Recent comments from SciRate

Nice work. By the way, your paper's arxiv metadata abstract field has a redundant copy of part of the abstract.

Proposition 7 for the SLD information is a known property called extended convexity; see S. Alipour and A. T. Rezakhani, PRA 91, 042104 (2015), http://dx.doi.org/10.1103/PhysRevA.91.042104. We proved it for multiple parameters by relating it to the strong concavity of the fidelity; see Ng et al., PR

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Thanks very much for your comment Jerry. As with other table-top tests of quantum gravity, we are proposing an experiment in which all forces other than gravity, e.g. the electromagnetic force, can be neglected. Then, due to the universal coupling of gravity, gravity couples to the kinetic and mass

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much thanks to Craig Gidney, for pointing out that the only linear-depth Clifford component can equivalently be implemented in logarithmic depth

Indeed, just focusing on T complexity is a bit too simplistic. I only quoted that number because your abstract focused on T complexity. The tradeoff between gate complexity and space complexity is why the abstract of [arXiv:1902.02134][1] emphasizes the reduction in surface code spacetime volume (a

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Hi Ryan,

I agree with your argument that the $10^{15}$ value is outdated at this point. I'll post an updated version that better reflects this. However, the $10^{11}$ figure is a swing too far in the opposite direction, I think. Even though the algorithm in [arXiv:1902.02134][1] is the most minimal

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The $10^{15}$ figure in the abstract refers to an older algorithm. More recent work has brought estimates for FeMoco to around $10^{11}$ (see [arXiv:1902.02134][1]), albeit with some ancilla (but even a version with very few ancilla improves from $10^{15}$ gates). That new work is based on qubitizat

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This is certainly an important result. However, it does seem to require the assumption that "the classical interaction would not induce quantum self-interaction". So I wonder how certain we can be that, for example, classical gravity might not induce a very small term (such as suggested in footno

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The code implementing the angle finding algorithm, together with an example of Hamiltonian simulation, is available at [GitHub][1].

[1]: https://github.com/alibaba-edu/angle-sequence

I was sure that somebody had won an Ig Nobel for doing this, but I think my memory mixed up the levitating-frog experiment with a stunt that they did back in the day at the MIT Magnet Lab, lowering the temperature of a whole workshop with LN2 until they could Meissner a magnet off the floor.

After reading footnote [32], I would like to enthusiastically urge everyone to cite this paper heavily via every medium. My homestead on the Tozitna River in interior Alaska is, in fact, engaged in a long-running and ongoing war with beavers. The dam critters keep building dam after dam across the

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A breakthrough!

now this is one paper on QKD that I think deserves many scites! :)

Tensorflow Quantum combines Tensorflow with [Cirq](https://github.com/quantumlib/Cirq). Are you asking for Cirq to be combined with pyTorch as well?

Cool, thanks. Can now somebody please port it to pyTorch?

https://qbnets.wordpress.com/2020/03/09/google-releases-tensorflow-quantum/

A quick question. Volume is complexity. Then the time that Alice needs to measure the volume is the complexity of complexity, just like

>Complexity of complexity is the number of simple logical steps that it would take to confirm
$\mathcal{C} \le \mathcal{C}_0$

Then why can we assume

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Thanks, Edgar, Vishal, for your feedback!

The title is an attempt at humor - no sensationalism intended. I don't think that a technical paper on gate decompositions will be understood as taking a stance on the validity of mystic medicine. (In the same way that the title of Scott Aaronson's book i

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I agree that scientists should suppress their tendency to *excessive* sensationalism, but I don't know that this title crosses the line. In fact, in this case, it seems to be a relatively apt description of the title and amusing to boot. It certainly caught my attention.

Perhaps a note somewhere

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I agree.

Perhaps it would be good to reconsider the title. As scientists, we should not succumb to the temptation for sensationalism - and we should try to mark a clearer distinction between real science and pseudoscience.
I think the work you did here is really impressive, and the title removes some of thi

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Takes a task that I thought required complicated self-testing techniques and achieves it with a beautifully simple protocol that requires almost no technology for the analysis. This should be taught in classes.

Regarding the name, I actually prefer "shadow estimation" for this task. (I suggested this as well to Scott, but he went with "shadow tomography" instead.) This is because tomography is the inverse problem of taking a shadow and reconstructing the object that produced the shadow. The term "shadow" d

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Good observation! The main theoretical result we proved for predicting quadratic functions with random Pauli measurements is given in Example 1, Appendix (A3). The number of measurements needed to predict $M$ quadratic functions to $\epsilon$ additive error is $\mathcal{O}(\log(M) 4^k / \epsilon^2)$

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Congratulations on this very exciting work! I have a question regarding the second Rényi entropy measurements in Figure 4b. The error in Brydges et al. scales like $\frac{1}{\sqrt{\text{num. of exper.}}}$ as expected. However, the figure suggests that the shadow protocol's error scales as $\frac{1}{

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I completely agree that the quantum problem has interesting new nuances and I look forward to reading your work as well as related papers; I'm just not sure about the necessity of the name "shadow tomography."

