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Yadong Wu Mar 13 2024 07:12 UTC

A closely related result about learning quantum states on infinite dimensional systems has already been obtained in this paper https://arxiv.org/abs/2303.05097.

Julio Magdalena Mar 12 2024 14:10 UTC

thanks for the response. It cleared out some confusion about the "self-correcting" errors you mention. Thanks!

M. Sohaib Alam Mar 07 2024 19:15 UTC

Dear Julio, thanks for pointing us to the square lattice construction in your nice paper. We'll be sure to mention it, and modify our statement in a later version.

Re: self-correcting errors, the 2-qubit errors this refers to here are actually check operators of the parent subsystem code, and so

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Julio Magdalena Mar 07 2024 12:33 UTC

Dear authors!
Thanks for posting this interesting paper. I was wondering if you could elaborate on a question I got while reading through. Additionally, I have a minor comment that might be interesting to you.

The question is on the phenomenon you call "self-correcting errors" in your paper. Can

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Sascha Heußen Mar 04 2024 08:27 UTC

Hi Jahan, extending the formalism to a multi-parameter noise model works straightforwardly by extending Eq. 2 to a product of binomial factors. This is described in detail, for example in https://arxiv.org/pdf/1801.07035.pdf, see Eq. 10 in there. Cheers!

Tuomas Laakkonen Feb 23 2024 14:25 UTC

Thanks! - so far as I can tell, the circuit constructed in that paper is for a specific case of the unary iteration circuit (where $P_i = R_a(\alpha_i)$ for some axis $a$ and angles $\alpha_i$). We have a more general circuit where each $P_i$ can be any Pauli operator (potentially on multiple qubits

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Ammar Daskin Feb 23 2024 06:36 UTC

cool paper!
I do not know if it is relevant, but for unitary iteration circuit, there is an exact simple decomposition (though not in terms of T gates) in "Möttönen, M., Vartiainen, J. J., Bergholm, V., & Salomaa, M. M. (2004). Quantum circuits for general multiqubit gates. Physical review letters,

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Kelly Pawlak Feb 06 2024 23:17 UTC

> a quantum black box that outputs a uniform superposition of such points

This isn't so farfetched. Craft a stabilizer that checks a radius condition, and alternately apply it with Hadamard gates as in the distribution preparation algorithms of arxiv:2310.20191. The only question is the exact scali

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Michael J Gullans Feb 06 2024 04:56 UTC

As the authors point out in the preprint, the cost of this exponential time algorithm can be increased from 2^(n/3) scaling to 2^n with the use of in-block permutation CNOTs for the [[8,3,2]] code. Such gates are readily implementable with the parallel control hardware that is available in the lab.

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Andrew Childs Jan 30 2024 13:52 UTC

Daniel, your question is addressed in arXiv:0705.2784, which considers closely related problems using similar techniques. If the dimension is odd, then the walk can be implemented efficiently. If the dimension is even, then the implementation of the walk is closely related to the problem of (approxi

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Lvzhou Li Jan 30 2024 10:36 UTC

Thanks for your comments. Yes, the adjacency matrix A is dense with $s_r≈q^{n-1}$ non-zero elements out of $q^n$ elements in each row (column), by its definition.

We are only interested in the number of samples, and we have not considered how to implement $e^{i\bar{A}t}$.

Daniel Ranard Jan 30 2024 06:02 UTC

Cool! Do I understand correctly that $A$ is dense? Is there an efficient way to implement $e^{iAt}$ (or $e^{i\bar{A}t}$) used in the main step? I'm not an expert, but I ask because maybe someone else has the same question. (Also, perhaps you are not interested in the circuit complexity, but just th

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Shu Kanno Jan 10 2024 07:37 UTC

Congratulations on the publication of your paper on real device execution of periodic systems. I believe that your quantum algorithm for crystalline systems will be important for chemical applications.

By the way, I was a little wondering about the statement in the introduction that "So far, expe

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Ansis Rosmanis Jan 08 2024 07:53 UTC

Regarding the aforementioned follow-up research, I have now recorded and published a video on the subject.
https://youtu.be/kLWgero0a0w
As for the write-up, I hope to finish it in the couple of next months.

