Randomized benchmarking with gate-dependent noise

Steve Flammia Mar 30 2017 20:12 UTCRobin Blume-Kohout Mar 30 2017 16:55 UTC

...(continued)I agree with much of your comment. But, the assertion you're disagreeing with isn't really mine. I was trying to summarize the content of the present paper (and 1702.01853, hereafter referred to as [PRYSB]). I'll quote a few passages from the present paper to support my interpretation:

1. "[T

Steve Flammia Mar 30 2017 15:41 UTC

...(continued)I disagree with the assertion (1) that the previous theory didn't give "the right answers." The previous theory was sound; no one is claiming that there are any mistakes in any of the proofs. However, there were nonetheless some issues.

The first issue is that the previous analysis of gate-depe

Robin Blume-Kohout Mar 30 2017 12:07 UTC

...(continued)That's a hard question to answer. I suspect that on any questions that aren't precisely stated (and technical), there's going to be some disagreement between the authors of the two papers. After one read-through, my tentative view is that each of the two papers addresses three topics which are pre

LogiQ Mar 30 2017 03:23 UTC

So what is the deal?

Does this negate all the problems with https://scirate.com/arxiv/1702.01853 ?

Laura Mančinska Mar 28 2017 13:09 UTC

Great result!

For those familiar with I_3322, William here gives an example of a nonlocal game exhibiting a behaviour that many of us suspected (but couldn't prove) to be possessed by I_3322.

gae spedalieri Mar 13 2017 14:13 UTC

...(continued)1) Sorry but this is false.

1a) That analysis is specifically for reducing QECC protocol to an entanglement distillation protocol over certain class of discrete variable channels. Exactly as in BDSW96. Task of the protocol is changed in the reduction.

1b) The simulation is not via a general LOCC b

Siddhartha Das Mar 13 2017 13:22 UTC

...(continued)We feel that we have cited and credited previous works appropriately in our paper. To clarify:

1) The LOCC simulation of a channel and the corresponding adaptive reduction can be found worked out in full generality in the 2012 Master's thesis of Muller-Hermes. We have cited the original paper BD

gae spedalieri Mar 13 2017 08:56 UTC

...(continued)This is one of those papers where the contribution of previous literature is omitted and not fairly represented.

1- the LOCC simulation of quantum channels (not necessarily teleportation based) and the corresponding general reduction of adaptive protocols was developed in PLOB15 (https://arxiv.org/

Noon van der Silk Mar 08 2017 04:45 UTC

...(continued)I feel that while the proliferation of GUNs is unquestionable a good idea, there are many unsupervised networks out there that might use this technology in dangerous ways. Do you think Indifferential-Privacy networks are the answer? Also I fear that the extremist binary networks should be banned ent

Qian Wang Mar 07 2017 17:21 UTC

"To get the videos and their labels, we used a YouTube video annotation system, which labels videos with their main topics."

Can anyone explain a bit about this?

Christopher Chamberland Mar 02 2017 18:48 UTC

A good paper for learning about exRec's is this one https://arxiv.org/abs/quant-ph/0504218. Also, rigorous threshold lower bounds are obtained using an adversarial noise model approach.

Anirudh Krishna Mar 02 2017 18:40 UTC

Here's a link to a lecture from Dan Gottesman's course at PI about exRecs.

http://pirsa.org/displayFlash.php?id=07020028You can find all the lectures here:

http://www.perimeterinstitute.ca/personal/dgottesman/QECC2007/index.html

Ben Criger Mar 02 2017 08:58 UTC

Good point, I wish I knew more about ExRecs.

Robin Blume-Kohout Feb 28 2017 09:55 UTC

...(continued)I totally agree -- that part is confusing. It's not clear whether "arbitrary good precision ... using a limited amount of hardware" is supposed to mean that arbitrarily low error rates can be achieved with codes of fixed size (clearly wrong) or just that the resources required to achieve arbitraril

James Wootton Feb 28 2017 08:54 UTC

...(continued)I think I was mostly reacting to where he tries to sell the importance of the work.

