Recent comments from SciRate

Yu Tong Feb 24 2021 17:42 UTC

Hello Professor Terhal, thank you for this very nice question! First as you correctly pointed out, we assume we start with a quantum state that only has a non-trivial overlap with the ground state, instead of the exact ground state. With this assumption a lot of phase estimation methods, such as the

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Barbara Terhal Feb 24 2021 07:18 UTC

Hi authors, interesting results! How does your work relate to Heisenberg-limited scaling in Theorem V.1 in https://arxiv.org/pdf/1502.02677.pdf in which one bounds the variance of the estimator. You write that your error is epsilon (which you get with high probability in Corollary 3), but this is no

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Sabee Grewal Feb 24 2021 01:10 UTC

Thanks for the question! Yes, we assume perfect free-fermion states. Also, we only require measurements in the standard basis, and we assume that they are performed without errors.

Thank you for sharing your paper on Fermion Sampling! Yes, based on your results, it appears that we wouldn't be abl

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Michal Oszmaniec Feb 23 2021 12:20 UTC

Very nice paper!

Does the result assume perfect free fermion states or some imperfection is allowed (say in trace distance)?

I also wanted to remark on two of the open problems stated in the end of the paper.

1) Learning pdfs corresponding to superpositions of free states.
I think that it is u

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Johannes Jakob Meyer Feb 17 2021 07:31 UTC

Is this a monotonic (aka non-increasing with respect to quantum channels) distance measure?

Mark M. Wilde Feb 16 2021 20:21 UTC

An important original contribution of this paper is that the author has identified conditions under which the relative entropy of Gaussian states is finite. The conditions depend only on the mean vectors and covariance matrices of the states being evaluated.

Ramis Movassagh Feb 05 2021 01:28 UTC

@Marcel Hinsche. Thank you for your question. I agree that polynomial extrapolation is notoriously ill-conditioned and suffers from the shortcoming you refer to. Our techniques might get you close to O(2^-n/poly(n)) for constant depth circuits but not close enough. Moreover, one loses the anti-conce

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Marcel Hinsche Feb 04 2021 16:47 UTC

Dear authors, if I understand correctly worst-case to average-case reductions via polynomial interpolation cannot possibly extend into the regime of additive errors of size $O(2^{-n}/poly(n))$ that would be needed to close the gap in the hardness of sampling argument for random circuit sampling. Thi

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Joe Fitzsimons Jan 28 2021 07:39 UTC

Robert: I believe in the 2002 paper there is a single additional system that is used to go from qubits to rebits, so locality is not preserved in the translation from qubit systems to rebit systems.

Robert Raussendorf Jan 28 2021 01:57 UTC

How does this fit with
https://arxiv.org/abs/quant-ph/0210187
?

Jalex Stark Jan 27 2021 17:33 UTC

If I understand correctly, the authors have made a grand achievement in experimental quantum foundations. Congratulations!

My understanding is as follows:
They construct something like a
tripartite Bell inequality [0], whose maximal violation is achieved with only 4 qubits. Any experimental

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Casper Gyurik Dec 18 2020 14:57 UTC

Today an updated version of the paper has been uploaded to arXiv. We have added new quantum algorithms along with complexity-theoretic evidence for the classical intractability of the underlying problems, we have identified families of instances (i.e., graphs) with a quantum speedup, and we have imp

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Nengkun Yu Nov 30 2020 19:36 UTC

Problem solved.

Markus Heinrich Nov 30 2020 08:58 UTC

Since today, an updated version of the paper is available on the arXiv. Besides having fixed the grammar mistake in the title, we have been able to extend our argumentation to show that the classes are already distinct for $n \geq 2$ qubits ($n\geq 3$ in v1) and agree for $n=1$.

Nengkun Yu Nov 30 2020 08:36 UTC

There seems to be an issue with the arXiv tex engine.
No idea why the system accepted our submission in the first place,
when everything seemed OK, but cannot compile it now.

However, it _does_ produce perfectly good Postscript, which you
can then convert to pdf or any other format.

Jiayu Zhang Nov 21 2020 01:46 UTC

I just realized arXiv does not favor frequent version updates... My update frequency is limited to once per month. See my personal website for the most recent version (which contains some typo fixes and font change etc compared to the previous versions) and sorry for the possible bothering.

