On character table of Clifford groups

Markus Heinrich Sep 28 2023 07:20 UTCJason Saied Sep 27 2023 21:15 UTC

...(continued)This is very interesting! I am sure the explicit character tables will be helpful in the future.

I just wanted to point out that Conjectures 5.4 and 5.5 are known (or follow directly from known results). In the below, always take $n\geq 3$. The main facts being used are the observation that $\ma

Jahan Claes Sep 25 2023 14:14 UTC

Is it clear if this protocol works for noise models where different Pauli errors occur with different probabilities? My understanding right now is that you have to assume each fault occurs with the same probability *p*, but maybe there is some way around that?

Adrian Müller Sep 24 2023 20:17 UTC

Ah, true, the hermitian conjugate is only equivalent to the inverse for unitaries, simple mistake. Thanks!

Oscar Higgott Sep 23 2023 14:46 UTC

...(continued)Yes the EM3 distance does usually match the embedded distance, although we found one case where they differed (for n=320, k=18 with EM3 noise the minimum-weight error included Pauli errors that caused time-separated detection events). Thank you for pointing me to your updated GitHub repo, and I agre

Alex Fischer Sep 21 2023 23:07 UTC

...(continued)The spectral decomposition you use in Lemma 1 is only valid for normal matrices, not all diagonalizable matrices. Of course, the lemma (trace = sum of eigenvalues) is true for all diagonalizable matrices, but for diagonal matrices that are not normal, the proof of that fact requires more than just a

Ali Fahimniya Sep 21 2023 23:00 UTC

...(continued)Thanks for your comment, Oscar! Yes, the DP1 distance the way you defined (and is equivalent to the code distance defined in our paper) equals to the lesser of "the embedded distance of the superlattice" and "twice the embedded distance of the dual of the superlattice". It is still interesting to me

Adrian Müller Sep 21 2023 14:30 UTC

Thanks a lot for the hints! I'm now surprised I haven't found them earlier in my own searches. I'll soon upload another version of the manuscript crediting their work appropriately.

Oscar Higgott Sep 21 2023 10:58 UTC

...(continued)Very interesting work, congratulations! Where you compare to our work you say "At similar encoding rates, the codes shown here have a larger relative code distance". The reason for the discrepancy is that we report the distance of our circuits, which include two-qubit errors, whereas you are reporti

Alex Fischer Sep 20 2023 17:08 UTC

Thanks for the references Josu. I see that what we called single-qubit site-dependent Pauli noise is something you have studied and called i.n.i.d noise. We will make sure to reference these works in the next version.

Josu Etxezarreta Martinez Sep 20 2023 15:30 UTC

...(continued)Very interesting manuscript. I see that you have considered Pauli noise that shows different probabilities for each of the qubits of the surface code, which I see that you named single-qubit, site-dependent Pauli noise. I attach here a couple of references regarding studies of surface codes with suc

Bartosz Regula Sep 20 2023 04:27 UTC

...(continued)The numerical efficiency of computing the fidelity in this way was previously pointed out in https://arxiv.org/abs/2211.02623.

(The expression itself appeared earlier; the similarity of the matrices was noted already in https://arxiv.org/abs/0805.2037, and I can find an explicit expression e.g. in

Paweł Cieśliński Sep 18 2023 07:49 UTC

I did not get one part. If we assume that the particle with mass M is not a dark matter particle, wouldn't we observe the same effect? Or the reasoning is based upon no corrections from other interactions?

Sergey Bravyi Sep 15 2023 20:53 UTC

...(continued)Hi Pavel, thanks a lot for your comments and suggestions. Most of our results are extensions of your BP-OSD work so I am really glad to get a feedback from you. The generalized bicycle code [[126,12,10]] is indeed very close to codes from our paper in terms of the distance and encoding rate. It is a

Tim Bode Sep 13 2023 06:16 UTC

https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.4.030335

Ruslan Shaydulin Sep 12 2023 13:18 UTC

...(continued)Dear Yiren,

Thank you for bringing this serial CPU-only Python implementation to our attention. We added a reference to it, as well as a note thanking you for pointing it out to us, in a v2 version that will appear on arXiv shortly.