Regarding the issue of non-commuting observables, it is interesting to note that the Ho

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From my understanding, semiparametric and nonparametric estimation focuses on the best approach to estimate a single (complicated) function of the underlying statistical object (probability distribution or quantum states). When we want to estimate a single linear function in the quantum state, Tr(O

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Correct me if I'm wrong, and I'm not questioning the novelty of recent works of this nature, but I think there's no need to create a new name such as "shadow tomography" for this type of problems. Classical statisticians have been studying the estimation of probability density functionals for many d

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The abstract differs slightly from the abstract in the article. Please refer to the abstract in the article for the most recent version:

We report, in a sequence of notes, our work on the Alibaba Cloud Quantum Development Platform (AC-QDP). AC-QDP provides a set of tools for aiding the developmen

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Here is the submitted TQC extended abstract, if you want to read a 3 page summary
https://earltcampbell.files.wordpress.com/2020/02/tqc_abstract.pdf

Nicolas, Christopher,

Thanks for your responses. The previous papers you cited assume no syndrome measurement error, which is an idealization. It's not obvious to me what the results in those papers would have been if syndrome measurement error were included.

Conversely, this new paper does co

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Sorry for the confusion, but as I mentioned in our earlier discussions, our paper [WMHY19](https://scirate.com/arxiv/1902.00869) is based on a different framework, and I'm not sure if they can be compared directly. As a simple illustration, the wiki page of ['AdaBoost'](https://en.wikipedia.org/wiki

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In fact, twirling when one has coherent noise can make the performance worse (see https://arxiv.org/abs/1612.02830).

That's correct. We focus on bit flips or Pauli noise. This seems reasonable since coherent errors generally do not degrade too much the performance of error correction as one can see with your repetition code paper [https://arxiv.org/abs/1612.03908] or with the surface code study of [https://arxiv.o

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This paper appears to consider only stochastic errors, i.e. bit-flips with probability p. Have you thought about how the results would change for coherent errors?

Shameless self-promotion: I studied the same problem (quantum estimation of one parameter among many unknown parameters) and also used geometric concepts extensively in this work:

https://scirate.com/arxiv/1906.09871 (first version on 24 Jun 2019, last update on 6 Feb 2020)

Now that Carl is wo

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Attention, this abstract caught, of this reader on account of the writing style. Curious, this reader perused the manuscript and found in it the following explanation:

"Unusual, it might be thought, is the style of this paper. An explanation is in order. Kip
Thorne’s recent biographical memoir o

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If anyone fancies giving these a whirl, a python package is now available here https://github.com/jcmgray/cotengra including some snazzy, if not necessarily informative, visualizations...

![Optimized contraction tree for a random regular graph.][1]

[1]: https://camo.githubusercontent.com/04c

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Very interesting research. It is a good starting point, but I think it must be improved using the existing algorithms.

John Brown

[Elatom][1]
[1]: http://elatom.com

For Theorem 3, it is worth mentioning that the the only $k$-transitive group actions for $k > 5$ are the symmetric and alternating groups (see https://en.wikipedia.org/wiki/Mathieu_group#Multiply_transitive_groups).

Congratulations on this excellent work. The use of the new MPI shared memory feature is particularly impressive. I would, however, have liked to have seen tables or plots of parallel efficiencies. For example, when you scale from ~500 to ~2000 CPU cores, it doesn't look like you are gaining much by

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A shorter (conference) version of this paper is here: https://arxiv.org/abs/2001.04887

For those looking to understand this from the "outside" operator algebras point of view:

The authors use complexity-theoretic language to recursively build a presentation for a very nasty C* algebra. In order to extract properties of the algebra from its presentation, they use the language of quan

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We know that protein folding and fluid dynamics are still hard to simulate classically. The point of quantum supremacy is that the hardness comes from interference in an exponentially large state space. So "analog supremacy" and "quantum supremacy" seem like different things.

Awesome framework, nice to see the paper online! :)

Awesome work! I've been advocating experimentalists to eventually do the test through IQP sampling and claim the \$25 reward for quite some time, I didn't imagine it would be broken classically!

Marvelous.

Wow, this is really neat - a completely different way of thinking about Grover's algorithm! It never occurred to me that one can think of the amplitudes of a $d$-dimensional quantum state as velocities of $d$ balls, and that the normalization of the state corresponds to the conservation of kinetic e

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Version 2 expands the penultimate section (on Fuchs and Peres 2000) in response to reader feedback.

I doubt money is the bottleneck, even though it will be expensive. More likely writing the code, optimizing it, testing it, and then scheduling the computation are just time consuming. If money were the only barrier to doing a validation, then this would have been done already.