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
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
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
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
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
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
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,
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
Thought I'd just comment here that we've rather significantly updated this paper.
off-loading is an interesting topic. Investigating the off-loading computation under the context of deep neural networks is a novel insight.
well written paper! State-of-art works that are good to publish to some decent conferences/journals
Very well written paper with formal problem formulation and extensive results on multiple benchmarks
Code is available here: https://github.com/iamaaditya/pixel-deflection
Interesting case study for computation offloading
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
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
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
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.
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
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.
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.
whoa, awesome! But why do you get that $d^3-d$ must be a divisor instead of $(d^3-d)/2$?
Nice observation, Steve! :-)
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.
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.
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
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]): by choosing the quantum walk Cesaro average as the goal distribution, it can be attained with a lifted Markov
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
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
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
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
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
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
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.
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
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 ), 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