Quantum states and knowledge: Between pure states and density matrices

Mankei Tsang Nov 17 2018 16:18 UTCThomas D. Galley Nov 16 2018 19:07 UTC

...(continued)To echo the above comment by Pavel. If Alice prepares her system $S$ in the Z basis using an unbiased coin $C$ and forgets the outcome (but not the preparation basis) her state is:

$\rho^Z_{S,C} = \frac{1}{2} (|0\rangle \langle 0|_S \otimes |H \rangle \langle H|_C + |1\rangle \langle 1|_S \otimes

Markus Heinrich Nov 16 2018 14:18 UTC

...(continued)To me, it seems that the authors don't like that the Heisenberg representation of a composed channel $\mathcal{E_1}\circ\mathcal{E}_2$ is given by $(\mathcal{E_1}\circ\mathcal{E}_2)^\dagger = \mathcal{E_2}^\dagger\circ\mathcal{E}_1^\dagger$ instead of $\mathcal{E_1}^\dagger\circ\mathcal{E}_2^\dagger

Oleg Kabernik Nov 15 2018 19:29 UTC

...(continued)This is not a resolution, just a possible refinement of the treatment.

It seems to me that Alice's choice of polarization axis should also be recorded in a separate notebook. The fact that Alice "remembers" the polarization axis after Charles stole the first notebook but does not "remember" the

Pavel Nov 15 2018 15:14 UTC

...(continued)If I was Alice my state would be like

$$

\frac{1}{2} |\uparrow \rangle\langle \uparrow |\otimes \rho(\text{notebook that someone have stolen says up})

$$

$$ +\frac{1}{2} |\downarrow\rangle\langle \downarrow|\otimes \rho(\text{notebook that someone have stolen says down}),$$which encodes the pr

Mankei Tsang Nov 15 2018 13:44 UTC

...(continued)I suspect that the object he's looking for is the hybrid density operator $\rho(x) = \rho_x P(x)$, where $\rho_x$ is the density operator conditioned on a classical variable being $x$ and $P(x)$ is the prior probability distribution of the random variable, so it incorporates both the method of prepa

Eleanor Rieffel Nov 13 2018 16:33 UTC

...(continued)Corrected!

This was not a casual error on my part, by the way. I first heard of Ewin Tang through Scott Aaronson's blog post https://www.scottaaronson.com/blog/?p=3880. The post itself has no indication of Ewin's gender, but comment #6 refers to Ewin as a "he" and Scott's response (comment #7) do

Andreas Nov 13 2018 11:39 UTC

*She: https://ewintang.com/ ("pronouns: she/her")

Eleanor Rieffel Nov 13 2018 05:54 UTC

And she did!

Earl Campbell Nov 12 2018 13:28 UTC

This made me laugh more than any other SciRate post. Well done.

Andreas Nov 12 2018 10:03 UTC

Ewin Tang, do your job! :-D

Ben Criger Nov 07 2018 09:02 UTC

The arXiv isn't automatically generating a pdf for this paper, at least right now. Downloading the PostScript and using `ps2pdf` seems to work, though.

Wojciech Kryszak Nov 07 2018 08:47 UTC

> I have to compile it from the source as arXiv says "Our automated source to PDF conversion system has failed to produce PDF for the paper: 1811.02192."

You needn't have it done, as there is the arxiv-vanity version (link above) as well!

Mankei Tsang Nov 07 2018 04:24 UTC

...(continued)Interesting work! But I have to compile it from the source as arXiv says "Our automated source to PDF conversion system has failed to produce PDF for the paper: 1811.02192."

Also I wonder how this is different from conventional stellar interferometry; see, e.g., https://en.wikipedia.org/wiki/Astr

Noon van der Silk Nov 06 2018 21:27 UTC

...(continued)This is an interesting result. I agree well-enough that here so-called "silly rules" can be used as a way to discover who the punishers are. But this doesn't really agree well with society, when we typically always know who the punishers are?

Seems like you don't even need silly rules anyway; this

Guillaume Verdon Nov 02 2018 03:01 UTC

Most definitely not the first fully quantum optimizer for neural networks

https://arxiv.org/abs/1806.09729

Markus Kesselring Oct 29 2018 10:01 UTC

In App. A the 8th point should start $a|_{x} \propto b.$

The full line then reads:

$a|_{x} \propto b$ if $a = b \otimes c$ is a Pauli operator on a system $x \otimes y$

Han-Hsuan Lin Oct 26 2018 15:23 UTC

Some parentheses seem to be missing in the equations.

