A provable separation between analogous quantum and classical circuit classes!
...(continued)Regarding the pre-2017 state of play, I think experimentalists knew there was a problem for large errors and theorists had known there was a potential problem (as shown by grant proposals for the QCVV program) but nobody had really sat down and thought about how everything behaved for small errors.
...(continued)I agree that we pretty much agree on all these points! For the record, though... when you describe the pre-2017 state of play as "...*someone wants to use this theory, but they can't match the sufficient conditions, so they appeal to heuristics to argue that they can use the theory anyway*," this i
...(continued)Yes, I did indeed mean that the results of the previous derivations are correct and that predictions from experiments lie within the stated error bounds. To me, it is a different issue if someone derives something with a theoretical guarantee that might have sufficient conditions that are too strong
...(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
...(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
...(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
So what is the deal?
Does this negate all the problems with https://scirate.com/arxiv/1702.01853 ?
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.
...(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
"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?
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.
Good point, I wish I knew more about ExRecs.
...(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
...(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
...(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
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.
...(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
...(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
...(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
...(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
...(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
You are correct, that is a mistake -- it should be $\\{0,1\\}^n\rightarrow\\{0,1\\}$. Thank you for spotting it!
In the abstract, should the domain of $f$ be $\lbrace0,1\rbrace^n$ instead of just $\lbrace0,1\rbrace$?
...(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
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.
...(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
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
What a nice book! And it's available for free on arXiv!
Indeed, Schur complement is the answer to the ultimate question!
Very good Insight on android security problems and malware. Nice Work !
Hi, How can i get it??
...(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
...(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
Thank you very much for the reply!
...(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
...(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
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?
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.
[magic mirrors][1] really?
[1]: http://buchderFarben.de
too optimistic
Is it [fantasy][1] or real?
[1]: http://buchderfarben.de
...(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
...(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
It's also available in the bar on the right of http://arxiv.org/abs/1609.06373
...(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
Thank you for your kind words. Indeed, we worked hard to achieve the attributes you mentioned.
Braneshop, and
the US National Science Foundation.
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