SIC-POVMs and the Stark conjectures

Blake Stacey Jul 20 2018 17:50 UTCTom 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

Zak Webb Jul 02 2018 18:33 UTC

...(continued)Thanks for reading the paper! I might have been able to include a couple extra steps in the derivation, but I didn't want this equation to take up too much space.

The basic idea is to expand the permutation operator $W_{1,2,3}$ as in equation (9), and then use the cyclic property of the trace op

Narayanan Rengaswamy Jul 02 2018 15:55 UTC

...(continued)Hi, thank you for the nice paper! Could you clarify the second and third equalities in eqn. (11)? Particularly, I am not sure how the tensor products vanished and also why the new subscripts are in the order 1,3,2 rather than a cyclic shift of 1,2,3 as suggested by the notation (123). Have you writt

Narayanan Rengaswamy Jun 28 2018 17:21 UTC

Thank you very much for the clarification!

Yusuke Kinoshita Jun 28 2018 01:29 UTC

...(continued)Thank you very much for your comment.

I'm sorry not to know the result.

However, it seems to us that the old proof does not work well,

or too ambiguousIn p.98, ' $\alpha |0\rangle|\psi_0\rangle+\beta|1\rangle|\psi_1\rangle$' is used,

but to apply Aaronson's technique, what we need is

'$\alph

Martin Schwarz Jun 27 2018 07:23 UTC

The main result of this paper has already been shown previously in [Salman Beigi's PhD thesis (2009)][1] (Appendix B, Theorem B.0.5, p.98).

[1]: https://dspace.mit.edu/handle/1721.1/50594

Māris Ozols Jun 26 2018 09:06 UTC

...(continued)Wow, this must be a breakthrough! So many people joining SciRate just to upvote it! Also, very creative user names:

[BladeMaster][1],

[KameBrown][2],

[siche][3],

[skyler][4],

[snow][5],

[zy z][6].

Will Blade Runner and Queen Elsa from Frozen also be joining to upvote this?**Update:** Looks like [B

Steve Flammia Jun 26 2018 01:40 UTC

...(continued)The group that we call "R(2)" in the paper, the "Realizable Group" is indeed generated by the physical unitaries in the left side of the table on page 2. This group, as a unitary matrix group, has 4,608 elements. However, the action on just the logical space is smaller, and there is a 4-to-1 homomor

Narayanan Rengaswamy Jun 25 2018 21:05 UTC

...(continued)Thank you for this timely work explaining standard tests run on the IBM machine!

Could you clarify what you refer to as the Realizable Group in the paper? Is it generated by the gates in the "Logical Equivalent" column in the table on page 2? This seems to correlate well with the statements in t

Jonas Helsen Jun 22 2018 12:43 UTC

That's correct. Thanks for spotting it ! The correct relation should be (1/|sigma_q|)sum_sigma = (1/(d-1))(dF-1). Another typo shows up in eq 41 which has essentially the same resolution. We'll correct this on the next update.

Zi-Wen Liu Jun 21 2018 16:38 UTC

...(continued)Here I would like to leave some comments only on the part about the notion of "resource destroying maps" introduced in our earlier work ([1606.03723][1]).

First, the definition of resource destroying maps stated in this article (and also an earlier work of one of the authors [1610.04247][2]) re

Soumya Mukherjee Jun 19 2018 12:50 UTC

This is really a great work.. should be implemented with all the required resources.

Pei Zeng Jun 15 2018 09:13 UTC

Nice work~ Is there any typo on the formula (33)? It seems not consistent with former average fidelity formula...

Raja Shekar Jun 03 2018 09:22 UTC

Good job

Noon van der Silk May 30 2018 07:05 UTC

You might be interested in this: https://cs.stanford.edu/people/karpathy/convnetjs/demo/image_regression.html

Rick Sarkar May 29 2018 05:24 UTC

Good job... The dynamic reference frame is quite an interesting topic. Can be very helpful if used to full potential.

subhabrata bhattacharya May 29 2018 03:43 UTC

Liked the dynamic reference frame concept.

Soumyadip Dutta May 28 2018 17:37 UTC

Very helpful article. An ensemble of classification and time series technique. Concept of lead time is also interesting.

Mark May 25 2018 17:22 UTC

Is the implementation of the cQASM compiler open-source and if yes, where can I find the code?

Max Lu Apr 25 2018 22:08 UTC

...(continued)"This is a very inspiring paper! The new framework (ZR = All Reality) it provided allows us to understand all kinds of different reality technologies (VR, AR, MR, XR etc) that are currently loosely connected to each other and has been confusing to many people. Instead of treating our perceived sens

Stefano Pirandola Apr 23 2018 12:23 UTC

...(continued)The most important reading here is Sam Braunstein's foundational paper: https://authors.library.caltech.edu/3827/1/BRAprl98.pdf published in January 98, already containing the key results for the strong convergence of the CV protocol. This is a must-read for those interested in CV quantum informatio

Mark M. Wilde Apr 23 2018 12:09 UTC

...(continued)One should also consult my paper "Strong and uniform convergence in the teleportation simulation of bosonic Gaussian channels" https://arxiv.org/abs/1712.00145v4 posted in January 2018, in this context. It is published in the June 2018 issue of Physical Review A and available at https://journals.aps

Stefano Pirandola Apr 23 2018 11:46 UTC

...(continued)Some quick clarifications on the Braunstein-Kimble (BK) protocol for CV teleportation

and the associated teleportation simulation of bosonic channels.