The sample complexities are

$$O\left(\frac{\log|C| + \log(1/ \delta)} { \epsilon^2}\right)$$

for pure states and

$$O\left(\frac{\log^3 |C|(\log |C|+\log(1/ \delta))} { \epsilon^2}\right)$$

for mixed states.

Toby Cubitt Oct 23 2018 17:36 UTC

Impressed at the speed with which you read up to page 54. I think there's still two pixels space left at the right margin :-)

Alexander Jahn Oct 23 2018 09:12 UTC

Interesting paper, but the equation formatting on p. 54 is quite daring.

Felipe Montealegre Oct 22 2018 10:37 UTC

...(continued)Theorem 3.7 seems to be off. The Gottesman-Knill theorem allows the efficient simulation of Clifford circuits when the initial state is in the stabilizer polytope (assuming one can sample from arbitrary convex combinations of stabilizers efficiently). It is not a statement about entanglement being n

Sanketh Menda Oct 20 2018 17:34 UTC

...(continued)The question of whether oracle access to $U$ is polynomially-equivalent to oracle access to $U$ and $U^{-1}$ is important in the context of *quantum oracle separations.* See page 4 of *[Quantum Versus Classical Proofs and Advice](https://scirate.com/arxiv/quant-ph/0604056)*.

But in that context,

Wojciech Kryszak Oct 18 2018 08:31 UTC

...(continued)Hello,

Thank you, it is a pleasure to read, especially those reminiscences at the end.

Where would we stand, were it not for his shoulders!

One comment, describing the problems (of those times) with Wheler-Feynman electrodynamics, you write: ,,spontaneous emission of a photon from an atom

Mark Everitt Oct 18 2018 06:07 UTC

...(continued)Just to add the the arxiv comment - this is a major update to the work. We have toned down the wording and added more graph invariants as well as a scheme for calculating more. We have attempted to address all issues raised here and in email correspondence.

Dave and Simone - thank you for your he

Han-Hsuan Lin Oct 10 2018 22:09 UTC

For those of you who wonder why this doesn't break fault tolerance: "The result here is actually consistent with the threshold theorem: it shows generic quantum circuits (except for a η-small subset) are classically simulatable under a constant level of error rate per physical gate."

Joseph Emerson Oct 08 2018 15:36 UTC

...(continued)The examples in this paper are not original and are now well understood. More importantly, the conclusions the paper draws are misleading as these issues have been fully resolved in these two papers:

https://arxiv.org/abs/1703.09835

https://arxiv.org/abs/1804.01122Proctor et al. [Phys. Rev. Lett.

Eddie Smolansky Sep 23 2018 20:49 UTC

Links:

- Understanding the backward pass through Batch Normalization Layer https://kratzert.github.io/2016/02/12/understanding-the-gradient-flow-through-the-batch-normalization-layer.html

- https://www.quora.com/Why-does-batch-normalization-help

Eddie Smolansky Sep 23 2018 20:47 UTC

...(continued)Sources:

- https://arxiv.org/pdf/1512.03385.pdf

- http://image-net.org/challenges/talks/ilsvrc2015_deep_residual_learning_kaiminghe.pdfSummary:

- Took the first place in Imagenet 5 main tracks

- Revolution of depth: GoogLeNet was 22 layers with 6.7 top-5 error,

Resnet is 152 layers wit

Eddie Smolansky Sep 23 2018 20:42 UTC

...(continued)- Implementations:

- https://hub.docker.com/r/mklinov/caffe-flownet2/

- https://github.com/lmb-freiburg/flownet2-docker

- https://github.com/lmb-freiburg/flownet2

- Explanations:

- A Brief Review of FlowNet - not a clear explanation

https://medium.com/towards-data-scien

Eddie Smolansky Sep 23 2018 20:40 UTC

...(continued)It's like mask rcnn but for salient instances.

code will be available at https://github.com/RuochenFan/S4Net.They invented a layer "mask pooling" that they claim is better than ROI pooling and ROI align.

>As can be seen, our proposed

binary RoIMasking and ternary RoIMasking both outperform

Shan-Ming Ruan Sep 17 2018 20:56 UTC

wonderful work！

Luke Govia Sep 13 2018 18:58 UTC

I think the supplemental material is the appendices at the back of the paper. Those seem to contain everything the authors refer to.

Ben Criger Sep 10 2018 11:30 UTC

Reference 22 says there's some supplemental material, is this material on the arXiv, or is it just the supplemental material in the back of the paper?