>Fault tolerant theorems show that an arbitrary good precision can be obtained using a limited amount of hardware...we unveil the role of an implicit assumption made in these mathematical theorems: the ability to

Robin Blume-Kohout Feb 27 2017 13:30 UTC

...(continued)@Chris: as Ben says, the model for measurement errors is "You measure in a basis that's off by a small rotation".

@Ben: I don't think either of the techniques you mention will directly resolve the paper's concern/confusion. That concern is with the post-QEC state of the system. That state isn't

James Wootton Feb 27 2017 13:10 UTC

Do any fault-tolerance theorems claim to hold for small codes without repeated measurement, as is the case in these supposed counter examples?

The assumption that no-one ever thought about this noise before is the faulty one here.

Ben Criger Feb 27 2017 09:04 UTC

...(continued)It seems like the problem is that the measurement basis is unknown (the actual operator being measured isn't exactly Z, for example, but some other Hermitian operator close to Z). However, this seems like it can be re-expressed using an unknown operation that occurs immediately before measurement of

Christopher Chamberland Feb 27 2017 04:26 UTC

...(continued)Could you be more specific by what you mean when you say "the ability to perform quantum measurements with infinite precision"? Several circuit level noise thresholds have been computed where measurement errors are taken into account. Even with measurement errors, thresholds as high as 10^-2 have be

Namit Anand Feb 24 2017 05:47 UTC

A nice and elegant proof!

Just a small typo that crossed my eye:

J. Phys. A: Math. Theor. 45 (**2012**) 025301 should be J. Phys. A: Math. Theor. 45 (**2011**) 025301. The year is 2011.

Māris Ozols Feb 21 2017 15:35 UTC

...(continued)I'm wondering if this result could have any interesting consequences for Hamiltonian complexity. The LCL problem sounds very much like a local Hamiltonian problem, with the run-time of an LCL algorithm corresponding to the range of local interactions in the Hamiltonian.

Maybe one caveat is that thi

Andrey Karchevsky Feb 17 2017 09:51 UTC

...(continued)Dear Authors,

This is in reference of your preprint arxiv 1702.0638.

Above all I must say that I am puzzled with the level of publicity your work has got at http://www.nature.com/news/long-awaited-mathematics-proof-could-help-scan-earth-s-innards-1.21439. Is this a new way for mathematicians t

Karl Joulain Feb 09 2017 15:50 UTC

...(continued)A **GREAT** paper. Where you learn how to extract work from the measurement of a qubit coupled to a drive. The authors build an engine with very unusual and interesting features such as efficiency of 1 (no entropy creation) arising for conditions where the power extrated is maximum! This maximum dep

Jānis Iraids Jan 25 2017 11:35 UTC

You are correct, that is a mistake -- it should be $\\{0,1\\}^n\rightarrow\\{0,1\\}$. Thank you for spotting it!

Christopher Thomas Chubb Jan 25 2017 02:27 UTC

In the abstract, should the domain of $f$ be $\lbrace0,1\rbrace^n$ instead of just $\lbrace0,1\rbrace$?

Robert Raussendorf Jan 24 2017 22:29 UTC

...(continued)Regarding Mark's above comment on the role of the stabilizer states: Yes, all previous works on the subject have used the stabilizer states and Clifford gates as the classical backbone. This is due to the Gottesman-Knill theorem and related results. But is it a given that the free sector in quantum

Planat Jan 24 2017 13:09 UTC

Are you sure? Since we do not propose a conjecture, there is nothing wrong. A class of strange states underlie the pentagons in question. The motivation is to put the magic of computation in the permutation frame, one needs more work to check its relevance.

Mark Howard Jan 24 2017 09:59 UTC

...(continued)It seems interesting at first sight, but after reading it the motivation is very muddled. It boils down to finding pentagons (which enable KCBS-style proofs of contextuality) within sets of projectors, some of which are stabilizer states and some of which are non-stabilizer states (called magic stat

Zoltán Zimborás Jan 12 2017 20:38 UTC

Here is a nice description, with additional links, about the importance of this work if it turns out to be flawless (thanks a lot to Martin Schwarz for this link): [dichotomy conjecture][1].

