Now this is useful work! Awesome!
If this is the best ML can do with respect to climate change; we're in big trouble.
I think that at a place like NeurIPS, and in a _workshop_ on _tackling climate change_, the kinds of things we as the ML community focus on should be much larger-ticket items.
Very nice paper! Is the Supplementary Material available somewhere? :)
Congratulations on the first use of "quantum pwenage" (as far as I am aware). Although, should it not be "quantum pwnage"?
Review now published in Contemporary physics. Available at
https://www.tandfonline.com/doi/full/10.1080/00107514.2019.1667078
https://www.researchers.one/article/2019-10-7
...(continued)The main text ends with a parable: "We close with a story. Alice and Bob, having successfully run their randomized boson-sampling experiment, are in Stockholm to pick up the Nobel Prize in Physics for the first demonstration of quantum supremacy. As the King of Sweden approaches to present the Nobel
See also https://scirate.com/arxiv/1901.07471
Also, the statement that "It is known that arbitrary n-qubit gate can be generated by arbitrary 1-qubit gates and the CNOT gates on any two qubits in time O((log d)^3)", where d = 2^n, is wrong, no?
...(continued)If you look at the transverse spatial wavefunction of a photon in a Laguerre-Gaussian mode, it has a radial index $p \in \mathbb N_0$ and an azimuthal index $l \in \mathbb Z$. The beam width, as measured by the standard deviation in space, grows as $\sim \sqrt{2p+|l|+1}W_0$, where $W_0$ is the width
How is one supposed to evaluate the Slater determinant in Eq. (20)? It is clearly not a square matrix since M is typically larger than N.
I do not understand why "standard quantum mechanics predicts that *none* of the photons should arrive early". E.g. in fig. 5, would not photons along the diagonal path arrive earlier than photons along the right-angle path, in standard quantum mechanics just as in Bohmian mechanics?
If you're wondering how this is possible, the exponential savings comes from using photon states with orbital angular momentum $\ell = 2^{\Omega(n)}$.
Dear Michel, thank you very much for bringing this to our attention. We will add an appropriate citation in the updated version of our paper.
Dear authors,
I suggest you read
https://arxiv.org/abs/1009.3858
"Pauli graphs when the Hilbert space dimension contains a square: why the Dedekind psi function ?"
for commuting Paulis, also the related papers.
Michel Planat.
Hi Eddie, thanks for your comments. Indeed, this information is too difficult to find. We will make improvements in a future version.
Noticed I forgot to include a corresponding author's email! If you have questions or comments, you can reach me at [first name].[last name] using the ibm.com domain.
Wow!
interesting figure:
Estimated climate footprint of the computations presented in this paper = 992 kg
Now published in PRA!
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.100.022304
Thank you to everyone who helped - because of your help and good questions we had a smooth refereeing process.
https://journals.aps.org/pra/accepted/d207eNe9R6210217390c06a5282cb5fb55447473c
Uncharacteristically readable paper involving Terry Tao! More about this [over on his blog](https://terrytao.wordpress.com/2019/08/13/eigenvectors-from-eigenvalues/).
For other readers who are also interested in what a MOVE operation is: It's defined in Fig. 6.
Great paper! Non-abelian quantum error correction is still a quite unexplored territory. Needs more attention from the QEC community. Going beyond stabilizer models leads to much more opportunities.
What a great idea! This is very exciting! Who's going to try implementing it as a quantum algorithm!?
Hi Arthur. Very happy to hear you've found my review useful! Feel free to email me if you have any more questions about QEC or quantum computing :)
I'm currently learning quantum error correction (as a grad student) and found your guide to be an incredibly useful resource, very clear and well written! Thanks a lot for sharing it :)
...(continued)Thanks a lot for your comment. Well, doing full Gate Set Tomography certainly gives a lot of information about your devices (assuming you can actually perform it). However, as far as I understand one cannot use this data directly to mitigate the errors. The point of our work is to use tomography of
Most unexpected paper title of the year?