Māris Ozols Aug 30 2018 09:18 UTC

...(continued)My overall impression about this survey is that its author has learned the material very recently and written this survey to summarize what he has learned. This is not an issue by itself, however it comes with several significant shortcomings.

First, the author is not familiar with (or for some r

Wojciech Kryszak Aug 22 2018 08:50 UTC

Were the Lord to be *boshaft* (in spite of all these evidences), He would need to hide his contrivances really deep in the past - so it seems.

Sai Aug 07 2018 15:56 UTC

...(continued)I also wanted to add one more comment about how our speedup can be implemented just using few-body interactions. It is possible to take time-dependant Hamiltonians with few-body interactions (and say, strong coupling) and construct a time-ordered unitary operator that implements the construction sug

Carlos A. Perez-Delgado Aug 07 2018 13:23 UTC

...(continued)Thank you for your interest in our paper. That is a really good question. Let me start by acknowledging that constructing higher-order Hamiltonians is currently hard in practice. Our result also applies when one restricts oneself to k-local Hamiltonians, in which case one obtains a speed increase th

Koen Groenland Aug 06 2018 11:37 UTC

...(continued)@Carlos Perez-Delgado, thanks for answering questions here!

I am also confused when it comes to `trading locality' as Stuart suggests. Perhaps the right question to ask is:> How would you construct the Hamiltonian $H_\text{#}(m) = \bigotimes_m H$ of

> equation (16) in a lab, for large $m$?To my

Carlos A. Perez-Delgado Aug 04 2018 13:20 UTC

...(continued)This is a good question and it is worth clearing this up.

> Isn't this paper just proposing to trade circuit size for locality,

> e.g. replace k-many 1-local gates with a single k-local gate?This part is essentially true. We are using non-locality as you call it (you can also say quantum correlat

Stuart Hadfield Aug 03 2018 23:29 UTC

Isn't this paper just proposing to trade circuit size for locality, e.g. replace k-many 1-local gates with a single k-local gate? Then changing the computational model to not count the cost of implementing the required k-local gates (which typically is ~k) to claim a 1/k speedup ?

Wojciech Kryszak Aug 01 2018 12:53 UTC

...(continued)Your SciNet for the current Solar System problem settles nicely in the mode of operation that is equivalent to the ,,stadard'' Heliocentric model wih positions encoded by Sun-angles relative to the fixed-stars background.

It would be very interesting to see what your SciNet would do when:

1. t

Blake Stacey Jul 20 2018 17:50 UTC

The browser cache strikes again! :-)

Tom Wong Jul 20 2018 17:48 UTC

Oops, I had to Shift+F5 https://arxiv.org/abs/1807.05877 in order to force my browser to ignore the cache. I also see underscores on both pages now.

Blake Stacey Jul 20 2018 17:43 UTC

When I go to https://arxiv.org/abs/1807.05877, I see an "ancillary files" list on the sidebar, in which the files are listed with underscores. Clicking them opens text files with some lovely parabolas of plus and minus signs. Going to https://arxiv.org/abs/1807.05877v1, I get exactly the same thing.

Tom Wong Jul 20 2018 17:29 UTC

The files still contain equal signs at https://arxiv.org/abs/1807.05877, and so they fail to open. But the files contain underscores instead at https://arxiv.org/abs/1807.05877v1, so they do open. Note v1 is the only version of the paper. Definitely an arXiv bug.

Wojciech Kryszak Jul 20 2018 08:43 UTC

...(continued)Your ,,comment'' is for me the most lucid explanation of the widely known (but - it seems - not seriously taken) fact that we can save locality at the cost of einsteinian (subject independent) reality.

The way it can work is immediately aprehensible once one relizes that Alice can get to know abo

Blake Stacey Jul 19 2018 23:19 UTC

It looks like the ancillary files have been renamed; they're accessible now.

Māris Ozols Jul 18 2018 17:01 UTC

Thanks, I will e-mail them. I posted this just to let people know that you can still access the files by other means. (The author could also solve the problem by just renaming them.)

Tom Wong Jul 18 2018 15:06 UTC

Thanks for pointing this out! Did you let the arXiv maintainers (help@arxiv.org) know about this bug? If not, I can email them and credit you.

Māris Ozols Jul 17 2018 17:18 UTC

Seems like arXiv doesn't like ancillary files whose filename contains "=" (only the last link on [this page][1] works). But you can always download the [entire source package][2] in a single file.

[1]: https://arxiv.org/src/1807.05877v1/anc

[2]: https://arxiv.org/src/1807.05877v1