Recent comments from SciRate

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

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.

> 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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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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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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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.

Thanks for your suggestion, but there is a reason why in this case I prefer a separate submission to an update.

The addendum is related to [arxiv:1912.03645]. Note that most readers only look at the latest updated version while remembering the submission date of the original version. If I update my

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The common thing people do is to simply update the arXiv submission. As arXiv keeps old versions stored, this seems a clean way to include an addendum.

I posted an addendum today:

https://vixra.org/abs/2007.0215

It is very unfortunate that the policy of arXiv does not allow an addendum as a separate submission so that I have to post it elsewhere. I am adding this comment here in order to advertise the addendum, for few people keep an eye on viXra

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Hi William, thanks for your comment. Please refer to Appendix I for the discussion about the more general settings beyond depolarization noise.

What are the conditions for the results regarding noisy learning to break down when you go beyond depolarizing noise?

This paper points out that it is unlikely that quantum resources will accelerate the convergence of the Hartree-Fock procedure. This timely analysis seems prompted by Google’s recent experimental demonstration of Hartree-Fock on a quantum computer ([arXiv:2004.04174][1]). But in case there is any do

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Do you have a reference/reason for k-local gates to have cost proportional to k?

The [repository][1], which contains the code for this paper, is now available open-source.

[1]: https://github.com/a-wozniakowski/scikit-physlearn

Discussions of this paper have transpired [here](https://golem.ph.utexas.edu/category/2020/06/getting_to_the_bottom_of_noeth.html) and [here](https://johncarlosbaez.wordpress.com/2020/06/29/noethers-theorem-2/).

The arXiv admin fixed it! The PDF should now work.

arXiv is somehow unable to produce a PDF, but the postscript version https://arxiv.org/ps/2007.04849 is fine. Will try to fix.

Beautiful illustrations. A simplified version of this would make for a wonderful undergrad homework problem, I think.

Eq. (1) defines a qubit SIC, for whatever that's worth.

If the initial state is $|\psi\rangle$ and the possible post-transition states are $|\phi_i\rangle$, then unitary transformations will leave invariant the [3-vertex Bargmann invariants](https://arxiv.org/abs/quant-ph/0107006) $\langle \psi | \phi_i \rangle\langle \phi_i | \phi_j \rangle \langle \phi

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This "paper" needs more likes! :D

Initially I thought that non-contextuality could be derived from invariance under unitary transformations, but that is wrong. If a set of orthonormal states is given as possible states after the transition, then their scalar products with the initial state remain unchanged under unitary transformati

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The assumptions that the transition probabilities are unchanged by unitary transformations, and that they must vanish for orthogonal states, are rather substantive assumptions. There is also the implicit assumption that they are non-contextual (since the notation which is used requires that transit

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The paper has now been updated.

Thanks for the update! (It's good to see such forthcoming/virtuous academic integrity :-) ) Also good idea to post it here, will have to remember it in the future.

Hi Henrik,

That certainly helps, thank you! I did read the other paper too.

Abhinav

The claim that we strengthen Matsumoto's result is incorrect. An update of the paper removing this claim is forthcoming.

Hi Abhinav,

thank you for your comment! I believe that any $P$ fulfilling $\exp(\mathrm i P)=U$ decays as $1/|x-y|$. But indeed, we don't show this in the paper and should have phrased the appendix a bit differently. We will update it.
(I would like to thank Zoltán Zimborás for discussions regar

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In short, the authors improved $\beta$ VAE Framework by reaching a better trade-off in terms of Reconstruction Quality vs Disentanglement (first contribution) according to a new metric they propose (second contribution)

The core idea comes from the fact the authors reached a deep understanding of t

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Really nice paper! Regarding Appendix D, how can I see that there cannot be a different generator giving rise to the same dynamics at discrete times? I mean that $U = \exp(iP)$ does not have a unique solution for $P$, so it does not rule out a quasi-local generator for $U$. Or are you claiming that

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Hi Filip, thank you for your interest. We are looking forward to making the code available once it is more user-friendly.

I'm going to cautiously advance the opposite of the italicized conjecture on p. 2 and hazard a guess that sets of $2d^2 - d$ equiangular lines will _not_ generally exist in $\mathbb{H}^d$. This inclination of mine is perhaps due to coming to the problem of equiangular lines from quantum theory, and

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> the idea (emerging from the above assertion)
that the event A gives rise, as effect, to an event which is absolutely not different from A, has to be
rejected as an absurdity

It reminds me of John Wheeler's Participatory (aka Self-observing) Universe, and it seems you have unwillingly strength

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Exciting work! May I kindly ask if you thought about making your optimization code publicly available? I believe that it would make using your methods much easier for a lot of people!

This is a clever and interesting paper. I am not a proponent of the "consciousness causes collapse hypothesis" (CCCH), but I nevertheless want to remark that somebody who is might attempt a defense of the CCCH along lines of the following:

Take the CCCH to say that wave-function collapse occurs w

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Cedric,

1) In Theorem 27, we show that if a promise problem is recognizable in O(log n) space and poly(n) time by a family of *general* quantum circuits, then it is also recognizable in O(log n) space and poly(n) time by a family of *unitary* quantum circuits. A bound on the hidden constants in t

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Great work! I haven't had time to gone through the paper in great detail, but I have two immediate questions:

1) You mention in the abstract that the procedure is simultaneously space-efficient and time-efficient, but I couldn't find a statement of this in the main body. Could you be more precise

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https://qbnets.wordpress.com/2020/06/07/anomaly-detection-with-quantum-computers-better-than-with-classical-computers/

A short talk based on this work is scheduled today at 16:30 (UTC+2): https://www.youtube.com/watch?v=h4uFaV6rFSc

More details (including a 3-page abstract) here: https://www.monoidal.net/paris2020/talk/qs12t1.html

Here's a short talk based on this, given today at QPL 2020: https://www.youtube.com/watch?v=uO08ci5dK6Q

From my perspective, everything until Section 5 follows directly from the fact that the group $\mathrm{DS}(2^w)$ (aka *real Pauli group*) as well as the projective and normal Pauli group form unitary 1-designs and thus a tight frame for the space of complex matrices which gives you the desired Parse

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It would be very interesting if one can show and realize the maximally localized Wannier functions in a digital quantum simulations.

Great work, please do keep it up! Minor gripe about abstract statement - the sentence about experimental systems is misleading, as far as I understand due primarily to the difficulty of reliable single-photon sources in the lab. I realize you say "in principle", but to the average CS person like mys

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The orthonormal operator bases defined in Eq. (9) were previously studied by Zhu, who proved that they saturate bounds defined using the negativity of quasi-probabilities [PRL **117** (2016), 120404, [arXiv:1604.06974\]][1].

[1]: https://scirate.com/arxiv/1604.06974

Simons Apers's talk at the Simons Institute: [https://simons.berkeley.edu/events/quantum-speedup-graph-sparsification-cut-approximation-and-laplacian-solving][1]

[1]: https://simons.berkeley.edu/events/quantum-speedup-graph-sparsification-cut-approximation-and-laplacian-solving

https://arxiv.org/abs/quant-ph/9805016
How to Compile a Quantum Bayesian Net

I am unsure about the reasoning presented in this paper. It seems to me that there is an issue with the reasoning used to upper-bound the query complexity of the multi-layer quantum search method.

On page 4, you begin by lower bounding the number of queries Q of the algorithm by a value Qmin (eq

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