Recent comments from SciRate

Did you experiment with varying the sizes of $n_{com}$ and $n_{buf}$? Intuitively, larger $n_{buf}$ means decreased error rate but increased overhead... and large $n_{com}$ decreases both but increases latency. Would be nice to see empirically the benefits or drawbacks of values other than d, especi

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A special case of your formula for the probability distribution $p(x | n, m, k, l)$ was obtained by Montanaro in [arXiv:0903.5466][1]. Namely, when $n = k$ and $m = l$ we have $p(x | k, l, k, l) = \mathrm{Pr}[x|l]$, where $\mathrm{Pr}[x|l]$ is given in Montanaro's Lemma 4. It denotes the probability

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Equation (25) appears to be incorrect to me, you are writing the second order Trotter formula as $U_2(dt) = \left[ U_1 (dt/2) U_1(dt/2)^T\right]^m$, but since $dt = t/m$ then this would correspond to a Trotter formula for $U_2(t)$ not $U_2(dt)$?

Hey, thanks for your question.
So in our work, we find that for the ansatze we consider, the onset of barren plateaus is related to the width of the causal cone of an observable.
The width itself expands via entangling gates like CNOTs in the circuit architecture.

In the qMPS ansatz, the ent

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Hi, congratulations to your work. From your work, you state that the barren plateau is absent for qMERA and qTTN, but exists for qMPS. From previous works, entanglement can induce barren plateau, and I assume the ensemble of states generated by qMPS has smaller entanglement than the other two and a

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Thanks! Indeed, there is a typo in the direction of the majorization symbol of Definition 1 in Appendix C.

Outstanding work. Small typo?: It seems like the direction of majorization symbol in Definition 1 of Appendix C is reversed.

This paper refers to the version of RQM that existed before the introduction of "cross-perspective links" in [arXiv:2203.13342](http://arxiv.org/abs/2203.13342), a change that amounts to saying, "Well, we didn't want all those 'relative facts' anyway."

Hi, Anthony! Thank you for pointing out the Oded Goldreich survey. I think it's really neat! I haven't read it yet before since the original paper [30] was written so well that I never needed to look anywhere else. I believe you are referring to the comment on page 3, where he indeed considers somet

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Hi Pavel,
You're right that ref [30] doesn't use double covers, although the overview from Oded Goldreich that came out a few weeks later did
https://eccc.weizmann.ac.il/report/2021/175/
Of course, we'll be happy to give you proper credit when we update the manuscript.
Best,
Anthony & Gilles

Congratulations! A very nice result with much shorter proofs than ever before! It is great that with all these recent simplifications each next paper rapidly approaches the high standards of simplicity and elegancy set by Sipser and Spielman in 1996. However, with all due respect, I believe, you inc

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Note that Eqs. 7 through 14 in the arXiv version of this paper are not correct. The correct expressions appear in the published version in Physical Review Letters. It's pretty straightforward to fix these equations if you are following the paper by hand, but be warned!

This is an outstanding paper in quantum Shannon theory. Congratulations to the author.

Thanks for pointing this out! The PDF should be working now. Sorry about the initial error.

The arXiv vanity version seems to work (to some extent): https://www.arxiv-vanity.com/papers/2207.14438/

Looks like arXiv is not able to produce the PDF file for this paper.

Very interesting!

It seems that our future AI overlords will have us all speaking Pirahã, then. :)

Very nice paper. You may be interested in this great paper by Montina:
https://arxiv.org/abs/1107.4647
that looks into the d>2 case that you mention in your discussion section. It seems this qubit case is quite exceptional and difficult to generalize.

Thanks Mark! I'm also looking forward to read your paper in detail.

Thanks a lot for your comment and for pointing out your paper. We'll definitely add a citation to your work in a revision of our paper. We're reading your paper now and will email you if we have any questions about it.

Congratulations for the nice result! I did not expect that estimation of multivariate trances (also known as Bargmann invariants) can be performed so easily. Still, I wanted to point out that in this earlier work https://scirate.com/arxiv/2109.10006 with Ernesto Galvao and Dan Brod we managed to co

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Hi William, Thanks for pointing out the error. Indeed, it should be

..., then $|{H_{ji}}|^2 = \sum_{kk'}h_kh_{k'}p_{kk'}^i(j)$ with $p_{kk'}^i(j)=\mathrm{Re}\langle i|U^\dagger P_k U\Pi_jU^\dagger P_{k'} U|i \rangle$ satisfying $\sum_j |p_{kk'}^i(j)|\le 1$.

The key point here is that by regar

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I've been reading your paper with interest but I think that the claim (top left of page 4) that $p^i_{kk'}(j) \geq 0$ and $\sum_j p^i_{kk'}(j) =1$ is incorrect.

I'd also be curious to know how you expect your algorithm to perform in the presence of sampling noise.

