What are the conditions for the results regarding noisy learning to break down when you go beyond depolarizing noise?
...(continued)This paper points out that it is unlikely that quantum resources will accelerate the convergence of the Hartree-Fock procedure. This timely analysis seems prompted by Google’s recent experimental demonstration of Hartree-Fock on a quantum computer ([arXiv:2004.04174][1]). But in case there is any do
Do you have a reference/reason for k-local gates to have cost proportional to k?
The [repository][1], which contains the code for this paper, is now available open-source.
[1]: https://github.com/a-wozniakowski/scikit-physlearn
Discussions of this paper have transpired [here](https://golem.ph.utexas.edu/category/2020/06/getting_to_the_bottom_of_noeth.html) and [here](https://johncarlosbaez.wordpress.com/2020/06/29/noethers-theorem-2/).
The arXiv admin fixed it! The PDF should now work.
arXiv is somehow unable to produce a PDF, but the postscript version https://arxiv.org/ps/2007.04849 is fine. Will try to fix.
Beautiful illustrations. A simplified version of this would make for a wonderful undergrad homework problem, I think.
Eq. (1) defines a qubit SIC, for whatever that's worth.
...(continued)If the initial state is $|\psi\rangle$ and the possible post-transition states are $|\phi_i\rangle$, then unitary transformations will leave invariant the [3-vertex Bargmann invariants](https://arxiv.org/abs/quant-ph/0107006) $\langle \psi | \phi_i \rangle\langle \phi_i | \phi_j \rangle \langle \phi
This "paper" needs more likes! :D
...(continued)Initially I thought that non-contextuality could be derived from invariance under unitary transformations, but that is wrong. If a set of orthonormal states is given as possible states after the transition, then their scalar products with the initial state remain unchanged under unitary transformati
...(continued)The assumptions that the transition probabilities are unchanged by unitary transformations, and that they must vanish for orthogonal states, are rather substantive assumptions. There is also the implicit assumption that they are non-contextual (since the notation which is used requires that transit
The paper has now been updated.
Thanks for the update! (It's good to see such forthcoming/virtuous academic integrity :-) ) Also good idea to post it here, will have to remember it in the future.
Hi Henrik,
That certainly helps, thank you! I did read the other paper too.
Abhinav
The claim that we strengthen Matsumoto's result is incorrect. An update of the paper removing this claim is forthcoming.
...(continued)Hi Abhinav,
thank you for your comment! I believe that any $P$ fulfilling $\exp(\mathrm i P)=U$ decays as $1/|x-y|$. But indeed, we don't show this in the paper and should have phrased the appendix a bit differently. We will update it.
(I would like to thank Zoltán Zimborás for discussions regar
...(continued)In short, the authors improved $\beta$ VAE Framework by reaching a better trade-off in terms of Reconstruction Quality vs Disentanglement (first contribution) according to a new metric they propose (second contribution)
The core idea comes from the fact the authors reached a deep understanding of t
...(continued)Really nice paper! Regarding Appendix D, how can I see that there cannot be a different generator giving rise to the same dynamics at discrete times? I mean that $U = \exp(iP)$ does not have a unique solution for $P$, so it does not rule out a quasi-local generator for $U$. Or are you claiming that
Hi Filip, thank you for your interest. We are looking forward to making the code available once it is more user-friendly.
...(continued)I'm going to cautiously advance the opposite of the italicized conjecture on p. 2 and hazard a guess that sets of $2d^2 - d$ equiangular lines will _not_ generally exist in $\mathbb{H}^d$. This inclination of mine is perhaps due to coming to the problem of equiangular lines from quantum theory, and
...(continued)> the idea (emerging from the above assertion)
that the event A gives rise, as effect, to an event which is absolutely not different from A, has to be
rejected as an absurdityIt reminds me of John Wheeler's Participatory (aka Self-observing) Universe, and it seems you have unwillingly strength
Exciting work! May I kindly ask if you thought about making your optimization code publicly available? I believe that it would make using your methods much easier for a lot of people!
