Recent comments from SciRate

Yupan Liu May 19 2024 03:43 UTC

Thanks for the interesting work! It would be helpful to mention a slightly generalized definition of ${\mathsf{stateBQP}_{\delta}}$ in [Definition 3.1, [arXiv:2303.01877][1]] to clarify why "B" (bounded-error) appears in the name of the class. Specifically, this class can be defined to prepare the s

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Ryan Babbush May 10 2024 16:20 UTC

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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Craig Gidney May 06 2024 00:25 UTC

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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Craig Gidney May 04 2024 18:54 UTC

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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Lorenzo Valentini May 04 2024 17:50 UTC

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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Craig Gidney May 03 2024 15:31 UTC

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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Josu Etxezarreta Martinez May 02 2024 11:23 UTC

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

Jason Saied Apr 24 2024 21:45 UTC

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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Frank Wappler Apr 10 2024 20:31 UTC

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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Andreas Winter Apr 02 2024 21:11 UTC

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.

Ned Stark Apr 01 2024 12:06 UTC

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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Jahan Claes Mar 25 2024 03:14 UTC

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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Farrokh Labib Mar 22 2024 09:08 UTC

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!

Ning Ning Mar 21 2024 14:17 UTC

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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Ning Ning Mar 21 2024 14:07 UTC

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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Victory Omole Mar 20 2024 12:48 UTC

> 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

Farrokh Labib Mar 19 2024 09:54 UTC

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!).

Yadong Wu Mar 13 2024 07:12 UTC

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.

Julio Magdalena Mar 12 2024 14:10 UTC

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

M. Sohaib Alam Mar 07 2024 19:15 UTC

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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Julio Magdalena Mar 07 2024 12:33 UTC

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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Sascha Heußen Mar 04 2024 08:27 UTC

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!

Tuomas Laakkonen Feb 23 2024 14:25 UTC

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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Ammar Daskin Feb 23 2024 06:36 UTC

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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Kelly Pawlak Feb 06 2024 23:17 UTC

> 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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Michael J Gullans Feb 06 2024 04:56 UTC

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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Andrew Childs Jan 30 2024 13:52 UTC

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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Lvzhou Li Jan 30 2024 10:36 UTC

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 $e^{i\bar{A}t}$.

Daniel Ranard Jan 30 2024 06:02 UTC

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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Shu Kanno Jan 10 2024 07:37 UTC

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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Ansis Rosmanis Jan 08 2024 07:53 UTC

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.

Ludovico Lami Jan 05 2024 16:16 UTC

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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Seok-Hyung Lee Jan 03 2024 09:24 UTC

Thanks a lot!

Craig Gidney Jan 03 2024 06:04 UTC

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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Seok-Hyung Lee Dec 28 2023 01:55 UTC

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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Matteo Lostaglio Dec 18 2023 09:55 UTC

Thanks Pedro, thanks Ryan!

William J. Huggins Dec 15 2023 17:13 UTC

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.

Ryan Babbush Dec 14 2023 15:09 UTC

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

Pedro C.S. Costa Dec 14 2023 05:06 UTC

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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Hanrui Wang Dec 09 2023 20:44 UTC

Hi Josu,

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

Junyu Liu Dec 08 2023 18:44 UTC

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

Jahan Claes Dec 06 2023 16:13 UTC

"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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Jingze Zhuang Nov 30 2023 11:17 UTC

Exciting!

Chae-Yeun Park Nov 29 2023 19:56 UTC

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

Josu Etxezarreta Martinez Nov 29 2023 11:10 UTC

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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Wojciech Kryszak Nov 27 2023 20:28 UTC

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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Craig Gidney Nov 27 2023 09:32 UTC

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

Craig Gidney Nov 27 2023 08:07 UTC

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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Craig Gidney Nov 23 2023 02:27 UTC

> 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?

Francisco Silva Nov 21 2023 13:34 UTC

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