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What an amazing trick

Although now that I'm thinking about it a little more, I don't understand why all this is necessary. In this proposition, you're assuming $\mathbb{S}=\mathbb{S}_d$ and trying to prove the twirl has no unit-modulus eigenchannels other than the depolarizing and identity channels. Why can't you just sa

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You can check on the arXiv for the email address of the person who submitted the work.

I'm having a little trouble understanding the last three sentences of the first column on page 19.

> Thus, because $\mathbb{S} = \mathbb{S}_{d}$ by assumption, the space of all superoperators preserved under conjugation by all elements of ${R}^{-1}\mathbb{G} $ contains $\mathbb{S}_d$, since we se

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Dear author and editors,

I am researching quantum unitary decomposition and find this work very interesting.

Please let me know if I can have the author's email address to further discuss this work.

Here is my Email (yize.sun@campus.lmu.de) if you need it.

BR,
Yize Sun

Thanks for the clarification!

Regarding the open problem on "MA containment of guidable stoqastic LH" in Section 1.3, I do not have a quick answer yet since I need to take a close look at Def 7 in your work. However, the corresponding paragraph in Section 1.3 is not totally precise:

i) Thres

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Dear Yupan Liu,

Thank you for pointing out your interesting work, with which we were not familiar. We will add this as a reference in a future update of our work.

However, we believe that our classically evaluatable states (and hence our notion of classical evaluability) are conceptually dif

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Thanks for this interesting result and extending the efficient query access in terms of quantum circuits!

However, I would like to emphasize that showing MA containment of a subclass of QMA using both query access (a.k.a, "classically evaluatable") and sample access, as well as so-called "dequanti

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The main claim of the paper, that by setting A=2/pi ((w, x) + b) the probability of measuring the state 1 resembles the output of a neural network with cos^2 actication function, is a tautology. By that same logic you can set A=sqrt(arccos({whatever you want})) and claim the single qubit is computin

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Hi, thanks for the great result!!
But I have a small question about the implementation of random Clifford unitaries.
Your paper said random Clifford unitaries (with $\epsilon$-error) can be achieved by single-qubit random Cliffords in the first section and random neighboring 2-qubit Clifford unitar

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Hello,

Thanks for the interesting paper.

I'm more curious about the section about the model for AIMC (ReRAM) and digital MACs.

In the paper, the value for each parameter is collected from several papers (as in Table IV). But I think the value will change if a different paper is chosen. Can

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Hello,

>[...] “in this universe, the extent of diverse
and complex things is increasing over time.” There are
undoubtedly many people who have already come to this
idea.

And one of them is also (or maybe even foremost) Julian Barbour. I would love to see some day how your general definition

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Fascinating work! Would be interesting to see comparisons or discussions around how this works fits in with thermodynamic capacity of quantum channels a la Faist, Berta, Brandao.

https://arxiv.org/abs/1807.05610

Hey Jahan, thanks for the pointer, we’ll plan to add that one to our citation list. As you say, this one, like another one preceding it we cite ( https://arxiv.org/pdf/0910.4074.pdf ) point out that you can have 10% interface error if the bulk error is substantially below threshold (0 to 0.1% errors

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You might want to compare to https://arxiv.org/abs/1509.07796, which analyzes a very similar setup but does not appear in your citations.

It's worth noting that this earlier paper used a fairly convoluted scheme to do error correction across the modules, which I never really understand the motiva

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This appears to be a major development for quantum rate-distortion theory.

Hi all,

It has been kindly pointed out to us that the proof of Lemma 5.13 has an error in it, and one cannot lower bound the code distance of a merged code in all generality -- we would require extra conditions to do so.

We will amend this in a future version (along with the header formatting!

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Just spotted this video abstract - what a great idea! Excellent way to communicate the essence of your work.

Check out our [video abstract][1]!

[1]: https://www.youtube.com/watch?v=Rli8yM_KkNM

What is the number of qubits for the numerical simulations? Reads like it is one fixed number but certainly that cannot be the case?

Thank you for your kind and detailed reply!

I think this is a fair question! We were guided to our construction by considering the XZZX cluster state, but that doesn't mean this is the only way to understand our construction.

Certainly, in the case of the 4-star construction, there *are* no qubits that correspond to the RHG/XZZX cluster stat

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Very interesting work! May I ask you a small question? I think the idea to confine erasure errors caused by failed fusions on 2D planes also can be applied to the normal Raussendorf's lattice. In other words, we can freely choose the fusion basis (two distinguishable Bell states) for each fusion so

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Thanks for the reference! This seems to be exactly the same result, but obtained in a slightly different manner.