[1]: http://processalgebra.blogspot.com/2017/01/has-feder-vardi-dichotomy-conjecture.html

Māris Ozols Dec 27 2016 19:34 UTC

What a nice book! And it's available for free on arXiv!

Māris Ozols Dec 16 2016 15:38 UTC

Indeed, Schur complement is the answer to the ultimate question!

J. Smith Dec 14 2016 17:43 UTC

Very good Insight on android security problems and malware. Nice Work !

Keshtidar Dec 13 2016 11:54 UTC

Hi, How can i get it??

Stefano Pirandola Nov 30 2016 06:45 UTC

...(continued)Dear Mark, thx for your comment. There are indeed missing citations to previous works by Rafal, Janek and Lorenzo that we forgot to add. Regarding your paper, I did not read it in detail but I have two main comments:

1- What you are using is completely equivalent to the tool of "quantum simulatio

Mark M. Wilde Nov 30 2016 02:18 UTC

...(continued)An update http://arxiv.org/abs/1609.02160v2 of this paper has appeared, one day after the arXiv post http://arxiv.org/abs/1611.09165 . The paper http://arxiv.org/abs/1609.02160v2 now includes (without citation) some results for bosonic Gaussian channels found independently in http://arxiv.org/abs/16

Felix Leditzky Nov 29 2016 16:34 UTC

Thank you very much for the reply!

Martin Schwarz Nov 24 2016 13:53 UTC

...(continued)Oded Regev writes [here][1]:

"Dear all,

Yesterday Lior Eldar and I found a flaw in the algorithm proposed

in the arXiv preprint. I do not see how to salvage anything from

the algorithm. The security of lattice-based cryptography against

quantum attacks therefore remains intact and uncha

Alex Wozniakowski Nov 22 2016 19:50 UTC

...(continued)Here, the string diagrams (for qudits, transformations, and measurements) may have charge. The manipulation of diagrams with charge requires para-isotopy, which generalizes topological isotopy; and the relation for para-isotopy is found on pg. 11, in eq. (22). Essentially, para-isotopy keeps track

Felix Leditzky Nov 22 2016 17:18 UTC

Could you give an example of a topological isotopy that transforms the transformation $T$ on p.3 into the one in eq. (6)? On a related note, how is a topological isotopy defined?

Daniel Lidar Nov 15 2016 04:40 UTC

All comments are very welcome. We list 10 open questions at the end of the review, and would be happy to expand the list. Accepted contributions will be acknowledged.

phaeladr Nov 14 2016 11:03 UTC

[magic mirrors][1] really?

[1]: http://buchderFarben.de

phaeladr Nov 14 2016 11:01 UTC

too optimistic

wiadealo Nov 07 2016 09:27 UTC

Is it [fantasy][1] or real?

[1]: http://buchderfarben.de

Zoltán Zimborás Oct 31 2016 23:12 UTC

...(continued)There is a lot of discussion about the paper by Atiyah (claiming to solve this famous question) in the math community - with a bit of skeptical edge - both on reddit and on mathoverflow:

https://www.reddit.com/r/math/comments/5aajsn/161009366_the_nonexistent_complex_6sphere_michael/

http://mathov

Māris Ozols Oct 21 2016 21:06 UTC

...(continued)Very nice! Now we finally know how to fairly cut a cake in a finite number of steps! What is more, the number of steps is expected to go down from the whopping $n^{n^{n^{n^{n^n}}}}$ to just barely $n^{n^n}$. I can't wait to get my slice!

https://www.quantamagazine.org/20161006-new-algorithm-solve

Jacob Bridgeman Oct 17 2016 03:28 UTC

It's also available in the bar on the right of http://arxiv.org/abs/1609.06373

Mark M. Wilde Oct 06 2016 15:44 UTC

...(continued)The following paper found a setting in which adaptive operations do not help in quantum channel discrimination:

https://arxiv.org/abs/1408.3373

It is published as

Communications in Mathematical Physics, vol. 344, no. 3, pages 797-829, June 2016

http://link.springer.com/article/10.1007%2