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Thank you very much for your comment.

I'm sorry not to know the result.
However, it seems to us that the old proof does not work well,
or too ambiguous

In p.98, ' $\alpha |0\rangle|\psi_0\rangle+\beta|1\rangle|\psi_1\rangle$' is used,
but to apply Aaronson's technique, what we need is
'$\alph

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The main result of this paper has already been shown previously in [Salman Beigi's PhD thesis (2009)][1] (Appendix B, Theorem B.0.5, p.98).

[1]: https://dspace.mit.edu/handle/1721.1/50594

Wow, this must be a breakthrough! So many people joining SciRate just to upvote it! Also, very creative user names:
[BladeMaster][1],
[KameBrown][2],
[siche][3],
[skyler][4],
[snow][5],
[zy z][6].
Will Blade Runner and Queen Elsa from Frozen also be joining to upvote this?

**Update:** Looks like [B

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The group that we call "R(2)" in the paper, the "Realizable Group" is indeed generated by the physical unitaries in the left side of the table on page 2. This group, as a unitary matrix group, has 4,608 elements. However, the action on just the logical space is smaller, and there is a 4-to-1 homomor

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Thank you for this timely work explaining standard tests run on the IBM machine!

Could you clarify what you refer to as the Realizable Group in the paper? Is it generated by the gates in the "Logical Equivalent" column in the table on page 2? This seems to correlate well with the statements in t

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That's correct. Thanks for spotting it ! The correct relation should be (1/|sigma_q|)sum_sigma = (1/(d-1))(dF-1). Another typo shows up in eq 41 which has essentially the same resolution. We'll correct this on the next update.

This is really a great work.. should be implemented with all the required resources.

Nice work~ Is there any typo on the formula (33)? It seems not consistent with former average fidelity formula...

Good job

You might be interested in this: https://cs.stanford.edu/people/karpathy/convnetjs/demo/image_regression.html

Good job... The dynamic reference frame is quite an interesting topic. Can be very helpful if used to full potential.

Liked the dynamic reference frame concept.

👍👍

Very helpful article. An ensemble of classification and time series technique. Concept of lead time is also interesting.

Is the implementation of the cQASM compiler open-source and if yes, where can I find the code?

"This is a very inspiring paper! The new framework (ZR = All Reality) it provided allows us to understand all kinds of different reality technologies (VR, AR, MR, XR etc) that are currently loosely connected to each other and has been confusing to many people. Instead of treating our perceived sens

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The most important reading here is Sam Braunstein's foundational paper: https://authors.library.caltech.edu/3827/1/BRAprl98.pdf published in January 98, already containing the key results for the strong convergence of the CV protocol. This is a must-read for those interested in CV quantum informatio

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One should also consult my paper "Strong and uniform convergence in the teleportation simulation of bosonic Gaussian channels" https://arxiv.org/abs/1712.00145v4 posted in January 2018, in this context. It is published in the June 2018 issue of Physical Review A and available at https://journals.aps

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Some quick clarifications on the Braunstein-Kimble (BK) protocol for CV teleportation
and the associated teleportation simulation of bosonic channels.
(Disclaimer: the following is rather technical and CVs might not be so popular on this blog...so I guess this post will get a lot of dislikes :)

1)

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[Fredrik Johansson][1] has pointed out to me (the author) the following about the multiplication benchmark w.r.t. GMP. This will be taken into account in the upcoming revision.

Fredrik Johansson wrote:
> You shouldn't be comparing your code to `mpn_mul`, because this function is not actually th

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A very nice approach! Could you clarify the conclusion a little bit though? The aspirational goal for a quantum benchmark is to test how well we approximate a *specific* representation of a group (up to similarity transforms), whereas what your approach demonstrates is that without additional knowle

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see my 2 papers on direction of vorticity (nov1996 + feb1999) = https://www.researchgate.net/profile/Philippe_Serfati (published author, see also mendeley, academia.edu, orcid etc)

see my 4 papers, 1998-1999, on contact and superposed vortex patches, cusps (and eg splashs), corners, generalized ones on lR^n and (ir/)regular ones =. http://www.researchgate.net/profile/Philippe_Serfati/ (published author).

Related Work:

- [Performance-Based Guidelines for Energy Efficient Mobile Applications](http://ieeexplore.ieee.org/document/7972717/)
- [Leafactor: Improving Energy Efficiency of Android Apps via Automatic Refactoring](http://ieeexplore.ieee.org/document/7972807/)

Comments are appreciated. Message me here or on twitter @moreisdifferent

Code is open source and available at :
[https://github.com/delton137/PIMD-F90][1]

[1]: https://github.com/delton137/PIMD-F90

Hello again Māris, many thanks for your patience. Your comments and questions have given me much food for thought, and scope for an amended version of the paper -- please see my responses below.

Please if any of the authors of [AST17 [arXiv:1712.01609](https://arxiv.org/abs/1712.01609)] have any fu

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The Igorots built an [online community][1] that helps in the exchange, revitalization, practice, and learning of indigenous culture. It is the first and only Igorot community on the web.

[1]: https://www.igorotage.com/

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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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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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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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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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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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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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}}+\frac{\mathit{A^{2}}}{K\phi^{4}}-\frac{\mathit{A^{\math

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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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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

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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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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/

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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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.

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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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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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.