...(continued)If anyone fancies giving these a whirl, a python package is now available here https://github.com/jcmgray/cotengra including some snazzy, if not necessarily informative, visualizations...
![Optimized contraction tree for a random regular graph.][1]
[1]: https://camo.githubusercontent.com/04c
Very interesting research. It is a good starting point, but I think it must be improved using the existing algorithms.
John Brown
[Elatom][1]
[1]: http://elatom.com
For Theorem 3, it is worth mentioning that the the only $k$-transitive group actions for $k > 5$ are the symmetric and alternating groups (see https://en.wikipedia.org/wiki/Mathieu_group#Multiply_transitive_groups).
...(continued)Congratulations on this excellent work. The use of the new MPI shared memory feature is particularly impressive. I would, however, have liked to have seen tables or plots of parallel efficiencies. For example, when you scale from ~500 to ~2000 CPU cores, it doesn't look like you are gaining much by
A shorter (conference) version of this paper is here: https://arxiv.org/abs/2001.04887
...(continued)For those looking to understand this from the "outside" operator algebras point of view:
The authors use complexity-theoretic language to recursively build a presentation for a very nasty C* algebra. In order to extract properties of the algebra from its presentation, they use the language of quan
We know that protein folding and fluid dynamics are still hard to simulate classically. The point of quantum supremacy is that the hardness comes from interference in an exponentially large state space. So "analog supremacy" and "quantum supremacy" seem like different things.
Awesome framework, nice to see the paper online! :)
Awesome work! I've been advocating experimentalists to eventually do the test through IQP sampling and claim the \$25 reward for quite some time, I didn't imagine it would be broken classically!
Marvelous.
...(continued)Wow, this is really neat - a completely different way of thinking about Grover's algorithm! It never occurred to me that one can think of the amplitudes of a $d$-dimensional quantum state as velocities of $d$ balls, and that the normalization of the state corresponds to the conservation of kinetic e
Version 2 expands the penultimate section (on Fuchs and Peres 2000) in response to reader feedback.
I doubt money is the bottleneck, even though it will be expensive. More likely writing the code, optimizing it, testing it, and then scheduling the computation are just time consuming. If money were the only barrier to doing a validation, then this would have been done already.
It would probably cost a lot and they would have to wait for the machine to be available. My back of the envelope estimate is $20k or so just for electricity. It would be nice to validate some of the Google outputs some day but this doesn't seem like a great use of resources right now.
...(continued)NB: The following is pure speculation. I just imagined what I would do if I were the authors, but I son’t know them and I don’t have their expertise.
I guess it would also remove much more weight to their budget... It would also take more time (to programme the thing), and prevent the publication
...(continued)From the introduction:
"While we did not carry out these computations, we provide a detailed description of the proposed simulation strategy as well as the time estimation methodology, which is based on published results and on internal benchmarks."
Why didn't IBM actually perform the computation
We recently published a Python [package][1] which calculates gradients via backpropagation for specific types of parametrized circuits.
[1]: https://github.com/frederikwilde/qradient
...(continued)We have significantly updated the paper with the following new material:
- We added a study of the generalized amplitude damping channel, a 2-parameter channel that models the dynamics of a qubit in contact with a thermal bath at finite temperature. Using our neural network state ansatz, we find
Is this a NISQy algorithm breaking lattice-based postquantum crypotography (if the numerical evidence are confirmed)? That’s how I read the abstract and the paper, but I’m neither a specialist of AQC, nor of postquantum cryptography.
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?
Braneshop, and
the US National Science Foundation.
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