Ludovico Lami Jan 05 2024 16:16 UTC

This is a very nice paper, and I congratulate the authors on that. However, there seems to be a significant issue with the proof, and as of now we believe it to be significant enough to undermine the main result. Here I'll be relaying the discussion on Twitter (= X): https://x.com/marcotomamichel/st

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Seok-Hyung Lee Jan 03 2024 09:24 UTC

Thanks a lot!

Craig Gidney Jan 03 2024 06:04 UTC

For (1): yes, I generalized it to work beyond just the triangular lattice, by using tour dragging to lift the solution. It should be able to decode things like holes being braided. I wouldn't say it works for all color codes (e.g. it can't decode color code circuits that cycle between measuring X th

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Seok-Hyung Lee Dec 28 2023 01:55 UTC

Congratulations on your great work! May I ask two small questions?

1. The previous Möbius decoder in [SB22] was applicable only to triangular color codes with three boundaries. It seems that your decoder doesn't have this limitation. Is it correct? Is it applicable to arbitrary color code lattice

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Matteo Lostaglio Dec 18 2023 09:55 UTC

Thanks Pedro, thanks Ryan!

William J. Huggins Dec 15 2023 17:13 UTC

It sounds like this outperforms QSVT in some regimes? Are there other regimes where QSVT is the right choice?

I'd love to hear more about when I should choose to use each technique.

Ryan Babbush Dec 14 2023 15:09 UTC

Indeed, thanks for this discussion. We would not have written the paper posted last night without it.

Pedro C.S. Costa Dec 14 2023 05:06 UTC

Dear Matteo,

The numerical results that Ryan mentioned previously are disclosed now at https://arxiv.org/abs/2312.07690. Notice that we do not even consider the simulation of the randomized method in some discrete framework, like queries of the block-encoding. Thus, we expected an even worse comple

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Hanrui Wang Dec 09 2023 20:44 UTC

Hi Josu,

Thanks a lot for the pointers! We have updated the arxiv to include and discuss the papers you mentioned.

Junyu Liu Dec 08 2023 18:44 UTC

If correct, it is one of the best results I have seen in several years. :) Congrats!

Jahan Claes Dec 06 2023 16:13 UTC

"All cluster states are local-Clifford equivalent to a stabilizer state" Did you mean the reverse: all stabilizer states are local-Clifford equivalent to a cluster state? Cluster states are already stabilizer states; the more interesting fact is that (as your GHZ example illustrates) an arbitrary st

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Jingze Zhuang Nov 30 2023 11:17 UTC

Exciting!

Chae-Yeun Park Nov 29 2023 19:56 UTC

FYI, definitions 5 and 7 in the paper do not work properly with topologically ordered states.

Josu Etxezarreta Martinez Nov 29 2023 11:10 UTC

Very interesting article. I see that you are considering scenarios where the noise fluctuates. I add you a couple of articles where we construct time-varying noise models due to the fluctuations of coherence times in superconducting qubits:

- https://www.nature.com/articles/s41534-021-00448-5

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Wojciech Kryszak Nov 27 2023 20:28 UTC

A few comments:

1. Your conditions for any scientific theory (NCT) does not seem to be required in lewisian sense, i.e. when the theory in question is treated as a ,,best system'' encapsulating (perhaps compressing in some algorithmic sense) our perceptions. MWI can be such a (meta)theory.

2

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Craig Gidney Nov 27 2023 09:32 UTC

Ah, the distinction might be rotated vs unrotated surface code. I just assumed you were using rotated since it's more efficient.

Craig Gidney Nov 27 2023 08:07 UTC

The claim that Y basis measurement along an entire row or column is survivable is correct. But I think it's underselling it. I think the claim that measuring Y along an entire diagonal will break the logical qubit is actually wrong. You can measure every single data qubit except for one and have the

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Craig Gidney Nov 23 2023 02:27 UTC

> Table 1: it'd take 30 million years of supercomputer time to do d=9 surface codes

> Conclusion: it's feasible to apply this technique to d=9 surface codes

...What?

