serfati philippe Feb 16 2018 10:57 UTC

+on (3 and more, 2008-13-14..) papers of bourgain etal (and their numerous descendants) on =1/ (t-static) illposednesses for the nd incompressible euler equations (and nse) and +- critical spaces, see possible counterexamples constructed on my nd shear flows, pressureless (shockless) solutions of in

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serfati philippe Feb 16 2018 10:44 UTC

+on (3 and more, 2008-13-14..) papers of bourgain etal (and their numerous descendants) on =1/ (t-static) illposednesses for the nd incompressible euler equations (and nse) and +- critical spaces, see possible counterexamples constructed on my nd shear flows, pressureless (shockless) solutions of in

...(continued)
serfati philippe Feb 15 2018 19:03 UTC

+on (3 and more, 2008-13-14..) papers of bourgain etal (and their numerous descendants) on =1/ (t-static) illposednesses for the nd incompressible euler equations (and nse) and +- critical spaces, see possible counterexamples constructed on my nd shear flows, pressureless (shockless) solutions of in

...(continued)
serfati philippe Feb 15 2018 19:03 UTC

+on (3 and more, 2008-13-14..) papers of bourgain etal (and their numerous descendants) on =1/ (t-static) illposednesses for the nd incompressible euler equations (and nse) and +- critical spaces, see possible counterexamples constructed on my nd shear flows, pressureless (shockless) solutions of in

...(continued)
serfati philippe Feb 15 2018 19:03 UTC

+on (3 and more, 2008-13-14..) papers of bourgain etal (and their numerous descendants) on =1/ (t-static) illposednesses for the nd incompressible euler equations (and nse) and +- critical spaces, see possible counterexamples constructed on my nd shear flows, pressureless (shockless) solutions of in

...(continued)
serfati philippe Feb 15 2018 13:29 UTC

on transport and continuity equations with regular speed out of an hypersurface, and on it, having 2 relative normal components with the same punctual sign (possibly varying) and better unexpected results on solutions and jacobians etc, see (https://www.researchgate.net/profile/Philippe_Serfati), pa

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serfati philippe Feb 15 2018 12:35 UTC

on transport and continuity equations with regular speed out of an hypersurface, and on it, having 2 relative normal components with the same punctual sign (possibly varying) and better unexpected results on solutions and jacobians etc, see (https://www.researchgate.net/profile/Philippe_Serfati), pa

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Beni Yoshida Feb 13 2018 19:53 UTC

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

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Abhinav Deshpande Feb 10 2018 15:42 UTC

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

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Elizabeth Crosson Feb 10 2018 05:49 UTC

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

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Abhinav Deshpande Feb 09 2018 20:21 UTC

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

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Elizabeth Crosson Feb 08 2018 04:27 UTC

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

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Danial Dervovic Feb 05 2018 15:03 UTC

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

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Michael A. Sherbon Feb 02 2018 15:56 UTC

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}}&plus;\frac{\mathit{A^{2}}}{K\phi^{4}}-\frac{\mathit{A^{\math

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Māris Ozols Feb 01 2018 17:53 UTC

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

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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

Luhao Wang Jan 30 2018 00:28 UTC

well written paper! State-of-art works that are good to publish to some decent conferences/journals

mahdi aliakbari Jan 29 2018 20:49 UTC

Very well written paper with formal problem formulation and extensive results on multiple benchmarks

aaditya prakash Jan 29 2018 19:58 UTC

Māris Ozols Jan 29 2018 13:09 UTC

\

Faraz Rabbani Jan 29 2018 07:53 UTC

Marco Piani Jan 28 2018 11:21 UTC

Hi Mizanur,

thanks to you for taking into account my comment. I am not sure of the jargon and nomenclature in mathematics; are/were the maps that are completely positive and also completely co-positive known as PPT maps? What I was pointing out is that in the quantum information community the nam

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Mizanur Rahaman Jan 27 2018 19:06 UTC

Hi Marco, thanks for pointing out the possible confusion. I will make it clear in the revised version. I think in this context what I should clearly state is that I am considering linear maps
which are completely positive and co-completely positive, that is, the map \Phi and \Phi\circleT
are compl

