Nice observation, Steve! :-)
...(continued)The following observation resolves in the affirmative a decade-old open conjecture from this paper, except for $d=3$.
The Conjecture asks if any unitary 2-design must have cardinality at least $d^4 - d^2$, a value which is achievable by a Clifford group. This is true for any group unitary 2-design
Hi Māris, you might well be right! Stabiliser QM with more qubits, I think, is also a good candidate for further investigation to see if we can close the gap a bit more between the analytical upper bound and the example-based lower bound.
...(continued)Interesting work. You don't require that the polar space has to be symplectic. In ordinary quantum mechanics the commutation of n-qudit observables is ruled by a symplectic polar space. For two qubits, it is the generalized quadrangle GQ(2,2). Incidently, in https://arxiv.org/abs/1601.04865 this pro
$E_7$ also has some nice properties in this regard (in fact, it might be even better than $E_8$). See https://arxiv.org/abs/1009.1195.
...(continued)Thank you for the insightful observations, Simon.
In response to the first point, there is a very short comment in the Discussion section to this effect. I felt an explicit dependence on $T$ as opposed to the diameter would make the implications of the result more clear. Namely, lifting can mix
...(continued)Thanks for the comment, Simone. A couple of observations:
- We noticed that Danial's result can in fact be proved more directly using the theorem that is used from ([arXiv:1705.08253][1]): by choosing the quantum walk Cesaro average as the goal distribution, it can be attained with a lifted Markov
...(continued)Closely related to
Simon Apers, Alain Sarlette, Francesco Ticozzi, Simulation of Quantum Walks and Fast Mixing with Classical Processes, https://scirate.com/arxiv/1712.01609
In my opinion, lifting is a good opportunity to put on a rigorous footing the relationship between classical and quantu
...(continued)Thank you for the helpful feedback.
Yes these are 14 pairs of graphs [This is an edit - I previously mistakenly posted that it was 7 pairs] that share the same equal angle slice. We have only just started looking at the properties of these graphs. Thank you for the link - that is a really useful r
...(continued)When looking at matrix spectra as graph invariants, it is easy to see that the spectrum of the adjacency matrix or the Laplacian fails for 4 vertices. Also, the spectrum of the adjacency matrix together with the spectrum of the adjacency matrix of the complement fail for 7 vertices. So, the algorith
...(continued)Thank you for this - its the sort of feedback we were after.
We have found 14 examples of 8 node graphs (of the possible 12,346) that break our conjecture.
We are looking into this now to get some understanding and see if we can overcome this issue. We will check to see if the failure of our algo
...(continued)A couple of comments:
1. To be a complete algorithm I think you need to specify how many of the equal angles you need to sample from (i.e. how many Euler angles)? And also maybe what "experimental accuracy means"? If those are exponential in order to work that's bad (but still very interesting
...(continued)We received some questions from Jalex Stark. To paraphrase, they asked if we could check if our method can discriminate non-isomorphic graphs that are:
1. "quantum isomorphism" as defined in https://arxiv.org/pdf/1611.09837.pdf
2. isospectral
3. fractional isomorphic
4. C3 equivalenlent (
Interesting title for a work on Mourre theory for Floquet Hamiltonians.
I wonder how this slipped through the prereview process in arXiv.
I am not sure, but the title is great.
I'm not against this idea; but what's the point? Clearly it's to provide some benefit to efficient implementation of particular procedures in Quil, but it'd be nice to see some detail of that, and how this might matter outside of Quil.
great！
This is an awesome paper; great work! :)
Paper source repository is here https://github.com/CQuIC/NanofiberPaper2014
Comments can be submitted as an issue in the repository. Thanks!
Here is a work in related direction: "Unification of Bell, Leggett-Garg and Kochen-Specker inequalities: Hybrid spatio-temporal inequalities", Europhysics Letters 104, 60006 (2013), which may be relevant to the discussions in your paper. [https://arxiv.org/abs/1308.0270]
Welcome to give the comments for this paper!
I am confortable with it. Good job
Well done
The initial version of the article does not adequately and clearly explain how certain equations demonstrate whether a particular interpretation of QM violates the no-signaling condition.
A revised and improved version is scheduled to appear on September 25.
What does this imply for https://scirate.com/arxiv/1608.00263? I'm guessing they still regard it as valid (it is ref [14]), but just too hard to implement for now.
Oh look, there's another technique for decoding surface codes subject to X/Z correlated errors: https://scirate.com/arxiv/1709.02154
The paper only applies to conformal field theories, and such a result cannot hold for more general 1-D systems by 0705.4077 and other papers (assuming standard complexity theory conjectures).