Francisco Silva Nov 21 2023 13:34 UTC

Checks out! I very much like how the paper is written, by the way :)

Craig Gidney Nov 21 2023 13:28 UTC

Misremembering the term would definitely explain why I wasn't able to find where I read about it.

Francisco Silva Nov 21 2023 13:12 UTC

Isn't the concept of boosting usually known as pumping? Or am I misunderstanding something?

You Zhou Nov 16 2023 06:01 UTC

Thanks for the reach out, and we enjoy reading your work with Prof. Dakic. Actually, we have cited it around Eq (16) (very nice formula). And we will also cite your work in Sec. V in the revised version.
In my opinion, it is very unfair to say “shows a strong degree of overlap”, and our work is dis

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John Nov 14 2023 10:18 UTC

Very similar to the recent publication Phys. Rev. Lett. 131, 083601 (2023)

Joschka Roffe Nov 07 2023 14:57 UTC

Thank you! Yes, in Proposition V.2 we explain how the spacetime graph for the overlapping window decoder can be constructed by taking the hypergraph product of the QLDPC code with a repetition code. Our understanding is that your result from Ref. [93] implies that all circuits constructed using this

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Jahan Claes Nov 03 2023 17:56 UTC

Enjoyed looking through this paper! I had a basic question about 3D surface codes, as they relate to my work on distance-preserving stabilizer circuits. You write "recent work suggests that the ordering of operations in the syndrome extraction circuit does not affect the
effective distance of the c

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Joshua Morris Nov 03 2023 13:12 UTC

Hello, I believe this result shows a strong degree of overlap with [a previous work][1] of my group, particularly the estimation of off diagonal elements (one of the main results given in the latter half of the paper).

Best,
Joshua Morris

[1]: https://arxiv.org/abs/1909.05880

Ansis Rosmanis Oct 23 2023 08:07 UTC

In a follow-up research, I found out that even if just a single known qubit of query registers is affected by the depolarizing noise of rate p, quantum search among n elements cannot be done any faster than in O(np) queries. This holds both when the affected qubit is one of the log(n) index qubits a

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Guanyu Zhu Oct 12 2023 22:26 UTC

I see. Thanks for mentioning this point and your paper to us!

Craig Gidney Oct 12 2023 17:59 UTC

This isn't really core to the paper or anything, but the CX*H*CX*H circuit in fig 16 can be optimized into CX*H*CX*Z because Z has the same action as H on the |Y> state ( as in https://arxiv.org/abs/1708.00054 ). Z is cheaper than H because it can be done in the classical tracking instead of on the

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Terry Bollinger Oct 12 2023 10:52 UTC

This is a well presented, innovative algorithm.

Jon Allcock Oct 12 2023 04:12 UTC

Agreed - really informative and well organized. A maintained version of this would be a very welcome resource for the community

Tongyin Lin Oct 09 2023 10:59 UTC

A really impressive work. It would be better if this is uploaded to a website so that the information can be updated.

Francesco Anna Mele Oct 03 2023 07:15 UTC

Thank you very much, Eric! Our model (depicted in Fig.2c) is defined by coupling Alice's input signals to environmental systems through unitary interactions. Consequently, this model is consistent with quantum mechanics and, in particular, it does not violate the quantum no-cloning theorem. Once inf

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Eric Aspling Oct 02 2023 11:03 UTC

Hi Francesco, this is excellent work! I'm always excited to see more ways to carry out QI transport. I have one conceptual question that may be answered in your paper in a way I did not fully understand. By thermal noise, one usually means phonon interactions. If a photon's QI is lost to the system

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Markus Heinrich Sep 28 2023 07:20 UTC

Very interesting paper and good comment by Jason. I agree that such insights should be clearly written up and simple to find in the literature!

I want to add that the fact that the Pauli group is not complemented within the Clifford group (i.e. there's no group $G$ in Jason's comment) is known from

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Jason Saied Sep 27 2023 21:15 UTC

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

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