Recent comments from SciRate

This study contains some nice insights regarding the use of matchgate shadows in conjunction with QC-QMC. One of the main limitations identified here is the high polynomial scaling of the classical post-processing required to compute local overlaps with matchgate shadows, reported in Table I to go a

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Here is a notebook where I do the timing correctly, for the sampling procedure you described: https://colab.research.google.com/drive/1xRINfTNgj-T7ZE_gnLPMDgMkKF7SqJNl?usp=sharing

You should be able to execute the notebook to confirm for yourself that the results are around half a microsecond per

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No wonder you're seeing nanosecond runtimes. You aren't counting the actual weighing up of the different paths, you're only counting the comparison of the weights at the end. That's like timing how long it takes to repair a car by timing how long it takes to close the hood.

Customers don't care a

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Thanks for the comment. Let us clarify on what is actually measured in the table. In our work $n_d$ is the number of defects in the lattice. Then, to measure the times we do the following:

1) We generate an error pattern at random.
2) If the error pattern has not exactly $n_d$ ones in the syndro

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In table 1, how are you measuring decoding times of less than 1 nanosecond for [[13,1,3]] with n_d = 1? The M2 processor you are using has a clock rate of 3.5 GHz, meaning you are claiming you solve the problem in around 3 clock cycles. How are you even jumping into and out of a subroutine in 3 cloc

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Very nice work! As I see that you are studying time-varying noise I add a couple of references on such by my group in case you are interested:

- https://www.nature.com/articles/s41534-021-00448-5
- https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.033055

UPDATE: The error mentioned below has been fixed, and in fact a stronger result has been proven. Please see the current version of the paper.

Please note that we have found an error in version 1 of our paper that does not affect any of the theorems regarding distillation. The error is in the v1 pr

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My comment (10.04.2024) on https://scirate.com/arxiv/2302.12209

A. V. Nenashev, S. D. Baranovskii

"How to detect the spacetime curvature without rulers and clocks"

(1) Nenashev and Baranovskii introduce an innovative and relevant notion; they even give it a unique name : "well-stitchedness" of (

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Dear Dr. Stark, thank you for your kind words. Your remarks, obviously somewhat complementary to our point of view, are well-taken. Most of all we appreciate your pointers to the literature, which we hope to incorporate in a future revision of our paper, to be released at a suitable point in time.

Dear authors, congratulations on your fantastic result! Your key lemma is simultaneously truly unbelievable and ridiculously convincing. Though your literature review is very exhaustive, I would like to point out one of my talks [1], also available on YouTube [2], which you probably missed.

[1]

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This is interesting work, and definitely the sort of question I wonder about when trying to evaluate the feasibility of FBEC schemes.

To engage in a little blatant self-promotion, I'd like to point out that the fusion schemes in the original FBEC paper are no longer the best known fusion schemes i

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Thank you for the reply and clarifying that your result is the quantum extension of the second kind. Also great to hear that now both quantum extensions to the converse are complete!

Thanks a lot to the colleagues that "Scited" this paper and and to those who introduced me to this site last night! This is a great site that we can exchange new research findings and advance quantum theory. Please feel free to reach me regarding quantum extensions of my expertise areas: stochastic

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Thank you so much for your message, Farrokh! Clearly, I was not aware of your paper; otherwise, I would have certainly cited it. In fact, we did not work on the same results.

As I mentioned in my paper (pages 2 and 3): "The converse of the expander mixing lemma has been articulated in two distinct

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> The most obvious open problem is to implement ACES in a near-term experiment.

We've run ACES on IBM Algiers and Osaka: https://scirate.com/arxiv/2403.12857

Very nice paper! Are you aware of the results in the following paper: https://arxiv.org/pdf/1908.06310.pdf?
I didn't go through all the details of your work, but I think you are proving roughly the same results here with different techniques (which makes it interesting!).

A closely related result about learning quantum states on infinite dimensional systems has already been obtained in this paper https://arxiv.org/abs/2303.05097.

thanks for the response. It cleared out some confusion about the "self-correcting" errors you mention. Thanks!

Dear Julio, thanks for pointing us to the square lattice construction in your nice paper. We'll be sure to mention it, and modify our statement in a later version.

Re: self-correcting errors, the 2-qubit errors this refers to here are actually check operators of the parent subsystem code, and so

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Dear authors!
Thanks for posting this interesting paper. I was wondering if you could elaborate on a question I got while reading through. Additionally, I have a minor comment that might be interesting to you.

The question is on the phenomenon you call "self-correcting errors" in your paper. Can

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Hi Jahan, extending the formalism to a multi-parameter noise model works straightforwardly by extending Eq. 2 to a product of binomial factors. This is described in detail, for example in https://arxiv.org/pdf/1801.07035.pdf, see Eq. 10 in there. Cheers!

Thanks! - so far as I can tell, the circuit constructed in that paper is for a specific case of the unary iteration circuit (where $P_i = R_a(\alpha_i)$ for some axis $a$ and angles $\alpha_i$). We have a more general circuit where each $P_i$ can be any Pauli operator (potentially on multiple qubits

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cool paper!
I do not know if it is relevant, but for unitary iteration circuit, there is an exact simple decomposition (though not in terms of T gates) in "Möttönen, M., Vartiainen, J. J., Bergholm, V., & Salomaa, M. M. (2004). Quantum circuits for general multiqubit gates. Physical review letters,

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> a quantum black box that outputs a uniform superposition of such points

This isn't so farfetched. Craft a stabilizer that checks a radius condition, and alternately apply it with Hadamard gates as in the distribution preparation algorithms of arxiv:2310.20191. The only question is the exact scali

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As the authors point out in the preprint, the cost of this exponential time algorithm can be increased from 2^(n/3) scaling to 2^n with the use of in-block permutation CNOTs for the [[8,3,2]] code. Such gates are readily implementable with the parallel control hardware that is available in the lab.

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Daniel, your question is addressed in arXiv:0705.2784, which considers closely related problems using similar techniques. If the dimension is odd, then the walk can be implemented efficiently. If the dimension is even, then the implementation of the walk is closely related to the problem of (approxi

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Thanks for your comments. Yes, the adjacency matrix A is dense with $s_r≈q^{n-1}$ non-zero elements out of $q^n$ elements in each row (column), by its definition.

We are only interested in the number of samples, and we have not considered how to implement $e^{i\bar{A}t}$.

Cool! Do I understand correctly that $A$ is dense? Is there an efficient way to implement $e^{iAt}$ (or $e^{i\bar{A}t}$) used in the main step? I'm not an expert, but I ask because maybe someone else has the same question. (Also, perhaps you are not interested in the circuit complexity, but just th

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Congratulations on the publication of your paper on real device execution of periodic systems. I believe that your quantum algorithm for crystalline systems will be important for chemical applications.

By the way, I was a little wondering about the statement in the introduction that "So far, expe

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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.