I think there is a mistake in the proof, which causes Theorem 2 to be incorrect. There should be an additional $2^n$ factor ($n$ is the number of qubits) in the number of experiments stated in Theorem 2. If Theorem 2 is true, then given any exponentially deep classical boolean circuits on $n$ bits,

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Thanks for pointing out this nice paper. Our main results relate to single copy measurements, not multi-copy measurements (e.g. Hillary's paper with noiseless circuits but also https://arxiv.org/abs/quant-ph/0111082, which we do cite). We have also entanglement conditions in terms of only the first

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Thank you for your reply, and I appreciate your revision in the next version.

Go right ahead! I'm glad you like it :D

Thanks Shu for the clarification. We will revise that description in the next version of our work.

I think they're supposed to be arm-wrestling, not making a deal. :)

This is beautiful, thank you, hahaha! A deal with the devil it is :D
Also... do you mind if I use this in a talk some day?

Corresponding software can be found here: [KadanoffBaym.jl][1]

[1]: https://github.com/NonequilibriumDynamics/KadanoffBaym.jl

Thank you for an interesting work and citation of our paper!
I'm reading your paper and noticed that our work is described as "Qubit and gate resources required for Trotterized Hamiltonian simulation algorithms of fully local Hamiltonians (without intercell interactions) have recently been investiga

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For an article whose title starts with "the battle of clean and dirty", and about barren plateaus, I felt compelled to make a meme with this classic template! I hope you enjoy! (Please understand that I'm not trying to make any religious statement here :) )

![a meme of Jesus and Satan fighting ab

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This paper for studying the optimality for collective measurements seems very interesting. One of the nice points of this paper is to apply error mitigation for metrology; however, our paper has already proposed error mitigation to metrology .... but it is not referred in this paper. Our paper demon

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This paper of Hilary Carteret

https://arxiv.org/abs/quant-ph/0309216

already put forward the method given, for estimating the moments of the partially transposed density matrix of a bipartite state. It does not appear to be cited in the manuscript.

This is a cool result. The Glynn-Kan operator looks correct, which is really neat because it formulates solving the matrix permanent in terms of the expectation value (over the uniform superposition of **2N** qubits) of a diagonal 2-local Hamiltonian with **N^2** terms, which is straightforward to s

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In order for this result to actually efficiently solve a #P hard problem, this result just needs to be able to approximate the permanent for any real matrix within *any* relative error. This is due to Corollary 6 of https://www.scottaaronson.com/papers/sharp.pdf.

If I recall correctly, the JSV al

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Your answer is very clear!! Thank you very much, and this result is very interesting, and I will read this paper!

Hi Suguru, thanks for your question! We find exponential concentration of observables, as in a normal noise induced barren plateau. However, in our setting now the exponent is now rescaled by the ratio of the number of noisy qubits to the total number of qubits. So indeed this can be thought of as m

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Thank you very much for a very interesting work! Does this work help the mitigation of noise induced barren plateau, i.e., the base of the exponential concentration of the observable is reduced?

Hi Steve, thanks for your comments.

Regarding your second concern:

This is addressed by the "Ising-type" recovery dissipators we define,
which have the form $aP$ with $a$ being the annihilation operator on a
given site and $P$ being a projector on a particular configuration of
domain walls surroun

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I guess I have two concerns. First, it seems that to get a mathematical threshold requires taking $N\to\infty$. This fact does not say anything about finite-size scaling (as you point out), but it does mean that this proposal requires infinite energy density to have a true threshold. If infinite ene

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Actually, our experiment and analysis goes up to 16 qubits, not 8 qubits, and uses a million measurements. Your paper estimates the number of measurements for 16 qubits at about 1e8, two orders of magnitude more pessimistic than what we found.

The quote I selected from our appendix mentions a certa

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Hi Steve, Thanks for the comment. While $N\to\infty$ is the ideal limit, the logical phase-flip error rate is exponentially small in $N$ so that for practical purposes $N$ might not need to be too big to achieve the desired level of accuracy (such as for a single cat qubit experiment). Similarly, we

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Ryan, mostly in the main text you write "...we propose a **scalable**, noise-resilient..." and "...the flexibility and **scalability** of our proposed approach..." etc. The emphasis on scalability certainly pervades the whole article and it's one of the main selling points. The appendix does not rea

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This construction achieves self-correction by requiring the mean photon number N → ∞, which costs infinite energy per subsystem.

In Appendix F we write: “Therefore, as the system size increases towards the thermodynamic limit, we would expect that QC-AFQMC formally requires exponentially more measurements to maintain the relative precision”. I’m sorry if you found that statement unclear (the point of that appendix was to eluc

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Several points of clarification are in order here:

1. We believe that referring to general computational complexity arguments to explain the intrinsic lack of scalability of a given algorithm only obfuscates the discussion and introduces further elements of confusion in the field.
The issue

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The challenge referred to in this paper was first identified and discussed extensively in the original text by Huggins et al. - see, e.g., Appendix F. Although there are some differences, the problem is similar in spirit to the vanishing of initial state overlaps when preparing ground states via qua

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