Recent comments from SciRate

Hi Thomas, I understand what you mean. Let me put it in another way: your statement means to be “any quantum circuit for which error mitigation is efficient ‘in the limit of very large n’ must be classically simulable.” While your current sentence can be misinterpreted as “a given quantum circuit of

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Hi Zhenyu, thank you so much for the comment and suggestions! Our statement holds for any arbitrarily small O(1) noise rate independent of the number of qubits n. For even smaller noise rates, e.g. scaling with the inverse of the number of qubits O(1/n), it is possible for both error mitigation to b

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I wanted to remark that efficient learning of unknown FLO unitaries has been already established in https://arxiv.org/pdf/2012.15825 (Part IX, Theorem 8). Therein, we gave an efficient reconstruction method that approximates unknown FLO transformation to additive precision in diamond norm. The meth

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This paper is published in New Journal of Physics, an open access journal with an article publication charge (APC) for authors. The journal offers various discounts:

1. The current APC is £1660/€1890/\$2485. According to the rate today, £1660=\$2157 and €1890=$2067. Everyone should choose € to sav

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Congratulations on a very interesting paper! A quick comment on the possible misinterpretation of the last sentence. I think a better statement would be ''any quantum circuit for which error mitigation scales efficiently with the amount of circuit noise must be classically simulable’’. Or ``any quan

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What is the overlap of this paper with https://arxiv.org/abs/2402.18665?

Ah. Right. Thanks!

I believe it's correct as written (it looks like you missed an inverse?), with:
$$Q \geq \beta^{-1} \ln 2 = ((k_B T)^{-1})^{-1}\ln 2 = k_B T \ln 2$$

Equation 1: $Q \geq B^{-1} \ln 2$, which can written as $Q \geq \frac{\ln 2}{(k_{B} T)}$, contradicts [Wikipedia's statement of Landauer's principle][1] ($Q \geq k_{B} T \ln 2 $).

Equation 1 claims that the theoretical lower bound energy dissipation of resetting a qubit is below the one for rese

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The problem of measurement/sampling is not discussed in this article. At one point, it is said that "$N_{shot}$ *is the number of shots/iteration (= 10,000)*" and only in the paragraph before the conclusion, it is mentioned that "*While our estimate [..] appears daunting at first sight, it [..] iden

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Hi Pau. Thanks for your comment.

In Figure 4a-c of the manuscript we have removed all elements of the QAOA pipeline to exclusively focus on the role that error suppression plays in executing a "plain vanilla" instance of QAOA .

"In all executions, the equal weights superposition state ser

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This manuscript shows that Q-CTRL’s implementation of QAOA with initial angle tuning attains a solution quality that strongly overlaps with random sampling (Figure 4). That is significantly poorer than the included alternatives Local Solver and D-Wave (without initial solution preparation).

The m

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Thank you for your feedback on our work. We provide additional information on the time to solution in the appendix:

"The smallest problems we solved (28–32 nodes MaxCut) implemented 12 optimization steps, which totals to 72 circuits, each executed with 6,000 shots for a total of 432,000 shots thr

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Hi Michał, thanks for your kind words! Of course we are happy to also cite your work prominently.

Congratulations for the nice result! It's great to see significant progress on the conjecture that spectral gaps of RQC are t- independent, at least for for exponentially large t.

However, I'd like to bring to your attention that Brown-Susskind conjecture from https://arxiv.org/pdf/1701.01107

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Hi Brian, thank you for bringing this omission to our attention! We will update our paper in the coming days.

I seem to be missing something about what is claimed about the gate $P(\alpha)_L$ defined in equation (4). For what values of $\alpha$ is it supposed to be a logical $P(\alpha)$ gate?

The gate defined in equation (4) does not implement a logical $P(\alpha)$ gate for all $\alpha$. It may seem that

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This paper fails to cite our prior work ([arxiv][1], [journal][2]) in which we obtained a linear-in-k time to reach a k-design in a closely related Brownian/stochastic model. This is so despite previous correspondence about our work with at least two of the authors of this paper. So I felt compelled

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> In the authors’ opinion, QRAM constitutes a fundamental requirement for any type of quantum computing

Is QRAM a *fundamental* requirement though? You can use QRAM to optimize Shor's algorithm but I'm under the impression that Shor's can be done just fine without QRAM. Ditto for [Grover (Circuit

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This is a nice paper showing, in my opinion, a lot of the concepts as how we can work towards quantum advantage in the NISQ era. Basically not shying away from extensive precomputation, preprocssing and post-processing. If we combine this with a holistic benchmarking of the entire workflow (solution

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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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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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