We note that the mixer implementation in (Sack & Serbyn, 2021) re

Yiren Lu Sep 12 2023 07:01 UTC

...(continued)Hello, I think similar idea seems to have appeared in the [source code](https://github.com/shsack/TQA-init.-for-QAOA/blob/master/TQA_QAOA.ipynb) of (Sack & Serbyn, 2021), which might be better to be included as related work.

Sack, S. H., & Serbyn, M. (2021). Quantum annealing initialization of

Kishor Bharti Sep 04 2023 23:32 UTC

Sure. Should I have any further comments/queries, I'll reach out via email. Thanks.

Soumik Ghosh Sep 04 2023 14:31 UTC

...(continued)Hi Kishor,

Thank you for your very kind words regarding our paper and for your helpful feedback!

1. Regarding your first comment, we are indeed aware of your nice paper on pseudo-random unitaries, which we cite in our work. Our work complements your discussion of other pseudo-resources, by con

Yiren Lu Sep 04 2023 01:22 UTC

Understood! Thanks a lot for the clarification!

Harold Nieuwboer Sep 01 2023 12:20 UTC

...(continued)Hi Yiren,

Thanks for the question. This is indeed a bit implicit in the literature, but well-known. One can for instance recover it from the lower bounds by Beals et al in \[1\]. Here is the short additional argument: Let $x \in \\{0,1\\}^N$ be a bit string and assume the Hamming weight of $x$ is e

Kishor Bharti Sep 01 2023 12:10 UTC

...(continued)Beautiful work! My congratulations to all the colleagues involved in this work.

Upon a quick glance, Tobias, Dax, and I wanted to respectfully bring a few points to your attention:1. In our recent paper on pseudorandomness ([https://scirate.com/arxiv/2306.11677][1]), we explore the concept of pseu

Yiren Lu Sep 01 2023 08:57 UTC

I have a simple and basic question: why the $\sqrt {Nk}$ query complexity is optimal? It seems to be a well-known result but I fail to find a reference.

Pavel Panteleev Aug 26 2023 00:25 UTC

...(continued)Very impressive and unexpected results! My congratulations to the authors!

I noticed that you mentioned our [[882, 24, ≤ 24]] code. I want to point out that in the same paper in Appendix C we also constructed a family of weight-6 generalized bicycle (GB) codes, which are obtained from two weight

Pierre-Emmanuel Emeriau Aug 24 2023 10:01 UTC

Probably contributions section of the year as well.

Theodore Yoder Aug 21 2023 21:44 UTC

Hi Oscar! Thanks for letting us know about your work. It looks very nice and relevant, and I'm sorry we missed it. We will be sure to cite it in the next version.

Komal Aug 21 2023 05:53 UTC

...(continued)In the [[10,3,3]] code (Fig. 8), let us write two sets of paths for 𝑋̅ – one with weight two and one with weight three. The operators of weight two commuting with the stabilizers are {𝑋1 𝑋3, 𝑋2 𝑋4, 𝑋7 𝑋9, 𝑋8 𝑋10}. The operators of weight three are {𝑋1 𝑋5 𝑋7, 𝑋3 𝑋5 𝑋7, 𝑋1 𝑋5 𝑋9, 𝑋3 𝑋5 𝑋9, 𝑋2 𝑋6 𝑋8, 𝑋

Oscar Higgott Aug 19 2023 10:54 UTC

...(continued)Congratulations on this very nice result! On page 6 you say "To the best of our knowledge, this provides the first example of high-rate LDPC codes achieving the pseudo-threshold close to 1% under the circuit-based noise model." In https://arxiv.org/abs/2010.09626 and https://arxiv.org/abs/2308.03750

Maxwell Aifer Aug 14 2023 03:06 UTC

...(continued)Thanks for bringing this interesting article to our attention! There does seem to be a comparison between the thermodynamic algorithms we presented and these Monte-Carlo algorithms, because 1) both are nondeterministic, and can be seen as Markov processes, and 2) both can achieve O(d^2) operations a

Ruslan Shaydulin Aug 11 2023 18:39 UTC

...(continued)Hi Alex,

Thank you for your very important question! Though we do think a lot about this, we do not have a good theoretical handle on the QAOA behavior. Let me say two things.

First, the speedup we observe is not unique; Boulebnane and Montanaro ([arXiv:2208.06909][1]) observed a similar speed

MJKastoryano Aug 11 2023 09:48 UTC

...(continued)I am curious about how your results relate to the various Monte Carlo algorithms for matrix inversion and linear algebra. From a superficial skim, your algorithms seem to be a continuous time formulation of an MC algorithm for Matrix inversion.