Very interesting result! A quick question on the unitary permutation inversion problem. I think this unitary permutation oracle was studied under the name of the in-place permutation, and a similar result was shown in https://arxiv.org/abs/1510.06750, Section 3.2. Is there any difference between the

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I thank for the comments of Jan Eisert, whose survey on the area law btw. has been a very illuminating work for me. Let me address the points made:

1. Indeed, the two papers look at different NPO (NP-Optimization) problems. To understand the NPO landscape, here is somewhat of a background. The t

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Nice work. I am not well versed with the literature in the field so I am a bit confused; Is the result that a unital qubit channel can be expressed as the average of 4 unitary channels (Theorem 3.1) new here? I think one can derive it from Corollary 1.3 of [arXiv:1802.01337][1] and that the set of

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We are excited to see that Mario Szegedy as a leading expert on the PCP theorem has looked at the problem that we lay out in our work arXiv:2212.08678 and has suggested an alternative proof of a similar statement as we present it in our work based on the PCP theorem. With this note, we would kindly

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Apologies for a bit of shameless self-promotion, but I wrote a paper on the connection between the Loschmidt echo and quantum metrology back in 2013: https://doi.org/10.1103/PhysRevA.88.021801, which is a bit earlier than a lot of the papers cited here, e.g., Macri, Smerzi, Pezze, "Loschmidt echo fo

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Minor but annoying errata: the future work section has the placeholder text "[reference to jupyter]" instead of an actual reference to the notebook.

The [web of science journal indexing][1] database indexes each article in journals. HIGS has a complete list of [Web of Science Journal list][2] . Get connected with our team now and download the list. Our team also provides so many free add-ons. [For More Information][3]

[1]: http://higssof

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I leave some references on Time-varying quantum channels which I missed in the article (I know I am the author of those, but there is little literature on the topic):

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

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.105.012432

https:/

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You write "the linearity of $H_{i,j}$" (penultimate paragraph). I think that should read "the existence of $H_{i,j}$"; the thing that is linear is the map. But a map from density matrices to probabilities is linear if and only if it can be written as the trace of $H \rho$ for some $H$. If your main

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We have written a response which can be found here https://scirate.com/arxiv/2212.03629

Yesterday's Quanta magazine article on this: [link][1].

[1]: http://www.quantamagazine.org/after-a-classical-clobbering-a-quantum-advantage-remains-20221207/

Note that Problem 1 of Appendix C is equivalent to the construction of a perfect [Golomb ruler][1] of length $m$. This problem admits no solution for $m \geq 5$.

We discuss some implications of this for the Fourier spectra of quantum models in ([2209:05523][2]).

[1]: https://en.wikipedia.

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In Fig. 4, it looks to me like the three logical qubits could be described by the following pairs of logical $Z$ and $X$:

* $Z_1 Z_2$ and $X_1 X_5 X_9$;
* $Z_3 Z_4$ and $X_1 X_3$;
* $Z_7 Z_8$ and $X_7 X_9$.

From these it seems that the code is in fact distance 2, rather than distance 3.

Am I miss

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Ah I see. Thanks for your reply!

Thank you for your question. Because the error of our scheme is larger than what we need in the hardness conjecture of that paper, our result does not contradict the conjecture.
Please refer to AA's original boson sampling paper, where a similar thing happened for the permanent and Gurvits's algorit

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Hi, amazing work! I was wondering if your results would affect the structure of proof in [https://www.science.org/doi/epdf/10.1126/sciadv.abi7894][1], which is based on the conjecture that |Haf|^2 is #P-hard to approximate to within *additive* error (Conjecture 2 in the paper)? Thanks!

[1]: h

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Amazing work! Look forward to reading it in more detail!

Thanks for the nice question. In this framework, in the simplest case, we have two systems (the main system and the heat bath) coupled by an energy-conserving interaction. Therefore, any change in the energy of the system
is equivalent to the same (with a minus sign) change on the bath (therefore

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I really like your axiomatic formalization!

One suggestion, though:
I would rename "efficiency" to "faithfulness".

Thanks for the reply. I have a small question content-wise. Is there no distinction between work and heat in this framework? It seems like all the energy influx into a system is counted as 'heat', but I think somehow work can be exchanged too between systems with different temperatures through a ene

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Thanks for the comment. You are right. The second statement about heat flows should be just as you wrote, i.e: "heat will flow from the environment". The right statement is captured by Eq. (5).

Thanks for mentioning the typos. We plan to update the arXiv version soon; We'll get rid of them :)

Classic work establishing, among other things, equivalence between establishing high entanglement fidelity and low diamond-norm error. However, the arxiv version has an incorrect proof of this fact (Thm 1 in section V.A); see the IEEE IT version for the correct proof.

Nice work. I am still reading the paper but I think "Heat will always flow towards the environment " and "the environment will always absorb
heat" on the first page mean the same thing. It seems like the second sentence should say that the heat will flow from the environment as it is hotter than $\r

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The proof that the stoquastic local Hamiltonian problem is in AM also applies to stoquastic Hamiltonians that are sparse, but non-local. On [page 5][1]:

"Moreover, we will prove that evaluation of the largest eigenvalue of any n-qubit non-negative matrix whose matrix elements are efficiently co

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I see. We are no experts in the technicalities here so we will correct the section here accordingly. I believe MA is correct since the Hamiltonian corresponding to a graph is frustration-free. But we will need to clarify this.

All we were trying to say (and the gist this holds) that the algorithm

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Thanks for this interesting result, but I am confused about the discussion regarding stochastic Hamiltonians (on Page 7):
> The problem of calculating the ground energy of stoquastic local Hamiltonians was shown to be contained in MA by Bravyi, Divincenzo, Oliveira, and Terhal [BDOT08].

As far as

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