Exciting work! Could you comment on how using your technique will be different than doing a full Gate Set Tomography?
Should probably have a reference to the original NMR experimental implementation: [Benchmarking Quantum Computers: The Five-Qubit Error Correcting Code
](http://dx.doi.org/10.1103/PhysRevLett.86.5811)
Thanks for your detailed comments. I'm now convinced that the questions addressed in your two papers are interesting, and I currently have nothing to add to the discussion of these questions.
...(continued)The statement in your first paragraph is partially correct, but also misleading. Part of the problem is that the word "measurement" has too many meanings. For the present purposes, let us say that a measurement consists of what Peres has called a "premeasurement" (i.e., a unitary interaction that
...(continued)Okay, now I understand that equations 10 and 13 are mathematically different, where before I had not. Is it correct to say that one of your key points here is something like "one must always set aside a subsystem of nontrivial dimension to be considered as inaccessible / unmeasured?"
A view that I
...(continued)The equivalence relation you describe is the standard one given in equation (10). It is not quite the same as the one I am proposing to use, which is the one given in equations (12) and (13). You are correct that the crucial question is which observables are allowed. Your circuit-size criterion i
...(continued)In your title you suggest that we should quotient the state of density matrices by an appropriate equivalence relation. Is your equivalence relation exactly
$\sigma \sim \rho \iff \operatorname{Tr}(P_i\sigma) = \operatorname{Tr}(P_i\rho)$ for all
"projections" $P_i$ which are part of the spectr
I'm happy to see that the bibliography I compiled for [arXiv:1703.07901][1] is becoming more and more out of date!
[1]: https://scirate.com/arxiv/1703.07901
https://qbnets.wordpress.com/2019/06/27/comments-on-quant-ph-arxiv1906-10726-quantum-causal-models-by-jonathan-barrett-robin-lorenz-ognyan-oreshkov/
Interesting work! Are the authors aware that there is other recent work which has formulated and examined the question of curing the sign problem from complexity and algorithmic perspectives: https://arxiv.org/abs/1802.03408 and https://arxiv.org/abs/1806.05405
...(continued)Reference 2, which is used to define QBism, is to Caves, Fuchs and Schack (2002). This is an incorrect attribution; Caves does not call himself a QBist and disagrees with some turns that the other two authors made in the following years. (One migh
Regarding your first point, the blocking strategy *can* be applied. See our reply to Earl Campbell's comment.
See the first sentence of the main text..
...(continued)=> A similar block decomposition as in the stabilizer case can be applied. Namely, for a total of n copies of |H>, one can expand the first set of k copies with respect to the robustness of our paper, and the other n/k -1 sets of k copies w.r.t. the (stabilizer) robustness of magic. For such very r
...(continued)=> There is nothing else to consider for classical simulation of QC with magic states. There may a priori be Clifford unitaries, but they can all be propagated past the last measurement, conjugating the measurements in this process. The measurement statistics are the same, for instance, see [20]. F
...(continued)All of these results are for Shor's algorithms. More specifically, the results are for various derivatives of Shor's original algorithms. These derivatives are specialized for problems that are relevant in cryptography. They provide various constant factor improvements with respect to the number of
How about using shor's algorithm?
...(continued)Regarding your first point, I have had exactly the same thoughts. It seems that the "blocking strategy" cannot be applied to the Raussendorf et. al robustness measure and I would be interested if there is a different way of extending low-dimensional solutions. Simulating a quantum circuit with $n$ m
Opp.... I wrote a reply yesterday but as a separate comment (see below). My main question is essentially the same as Patrick's above: these LPs are typically only tractable up to 5 qubits so you need some suboptimal method to perform larger simulations.
...(continued)The last point confuses me somewhat: if I understand correctly your algorithm only supports potentially non-classical input states followed by Pauli measurements. How can this be used to simulate an arbitrary quantum circuit? With an MBQC approach, the initial state would have to scale with the size
Braneshop, and
the US National Science Foundation.
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