...(continued)This is a clever and interesting paper. I am not a proponent of the "consciousness causes collapse hypothesis" (CCCH), but I nevertheless want to remark that somebody who is might attempt a defense of the CCCH along lines of the following:
Take the CCCH to say that wave-function collapse occurs w
...(continued)Cedric,
1) In Theorem 27, we show that if a promise problem is recognizable in O(log n) space and poly(n) time by a family of *general* quantum circuits, then it is also recognizable in O(log n) space and poly(n) time by a family of *unitary* quantum circuits. A bound on the hidden constants in t
...(continued)Great work! I haven't had time to gone through the paper in great detail, but I have two immediate questions:
1) You mention in the abstract that the procedure is simultaneously space-efficient and time-efficient, but I couldn't find a statement of this in the main body. Could you be more precise
https://qbnets.wordpress.com/2020/06/07/anomaly-detection-with-quantum-computers-better-than-with-classical-computers/
A short talk based on this work is scheduled today at 16:30 (UTC+2): https://www.youtube.com/watch?v=h4uFaV6rFSc
More details (including a 3-page abstract) here: https://www.monoidal.net/paris2020/talk/qs12t1.html
Here's a short talk based on this, given today at QPL 2020: https://www.youtube.com/watch?v=uO08ci5dK6Q
...(continued)From my perspective, everything until Section 5 follows directly from the fact that the group $\mathrm{DS}(2^w)$ (aka *real Pauli group*) as well as the projective and normal Pauli group form unitary 1-designs and thus a tight frame for the space of complex matrices which gives you the desired Parse
It would be very interesting if one can show and realize the maximally localized Wannier functions in a digital quantum simulations.
...(continued)Great work, please do keep it up! Minor gripe about abstract statement - the sentence about experimental systems is misleading, as far as I understand due primarily to the difficulty of reliable single-photon sources in the lab. I realize you say "in principle", but to the average CS person like mys
The orthonormal operator bases defined in Eq. (9) were previously studied by Zhu, who proved that they saturate bounds defined using the negativity of quasi-probabilities [PRL **117** (2016), 120404, [arXiv:1604.06974\]][1].
[1]: https://scirate.com/arxiv/1604.06974
Simons Apers's talk at the Simons Institute: [https://simons.berkeley.edu/events/quantum-speedup-graph-sparsification-cut-approximation-and-laplacian-solving][1]
[1]: https://simons.berkeley.edu/events/quantum-speedup-graph-sparsification-cut-approximation-and-laplacian-solving
https://arxiv.org/abs/quant-ph/9805016
How to Compile a Quantum Bayesian Net
...(continued)I am unsure about the reasoning presented in this paper. It seems to me that there is an issue with the reasoning used to upper-bound the query complexity of the multi-layer quantum search method.
On page 4, you begin by lower bounding the number of queries Q of the algorithm by a value Qmin (eq
Nice work. By the way, your paper's arxiv metadata abstract field has a redundant copy of part of the abstract.
...(continued)Proposition 7 for the SLD information is a known property called extended convexity; see S. Alipour and A. T. Rezakhani, PRA 91, 042104 (2015), http://dx.doi.org/10.1103/PhysRevA.91.042104. We proved it for multiple parameters by relating it to the strong concavity of the fidelity; see Ng et al., PR
...(continued)Thanks very much for your comment Jerry. As with other table-top tests of quantum gravity, we are proposing an experiment in which all forces other than gravity, e.g. the electromagnetic force, can be neglected. Then, due to the universal coupling of gravity, gravity couples to the kinetic and mass
much thanks to Craig Gidney, for pointing out that the only linear-depth Clifford component can equivalently be implemented in logarithmic depth
...(continued)Indeed, just focusing on T complexity is a bit too simplistic. I only quoted that number because your abstract focused on T complexity. The tradeoff between gate complexity and space complexity is why the abstract of [arXiv:1902.02134][1] emphasizes the reduction in surface code spacetime volume (a
...(continued)Hi Ryan,
I agree with your argument that the $10^{15}$ value is outdated at this point. I'll post an updated version that better reflects this. However, the $10^{11}$ figure is a swing too far in the opposite direction, I think. Even though the algorithm in [arXiv:1902.02134][1] is the most minimal
...(continued)The $10^{15}$ figure in the abstract refers to an older algorithm. More recent work has brought estimates for FeMoco to around $10^{11}$ (see [arXiv:1902.02134][1]), albeit with some ancilla (but even a version with very few ancilla improves from $10^{15}$ gates). That new work is based on qubitizat
...(continued)This is certainly an important result. However, it does seem to require the assumption that "the classical interaction would not induce quantum self-interaction". So I wonder how certain we can be that, for example, classical gravity might not induce a very small term (such as suggested in footno
The code implementing the angle finding algorithm, together with an example of Hamiltonian simulation, is available at [GitHub][1].
[1]: https://github.com/alibaba-edu/angle-sequence
I was sure that somebody had won an Ig Nobel for doing this, but I think my memory mixed up the levitating-frog experiment with a stunt that they did back in the day at the MIT Magnet Lab, lowering the temperature of a whole workshop with LN2 until they could Meissner a magnet off the floor.
...(continued)After reading footnote [32], I would like to enthusiastically urge everyone to cite this paper heavily via every medium. My homestead on the Tozitna River in interior Alaska is, in fact, engaged in a long-running and ongoing war with beavers. The dam critters keep building dam after dam across the
A breakthrough!
Braneshop, and
the US National Science Foundation.
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