(Disclaimer: the following is rather technical and CVs might not be so popular on this blog...so I guess this post will get a lot of dislikes :)1)

NJBouman Apr 22 2018 18:26 UTC

...(continued)[Fredrik Johansson][1] has pointed out to me (the author) the following about the multiplication benchmark w.r.t. GMP. This will be taken into account in the upcoming revision.

Fredrik Johansson wrote:

> You shouldn't be comparing your code to `mpn_mul`, because this function is not actually th

Joel Wallman Apr 18 2018 13:34 UTC

...(continued)A very nice approach! Could you clarify the conclusion a little bit though? The aspirational goal for a quantum benchmark is to test how well we approximate a *specific* representation of a group (up to similarity transforms), whereas what your approach demonstrates is that without additional knowle

serfati philippe Mar 29 2018 14:07 UTC

see my 2 papers on direction of vorticity (nov1996 + feb1999) = https://www.researchgate.net/profile/Philippe_Serfati (published author, see also mendeley, academia.edu, orcid etc)

serfati philippe Mar 29 2018 13:34 UTC

see my 4 papers, 1998-1999, on contact and superposed vortex patches, cusps (and eg splashs), corners, generalized ones on lR^n and (ir/)regular ones =. http://www.researchgate.net/profile/Philippe_Serfati/ (published author).

Luis Cruz Mar 16 2018 15:34 UTC

Related Work:

- [Performance-Based Guidelines for Energy Efficient Mobile Applications](http://ieeexplore.ieee.org/document/7972717/)

- [Leafactor: Improving Energy Efficiency of Android Apps via Automatic Refactoring](http://ieeexplore.ieee.org/document/7972807/)

Dan Elton Mar 16 2018 04:36 UTC

Comments are appreciated. Message me here or on twitter @moreisdifferent

Code is open source and available at :

[https://github.com/delton137/PIMD-F90][1][1]: https://github.com/delton137/PIMD-F90

Danial Dervovic Mar 01 2018 12:08 UTC

...(continued)Hello again Māris, many thanks for your patience. Your comments and questions have given me much food for thought, and scope for an amended version of the paper -- please see my responses below.

Please if any of the authors of [AST17 [arXiv:1712.01609](https://arxiv.org/abs/1712.01609)] have any fu

igorot Feb 28 2018 05:19 UTC

The Igorots built an [online community][1] that helps in the exchange, revitalization, practice, and learning of indigenous culture. It is the first and only Igorot community on the web.

[1]: https://www.igorotage.com/

Beni Yoshida Feb 13 2018 19:53 UTC

...(continued)This is not a direct answer to your question, but may give some intuition to formulate the problem in a more precise language. (And I simplify the discussion drastically). Consider a static slice of an empty AdS space (just a hyperbolic space) and imagine an operator which creates a particle at some

Abhinav Deshpande Feb 10 2018 15:42 UTC

...(continued)I see. Yes, the epsilon ball issue seems to be a thorny one in the prevalent definition, since the gate complexity to reach a target state from any of a fixed set of initial states depends on epsilon, and not in a very nice way (I imagine that it's all riddled with discontinuities). It would be inte

Elizabeth Crosson Feb 10 2018 05:49 UTC

...(continued)Thanks for the correction Abhinav, indeed I meant that the complexity of |psi(t)> grows linearly with t.

Producing an arbitrary state |phi> exactly is also too demanding for the circuit model, by the well-known argument that given any finite set of gates, the set of states that can be reached i

Abhinav Deshpande Feb 09 2018 20:21 UTC

...(continued)Elizabeth, interesting comment! Did you mean to say that the complexity of $U(t)$ increases linearly with $t$ as opposed to exponentially?

Also, I'm confused about your definition. First, let us assume that the initial state is well defined and is $|\psi(0)\rangle $.

If you define the complexit

Elizabeth Crosson Feb 08 2018 04:27 UTC

...(continued)The complexity of a state depends on the dynamics that one is allowed to use to generate the state. If we restrict the dynamics to be "evolving according a specific Hamiltonian H" then we immediately have that the complexity of U(t) = exp(i H t) grows exponentially with t, up until recurrences that

Danial Dervovic Feb 05 2018 15:03 UTC

...(continued)Thank you Māris for the extremely well thought-out and articulated points here.

I think this very clearly highlights the need to think explicitly about the precompute time if using the lifting to directly simulate the quantum walk, amongst other things.

I wish to give a well-considered respons

Michael A. Sherbon Feb 02 2018 15:56 UTC

...(continued)Good general review on the Golden Ratio and Fibonacci ... in physics, more examples are provided in the paper “Fine-Structure Constant from Golden Ratio Geometry,” Specifically,

$$\alpha^{-1}\simeq\frac{360}{\phi^{2}}-\frac{2}{\phi^{3}}+\frac{\mathit{A^{2}}}{K\phi^{4}}-\frac{\mathit{A^{\math

Māris Ozols Feb 01 2018 17:53 UTC

...(continued)This paper considers the problem of using "lifted" Markov chains to simulate the mixing of coined quantum walks. The Markov chain has to approximately (in the total variational distance) sample from the distribution obtained by running the quantum walk for a randomly chosen time $t \in [0,T]$ follow

Johnnie Gray Feb 01 2018 12:59 UTC

Thought I'd just comment here that we've rather significantly updated this paper.

wenling yang Jan 30 2018 19:08 UTC

off-loading is an interesting topic. Investigating the off-loading computation under the context of deep neural networks is a novel insight.