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Michael Moshe Jan 26 2018 16:27 UTC

/

Marco Piani Jan 24 2018 03:34 UTC

Great work! One thing that might potentially confuse readers is the use of "PPT channel" to indicate that the partial action of the channel produces a PPT state. There might be some ambiguity in literature, but many call "PPT channels" those channels that act jointly on two parties, and that preserv

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Mizanur Rahaman Jan 23 2018 23:20 UTC

Thanks for the comment. I was not aware of the "entanglement breaking index" paper.
I will include it in a revised version. I will make a remark about the other deduction as well.
Thanks.

Ludovico Lami Jan 19 2018 00:08 UTC

Very nice work, congratulations! I just want to point out that the "index of separability" had already been defined in arXiv:1411.2517, where it was called "entanglement-breaking index" and studied in some detail. The channels that have a finite index of separability had been dubbed "entanglement-sa

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Blake Stacey Jan 17 2018 20:06 UTC

Eq. (14) defines the sum negativity as $\sum_u |W_u| - 1$, but there should be an overall factor of $1/2$ (see arXiv:1307.7171, definition 10). For both the Strange states and the Norrell states, the sum negativity should be $1/3$: The Strange states (a.

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serfati philippe Jan 11 2018 18:49 UTC

on (x,t) localized regularities for the nd euler eqs, my "Presque-localité de l'équation d'Euler incompressible sur Rn et domaines de propagation non lineaire et semi lineaire" 1995 (https://www.researchgate.net/profile/Philippe_Serfati) and eg "Local regularity criterion of the Beale-Kato-Majda typ

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serfati philippe Jan 11 2018 18:49 UTC

on (x,t) localized regularities for the nd euler eqs, my "Presque-localité de l'équation d'Euler incompressible sur Rn et domaines de propagation non lineaire et semi lineaire" 1995 (https://www.researchgate.net/profile/Philippe_Serfati) and eg "Local regularity criterion of the Beale-Kato-Majda typ

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serfati philippe Jan 08 2018 11:27 UTC

+Approximated positive vortex dirac for euler2d, (very) weak L°° initial bounds and non-trivial x-diameters of t-expansions = about 3/ "Euler evolution of a concentrated vortex in planar bounded domains" Daomin Cao, Guodong Wang (Submitted on 5 Jan 2018) https://arxiv.org/abs/1801.01629v1, see my 2

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Steve Flammia Dec 18 2017 20:59 UTC

It splits into even and odd cases, actually. I was originally sloppy about the distinction between integer and polynomial division, but it's fixed now. There is a little room left in the case $d=3$ now though, but it's still proven in every other dimension.

Aram Harrow Dec 18 2017 19:30 UTC

whoa, awesome! But why do you get that $d^3-d$ must be a divisor instead of $(d^3-d)/2$?

David Gross Dec 17 2017 20:28 UTC

Nice observation, Steve! :-)

Steve Flammia Dec 17 2017 20:25 UTC

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

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Andrew W Simmons Dec 14 2017 11:40 UTC

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.

Planat Dec 14 2017 08:43 UTC

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

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Māris Ozols Dec 12 2017 19:41 UTC

$E_7$ 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.

Danial Dervovic Dec 10 2017 15:25 UTC

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

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Simon Apers Dec 09 2017 07:54 UTC

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

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Simone Severini Dec 07 2017 02:51 UTC

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

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Mark Everitt Dec 05 2017 07:50 UTC

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

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Simone Severini Dec 05 2017 01:13 UTC

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

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Mark Everitt Dec 04 2017 17:52 UTC

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

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Dave Bacon Dec 02 2017 00:08 UTC

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

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Mark Everitt Nov 29 2017 22:13 UTC

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 (

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Zoltán Zimborás Nov 17 2017 07:59 UTC

Interesting title for a work on Mourre theory for Floquet Hamiltonians.
I wonder how this slipped through the prereview process in arXiv.

Aram Harrow Nov 07 2017 08:52 UTC

I am not sure, but the title is great.

Noon van der Silk Nov 07 2017 05:13 UTC

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.