Thanks for the clarification, Philippe!
...(continued)Hi Felix, thanks for the good question.
We've found it more convenient to consider trace-nonincreasing and $\Gamma$-sub-preserving maps (and this is justified by the fact that they can be dilated to fully trace-preserving and $\Gamma$-preserving maps on a larger system). The issue arises because
What is the reason/motivation to consider trace-non-increasing maps instead of trace-preserving maps in your framework and the definition of the coherent relative entropy?
Thanks for the reference Ashley. If I understand your paper, you are still measuring stabilizers of X- and Z-type at the top layer of the code. So it might be that we can improve on the factor of 2 that you found if we tailor the stabilizers to the noise bias at the base level.
...(continued)We followed Aliferis and Preskill's approach in [https://arxiv.org/abs/1308.4776][1] and found that the fault-tolerant threshold for the surface code was increased by approximately a factor of two, from around 0.75 per cent to 1.5 per cent for a bias of 10 to 100.
[1]: https://arxiv.org/abs/1308.
...(continued)Following on from Steve's comments, it's possible to use the bias-preserving gate set in Aliferis and Preskill directly to do the syndrome extraction, as you build up a CNOT gadget, but such a direct application of your methods would be very complicated and involve a lot of gate teleportation. If y
...(continued)We agree that finding good syndrome extraction circuits if an important question. At the moment we do not have such circuits, though we have started to think about them. We are optimistic that this can be done in principle, but it remains to be seen if the circuits can be made sufficiently simple to
...(continued)Hi Steves and David. When we wrote https://arxiv.org/abs/0710.1301 our viewpoint was that a gate with highly biased (primarily Z) noise would need to commute with Z. So we built our fault-tolerant gadgets from such gates, along with preparations and measurements in the X basis.
Can you easily ext
We haven't tried the Wen model yet. We thought about doing it, but decided to try this first. When it worked as well as it did we just didn't bother trying the Wen model, but it's a natural question, and I am curious about the answer.
Seems so obvious now you say it! Well done for trying this out.
Do you know how the results compare to Wen style stabilizers, where both plaquette and vertex stabilizers alternate between two Paulis? I guess using Y and Z would be best for biased noise, given your results.
...(continued)Wanted to let you know this paper has been updated with new technical results. In particular, we have provided a new section which gives a generalization of [local asymptotic normality](https://en.wikipedia.org/wiki/Local_asymptotic_normality) that is applicable to models with convex constraints (wh
+1 for "Alisha" and "Babu"! :D
...(continued)If I'm not mistaken, what you describe here is equivalent to the [QR decomposition][1]. The matrices $R_{ij}$ that act non-trivially only in a two-dimensional subspace are known as [Givens rotations][2]. The fact that any $n \times n$ unitary can be decomposed as a sequence of Givens rotations is ex
...(continued)For those interested in the literature on teleportation simulation of quantum channels, a detailed and *comprehensive* review is provided in Supplementary Note 8 of https://images.nature.com/original/nature-assets/ncomms/2017/170426/ncomms15043/extref/ncomms15043-s1.pdf
The note describes well the t
...(continued)In what sense is the ground state for large detuning ordered and antiferromagnetic? I understand that there is symmetry breaking, but other than that, what is the fundamental difference between ground states for large negative and large positive detunings? It seems to be they both exhibit some order
The performance of the memory assisted MDI-QKD with "quasi-EPR" sources is remarkable. It improves the key rate by 5 orders of magnitude over the PLOB bound at about 600 km (take a look at Figure 4).
Conway's list still has four other $1000 problems left:
https://oeis.org/A248380/a248380.pdf
I am still working on improving this survey. If you have any suggestions, questions or find any mistakes, please do not hesitate to contact me: shuai.zhang@student.unsw.edu.au.
...(continued)This paper has just been updated and we thought it would be a good
idea to advertise it here. It was originally submitted a year ago, and
it has now been essentially rewritten, with two new authors added.We have fixed some of the original results and now we:
-Show how some fundamental theorem
...(continued)Actually, there is even earlier work that shows this result. In [arXiv:1109.6887][1], Magesan, Gambetta, and Emerson showed that for any Pauli channel the diamond distance to the identity is equal to the trace distance between the associated Choi states. They prefer to phrase their results in terms
This is very interesting. In my reading list!
...(continued)In relation with the discussion at page 21 of this paper. Consider depolarizing channels (including the trivial case of the identity channel) which are teleportation covariant as in the definition Eq. (9) of https://arxiv.org/abs/1510.08863 [Nature Communications 8, 15043 (2017)]. The diamond norm b
Braneshop, and
the US National Science Foundation.
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