See for instance

https://link.springer.com/conten

Alex Meiburg Aug 10 2023 00:04 UTC

...(continued)Reaching+beating state of the art performance is great and certainly the most important metric, but is there a deep theory here *why* QAOA would be expected to do well here? Something about the geometry of the Hilbert space to naturally reflect the problem? I'd be curious to know, in the authors' es

Evan McKinney Aug 09 2023 17:41 UTC

The circuit qftentangled in Table 3 has 279 2Q gates, (typo in paper says 0). This will be fixed in next version.

Kishor Bharti Aug 09 2023 14:47 UTC

:)

Oscar Higgott Aug 09 2023 14:45 UTC

Hi Kishor, many thanks for highlighting this, we're looking forward to seeing your upcoming work.

Kishor Bharti Aug 09 2023 14:03 UTC

Nice work. Awesome. Congratulations. I just wanted to point out that we also have one paper under preparation on hyperbolic Floquet codes :)

Here is the APS March meeting version.

https://meetings.aps.org/Meeting/MAR23/Session/N64.9

Zhan Yu Aug 05 2023 23:34 UTC

...(continued)Hi LC,

Firstly I would like to thank you for your interests in our work. It’s great to see that you have applied some results of the QPP model in your work, and I would be certainly interested in reading the paper when it’s available!

Thank you for your valuable comments that help to clarify the d

Zhan Yu Aug 05 2023 23:04 UTC

...(continued)Hi Danial,

Thank you for your reply. We appreciate it that you take a look at our paper and discuss the differences of these two models.

For the bound condition, as LC pointed out (with thanks), we could simply replace the bound on coefficients 1-norm with the bound on the polynomial in our th

LC Aug 05 2023 21:24 UTC

...(continued)Hi all, first of all, thanks to you both for amazing papers. These are really neat results, and look to be pretty game-changing contributions to the theory of QSP!

I just wanted to quickly make a point–I've been using some of the results in the QPP paper in my own work over the past couple months

Danial Motlagh Aug 05 2023 19:48 UTC

...(continued)Dear Zhan Yu,

Thanks for your message (I also received your email). I agree that your QPP model closely resembles our work, although at a first glance there seem to be a few differences such as the use of both $U$ and $U^{\dagger}$ in your method (leading to negative degrees in the trigonometric po

Zhan Yu Aug 05 2023 18:06 UTC

...(continued)Dear Danial and Nathan,

I would like to kindly point out that the generalized QSP model in this work looks pretty similar to the quantum phase processing (QPP) model proposed in our previous paper https://scirate.com/arxiv/2209.14278. The motivation mentioned in the introduction of this work also

Seok Hyung Lie Aug 04 2023 05:13 UTC

Hi Patryk,

Thanks for clarifying! Glad that my comments were helpful.

Patryk Lipka-Bartosik Aug 01 2023 07:08 UTC

...(continued)Hi Seok,

Many thanks for your comments and for spotting some unclear statements about our work! Also, sorry for quite a late reply.

In short, we agree with you that the current proof of Theorem 1 omits several important details. In the upcoming version we will add all the missing details.

Anthony Polloreno Jul 28 2023 17:07 UTC

Hahaha. Thanks Kunal - I should have then said that the original arXiv title doesn't help with the fishiness!

Kunal Marwaha Jul 28 2023 11:33 UTC

I think SciRate stores the original arXiv title, which had a typo. I updated it manually.

Anthony Polloreno Jul 27 2023 17:19 UTC

Haha, the mis-parsing of scirate doesn't help the fishiness. "Firs".

Jonas Helsen Jul 26 2023 19:00 UTC

So.. do we have any experts on high Tc superconductors around to comment on this? It smells pretty fishy to me, but this is not my neck of the woods.

Seok Hyung Lie Jul 17 2023 10:55 UTC

...(continued)Thanks for your answers. After reading a bit more, I also have a few comments:

When you defined the decomposition of $\Pi_\nu=\sum_n |\mathcal{E}^\nu_n\rangle\langle\mathcal{E}^\nu_n|$ on Page 3, I think you meant the order of non-decreasing local energies of $A$, not non-increasing. Moreover, since