...(continued)Correct me if I'm wrong, and I'm not questioning the novelty of recent works of this nature, but I think there's no need to create a new name such as "shadow tomography" for this type of problems. Classical statisticians have been studying the estimation of probability density functionals for many d
...(continued)The abstract differs slightly from the abstract in the article. Please refer to the abstract in the article for the most recent version:
We report, in a sequence of notes, our work on the Alibaba Cloud Quantum Development Platform (AC-QDP). AC-QDP provides a set of tools for aiding the developmen
Here is the submitted TQC extended abstract, if you want to read a 3 page summary
https://earltcampbell.files.wordpress.com/2020/02/tqc_abstract.pdf
...(continued)Nicolas, Christopher,
Thanks for your responses. The previous papers you cited assume no syndrome measurement error, which is an idealization. It's not obvious to me what the results in those papers would have been if syndrome measurement error were included.
Conversely, this new paper does co
...(continued)Sorry for the confusion, but as I mentioned in our earlier discussions, our paper [WMHY19](https://scirate.com/arxiv/1902.00869) is based on a different framework, and I'm not sure if they can be compared directly. As a simple illustration, the wiki page of ['AdaBoost'](https://en.wikipedia.org/wiki
In fact, twirling when one has coherent noise can make the performance worse (see https://arxiv.org/abs/1612.02830).
...(continued)That's correct. We focus on bit flips or Pauli noise. This seems reasonable since coherent errors generally do not degrade too much the performance of error correction as one can see with your repetition code paper [https://arxiv.org/abs/1612.03908] or with the surface code study of [https://arxiv.o
This paper appears to consider only stochastic errors, i.e. bit-flips with probability p. Have you thought about how the results would change for coherent errors?
...(continued)Shameless self-promotion: I studied the same problem (quantum estimation of one parameter among many unknown parameters) and also used geometric concepts extensively in this work:
https://scirate.com/arxiv/1906.09871 (first version on 24 Jun 2019, last update on 6 Feb 2020)
Now that Carl is wo
...(continued)Attention, this abstract caught, of this reader on account of the writing style. Curious, this reader perused the manuscript and found in it the following explanation:
"Unusual, it might be thought, is the style of this paper. An explanation is in order. Kip
Thorne’s recent biographical memoir o
...(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
Braneshop, and
the US National Science Foundation.
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