haven't found them earlier in my own searches. I'll soon upload another version of the manuscript crediting their work appropriately.

Very interesting work, congratulations! Where you compare to our work you say "At similar encoding rates, the codes shown here have a larger relative code distance". The reason for the discrepancy is that we report the distance of our circuits, which include two-qubit errors, whereas you are reporti

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Thanks for the references Josu. I see that what we called single-qubit site-dependent Pauli noise is something you have studied and called i.n.i.d noise. We will make sure to reference these works in the next version.

Very interesting manuscript. I see that you have considered Pauli noise that shows different probabilities for each of the qubits of the surface code, which I see that you named single-qubit, site-dependent Pauli noise. I attach here a couple of references regarding studies of surface codes with suc

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The numerical efficiency of computing the fidelity in this way was previously pointed out in https://arxiv.org/abs/2211.02623.

(The expression itself appeared earlier; the similarity of the matrices was noted already in https://arxiv.org/abs/0805.2037, and I can find an explicit expression e.g. in

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Hi Pavel, thanks a lot for your comments and suggestions. Most of our results are extensions of your BP-OSD work so I am really glad to get a feedback from you. The generalized bicycle code [[126,12,10]] is indeed very close to codes from our paper in terms of the distance and encoding rate. It is a

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https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.4.030335

Dear Yiren,

Thank you for bringing this serial CPU-only Python implementation to our attention. We added a reference to it, as well as a note thanking you for pointing it out to us, in a v2 version that will appear on arXiv shortly.

We note that the mixer implementation in (Sack & Serbyn, 2021) re

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