Since

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Jiayu Zhang Nov 17 2020 19:43 UTC

(Updates: improved talk in https://www.youtube.com/watch?v=ri8uOOreEJU after a little bit of practicing. Resources in http://cs-people.bu.edu/jyz16 )

Māris Ozols Nov 16 2020 08:56 UTC

Maybe tone down the "epidemiology" bit in the abstract or substantiate it somewhere in the paper? You don't want some popular science journalist to draw the wrong conclusions.

Junyu Liu Nov 15 2020 06:47 UTC

It is my first time to see that a paper in quantum finance is using the JHEP style latex preprint.

Noon van der Silk Nov 13 2020 06:23 UTC

Thanks for Angelo for reporting this on github - https://github.com/scirate/scirate/issues/396 - it's the font! Great discovery.

Ruslan Shaydulin Nov 12 2020 14:36 UTC

Wow what an awesome random bug tantan
(confirmed in Safari 14.0 on macOS 10.15.7)

Anthony Polloreno Nov 11 2020 20:59 UTC

Scirate question - why does `tantan` render as tantan (a smiley face in my browser)?

Ryan Babbush Nov 10 2020 19:48 UTC

Thanks for the comment! Indeed, part of our motivation for writing this perspective was to provoke the community into describing ways of implementing quadratic speedup algorithms that might defy this analysis. But if I understand your suggestion correctly I do not think it would work. Usually the "c

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Ruslan Shaydulin Nov 10 2020 14:53 UTC

Great perspective. One wonders if some kind of hybridization is possible, where at each step the classical logic primitive is computed on a classical computer based on information obtained via partial measurement and the result fed into the quantum algorithm. E.g. for optimization, the value of the

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Jiayu Zhang Nov 10 2020 06:04 UTC

Dear all who are interested in this paper:
This paper has gone through significant rewrites in this half a year and recently and hopefully is more understandable than previous versions. The most suggested talk so far can be found in https://www.youtube.com/watch?v=PqGwYDeBvQU&feature=youtu.be which

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Hsin-Yuan Huang Nov 06 2020 17:40 UTC

A tutorial on Tensorflow Quantum [https://www.tensorflow.org/quantum/tutorials/quantum_data][1] provides an implementation of the numerical experiments.

It shows how classical and quantum ML models can both easily achieve near-zero training error but the quantum model can generalize better on eng

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Angelo Lucia Nov 03 2020 18:56 UTC

The referenced paper is https://scirate.com/arxiv/2004.01469

Mark M. Wilde Oct 22 2020 17:51 UTC

This is a strong and interesting result for the resource theory of thermodynamics and the resource theory of asymmetric distinguishability. I send my congrats to the authors.

Blake Stacey Oct 02 2020 00:44 UTC

Yes, it certainly *seems* like the operational argument (at the end of section IV.A) would apply to Bohmian mechanics.

Jerry Finkelstein Oct 01 2020 19:24 UTC

In this paper, there is an operational argument in support of the assumption which is labeled P3 (that the two-time probability is a linear function of the quantum state). One might have supposed that this argument would apply equally-well to Bohmian mechanics; however, (as noted in the paper), a

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Simon Apers Sep 29 2020 19:36 UTC

A nice perspective by one of the authors: [https://mycqstate.wordpress.com/2020/09/29/it-happens-to-everyonebut-its-not-fun/](https://mycqstate.wordpress.com/2020/09/29/it-happens-to-everyonebut-its-not-fun/)

Johannes Bausch Sep 23 2020 11:56 UTC

Or, shamelessly advertising myself here, "Recurrent Quantum Neural Networks", http://arxiv.org/abs/2006.14619 (2020)

quantum_hn Sep 18 2020 13:18 UTC

At the bottom of p. 2 the authors comment "However, the problem of learning sequential data, to our best knowledge, has not been investigated in the quantum domain."

However, with the ubiquity of modern search engines, it would not have taken too much effort to find that in fact there have been s

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C. Jess Riedel Sep 15 2020 19:25 UTC

Thanks!

Weilei Zeng Sep 15 2020 17:40 UTC

They actually work by copying and pasting, but the embedded URLs leads to the wrong places.

