Markus Heinrich May 28 2020 09:38 UTC

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

...(continued)
Yuanjia Wang May 21 2020 06:51 UTC

A dumb question: If one wants to reduce noise on NISQ devices, it's likely that the quantum autoencoder needs to be implemented on a NISQ device as well. The circuit depth and the decoherence would limit the autoencoder's design and performance. Can we still get good mitigation results using those i

...(continued)
Mao LIN May 19 2020 05:11 UTC

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

Sevag Gharibian May 12 2020 08:52 UTC

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

...(continued)
Blake Stacey May 09 2020 23:15 UTC

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

Ben May 05 2020 01:04 UTC

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

Robert Tucci May 01 2020 04:03 UTC

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

...(continued)
Varun Narasimhachar Apr 24 2020 03:52 UTC

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

Mankei Tsang Apr 23 2020 03:39 UTC

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

...(continued)
Richard Howl Apr 16 2020 07:07 UTC

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

...(continued)
Kianna Wan Apr 14 2020 23:36 UTC

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

Ryan Babbush Apr 13 2020 17:57 UTC

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

...(continued)
Sam Pallister Apr 13 2020 16:57 UTC

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

...(continued)
Ryan Babbush Apr 13 2020 05:13 UTC

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

...(continued)
Jerry Finkelstein Apr 09 2020 16:43 UTC

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

...(continued)
Cupjin Huang Apr 06 2020 18:36 UTC

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

Blake Stacey Apr 01 2020 19:33 UTC

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.

Robin Blume-Kohout Apr 01 2020 13:12 UTC

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

...(continued)
Māris Ozols Apr 01 2020 12:13 UTC

A breakthrough!

Mark M. Wilde Mar 17 2020 02:34 UTC

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

Victory Omole Mar 11 2020 14:39 UTC

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

Andreas Wendt Mar 10 2020 02:44 UTC

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

rrtucci Mar 09 2020 08:24 UTC

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

...(continued)
David Gross Mar 04 2020 07:39 UTC

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

...(continued)
Christopher Chubb Mar 04 2020 02:30 UTC

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

...(continued)
Vishal Katariya Mar 03 2020 17:17 UTC

I agree.

Edgar A Aguilar Mar 03 2020 10:22 UTC

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

...(continued)
Jalex Stark Mar 02 2020 16:21 UTC

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.

Steve Flammia Feb 24 2020 20:43 UTC

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

...(continued)
Robert Huang Feb 24 2020 19:28 UTC

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 $\mathcal{O}(\log(M) 4^k / \epsilon^2)$

...(continued)
Alireza Seif Feb 24 2020 15:25 UTC

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}{ ...(continued) Mankei Tsang Feb 21 2020 05:52 UTC 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 ...(continued) Robert Huang Feb 21 2020 05:13 UTC 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 ...(continued) Mankei Tsang Feb 21 2020 03:22 UTC 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 ...(continued) Cupjin Huang Feb 21 2020 02:38 UTC 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 ...(continued) Earl Campbell Feb 20 2020 01:56 UTC 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 Daniel Greenbaum Feb 19 2020 00:40 UTC 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 ...(continued) Ximing Wang Feb 17 2020 08:18 UTC 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 ...(continued) Christopher Chamberland Feb 15 2020 00:25 UTC In fact, twirling when one has coherent noise can make the performance worse (see https://arxiv.org/abs/1612.02830). Nicolas Delfosse Feb 14 2020 23:51 UTC 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 ...(continued) Daniel Greenbaum Feb 14 2020 20:40 UTC 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? Mankei Tsang Feb 11 2020 14:31 UTC 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 ...(continued) Ravi Kunjwal Feb 10 2020 11:28 UTC 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 ...(continued) Johnnie Gray Feb 10 2020 02:27 UTC 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 ...(continued) John Brown Jan 31 2020 23:27 UTC 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 William Kretschmer Jan 28 2020 03:05 UTC 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).

Paul Secular Jan 16 2020 17:20 UTC

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

...(continued)
Narayanan Rengaswamy Jan 15 2020 22:09 UTC

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