Weilei Zeng Sep 15 2020 17:37 UTC

Interesting result. Just as a feedback, the two google links on Page 4 are not available.

Anthony Leverrier Sep 10 2020 13:23 UTC

Ah yes! Thanks for the explanation.

Matt Hastings Sep 10 2020 12:58 UTC

Glad you like it! I must admit, we also thought it was N^{5/8} for a while. But, I think N^{3/5} is indeed what follows from balancing. Though, if we miss something, please let us know so we can get that extra 0.025 power in the exponent.

Ignoring polylogs, one has distances N^{1/2} and N^{3/4

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Anthony Leverrier Sep 10 2020 11:55 UTC

Amazing! Unless I'm missing something, the distance should even be $N^{5/8}$ instead of $N^{3/5}$, unless the balancing trick (or the final weight reduction) causes the expected distance to decrease.

Namit Anand Sep 10 2020 05:30 UTC

Yes, please do post it here if you find something interesting -- you're also welcome to just send me an email! Also, thanks for pointing to its role as a biodiversity measure -- I never would have found that (in fact, they use the entire family of Rényi entropies).

Blake Stacey Sep 10 2020 03:09 UTC

Thanks for the reply!

The first time I encountered a quantity of the form $\sum_i p(i)^2$ was in the context of Rényi entropy, and then as a [biodiversity measure](https://www.maths.ed.ac.uk/~tl/mdiss.pdf), so it defintely does appear under many names! I'll look around for earlier references conn

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Namit Anand Sep 08 2020 18:05 UTC

Hi Blake, thanks for the comment. In fact, the connection between $l_2$-norm of coherence and participation ratio was already used in a previous paper by a subset of the authors: https://arxiv.org/abs/1906.09242; see Appendix C (where it is implicitly used). But for some reason, we had forgotten to

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Blake Stacey Sep 08 2020 17:28 UTC

In Eq. (5), the authors state that given a pure state and a basis, the second moment of the probabilities for that state measured in that basis is equal to 1 minus the [$l_2$-norm of coherence](https://arxiv.org/abs/1311.0275), and they say that "To the best of our knowledge", they make that connect

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Gil Kalai Aug 28 2020 06:13 UTC

Victory asked if my theory does not contradict the (excellent) paper "Quantum advantage with noisy shallow circuits in 3D" by Sergey Bravyi, David Gosset, Robert Koenig, and Marco Tomamichel (BGKT).

This is a good question.

The crucial point is that my theory excludes the ability of NISQ s

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Junyu Liu Aug 26 2020 12:35 UTC

I like the title of this paper! It is very cyberpunkian!

Giacomo Nannicini Aug 24 2020 19:55 UTC

Thanks for the very detailed comments, this was extremely helpful.

I posted a revision based on your suggestions. Let me remark that this introduction is meant for non-physicists that may not be comfortable with the more traditional approach.

Victory Omole Aug 13 2020 06:30 UTC

> The computational complexity class describing NISQ circuits is LDP (low-degree polynomial) and
this class is contained in the familiar class of distributions that can be approximated by bounded-depth
(classical) computation.
) Distributions that can be (approximately) described by bounded-degre

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Matt Mercer Aug 12 2020 02:17 UTC

Belief Propagation was invented by Judea Pearl for Bayesian Networks, not Tensor Networks.
Guiffre Vidal's first paper (2005) where he uses the term “Tensor Networks” https://arxiv.org/abs/quant-ph/0511070

First paper (1997) to use Quantum Bayesian Networks in quantum computing
https://arxiv.or

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Blake Stacey Aug 11 2020 23:06 UTC

I've had some notes about a mild generalization of Proposition III.4 sitting around since about the time this appeared. Since I don't seem to be doing anything else with them, I figured I might as well post them here.

For an arbitrary square-free integer $n \geq 2$, we can find a dimension $d \ge

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Yichen Huang Aug 04 2020 02:48 UTC

After several rounds of negotiations with arXiv moderators, the addendum is accepted by arXiv and appears today:

https://scirate.com/arxiv/2008.00944

I would like to thank arXiv moderators for reviewing my case and understanding the situation.