Recent comments from SciRate

Hi Simon, thanks for the comment! This is noted in footnote [2] ("More precisely,...") , but perhaps it would help avoid confusion if we moved it to the main text.

S_6 is isomorphic to Sp(4,F_2) which is not the Clifford group on two qubits, only a quotient thereof.

Hey! Thanks for engaging!

Let me jump in on the fun.

In terms of Chae-Yeun's point 1 and Alex's point. I fully agree that "in a sense" is doing a lot of work but the aim of *that* paragraph was in a large part to point out the positive side of being able to often classically simulate/surroga

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Yay, I also want to join to the party and drop my opinions :D

Re-Re point one: My general feel is that we as a community should aim at being as transparent as possible. In the present case, we should do our best to not -- not even unintentionally -- sweep implicit assumptions under the carpet. C

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Hi Andrea, thank you very much for your message. We will acknowledge this work in the next version of the manuscript.

I would like to mention that ZNE on logical qubits was theoretically and numerically studied in this work: [https://arxiv.org/abs/2304.14985][1]

Having said that, it's great to see a real experiment! It shows that error mitigation will continue to help beyond NISQ.

[1]: https://arxiv.org/abs/2

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There's a nice paper addressing your first point on warm-starting [here][1], see, e.g., around Eq. (12); the authors show in a certain setting that where one has provable guarantees on good gradients in a warm-started region, you also can construct a classical surrogate model in that region.

For

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Thank you for sharing your nice perspective.

Here are some of my comments on Myth 4:

1. "While there have been a number of approaches that have been proposed to avoid barren plateaus, it has recently been argued that in all those standard cases (that can be proven to avoid them) the resulting

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Thanks a lot for the comment, Ruslan. We will update Table I. (As for the citation, I will have a look at this paper, and get back to you by email.)

I believe there is a typo in Table I. As of June 2024, Quantinuum H2 has 56 qubits (https://www.quantinuum.com/press-releases/quantinuum-launches-industry-first-trapped-ion-56-qubit-quantum-computer-that-challenges-the-worlds-best-supercomputers), not 30 as stated in the table.

Additionally, it m

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Thanks for spotting this, @Joe Gibbs. We will fix this typo in the updated version of the manuscript.

I believe there is a typo in the line under Myth 2: 'circuits of size $\mathcal{O}(\epsilon)$ can be executed without prohibitive overhead', this should be $\mathcal{O}(1/\epsilon)$ ?

Steve Flammia gave [a talk at QIP2024](https://www.youtube.com/watch?v=cUSV0unYHw4) that may be a gentler introduction than the paper, which is a big slab of very mathy math.

Dear Dominik and Gergely,

thank you very much for your highly interesting arXiv:2412.15912 on the relationship of stabilizer Rényi entropy (SRE) and T-doped Clifford circuits.

Here, I would like to point out our recent https://arxiv.org/abs/2406.04190:

- We show analytically that each T-gat

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This is basically using unary, right? I think the abstract should advertise a little more clearly that the energy cost is O(N).

Hi,

Yes, as you say, all these factors (circuit noise model, shuttling noise, etc) will further reduce the performance of the protocol over what is shown in the numerics. For these reasons we do not intend for the numerical performance values presented here to be taken as actual estimates of rea

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Hi Tom,

Thanks for the answer! I know it is difficult to estimate without the data, it was just to see if you had some intuition behind. For the conclusions I meant the bit where you discuss the overhead for $P_{ccz}=10^{−7}$, since the extra overhead required for the CLN case may inply that the co

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Hi,

Thanks for your interest. To answer points 1 and 2, it is difficult to estimate exactly how much of an effect a circuit noise model would have on the logical error rates for the JIT decoder due to the lack of data on this, and I wouldn't feel confident making any kind of guess. The decoder do

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Dear Authors,

This is a very interesting approach. However, I have a couple of questions regrding it:

- As far I see, the analysis for the new approach is done considering a phenomenological noise model. While you acknowledge that considering a circuit-level noise model will lead to requiring

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I have updated this paper to v2. The decoder is now much more accurate (25% more than Union–Find over the tested regime) and faster than before, due to a small modification I call the '2:1 schedule'.

Weyl fermions by definition cannot exist in 2 dimensions. Dirac fermions can, and those have long been observed (graphene).

I believe that such a Pauli correction always exists. This is reflected in Remark 3 of [arXiv:1910.09333][1]. My intuition is that one can find a basis for the $Z$-type stabilizers as $O_1, O_2, \ldots, O_r$ such that there exist (using a linear algebra argument on symplectic spaces) Pauli operators

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Thanks for the clarification! I agree that the result is unaffected by Pauli corrections.

However, my concern also has a more general aspect to it, namely, is it always possible to find a character vector (or equivalently, Pauli corrections) that satisfies the sign condition and make the quantum C

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Hi Shubham,

Thank you for your comment. Your observation is indeed relevant, and an X-type Pauli correction must be applied to map to the correct code space. However, in this case, the Pauli correction does not affect our final result. Specifically, in the example you mentioned above, the corresp

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Dear Markus,

Thank you for your answer, it really helps a lot!

As for the self-refuting mode of reasoning: yes, it is a much more general problem, and the accusal is perhaps a century old. "Nine to five" it is wise to make science as usual and leave such troubles for the evening, with hopes fo

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This is impressive work.

However, for a fair comparison against pytket you should have implemented the block encoding with the ripple carry adders aswell.

Also, your block encoding in pytket using the controlled QFT adder is sub-optimal because you do not exploit the conjugation structure in the Q

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Dear authors,

Great results!
Maybe I am missing something but I think equation (7) does not hold for all even CSS-T codes. For example: the $[[6,2,2]]$ CSS-T code mentioned in [arxiv:1910.09333][1] is an even CSS-T code by your definition but there doesn't exist any logical OP corresponding to $ T

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Hi Tom,

Thank you for your question. Yes, your interpretation is completely correct indeed. It may be true that the wording there may be a bit ambiguous, with the reason being that we are using the CSS-T code terminology, i.e. those codes are in general defined as codes whose codespace is preserv

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Dear Wojciech,

thank you so much for your thoughts and comments. Let me try to answer step by step.

First for something brief: in your item 1., you say that algorithmic idealism might be self-refuting for the following reason:
“if my cognitive abilities depend on my x that stems from some b

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Am I correct in understanding that the logical action of a transversal non-Clifford operation on a code produced by your construction will always be a logical Clifford/Pauli/identity and never a logical non-Clifford? I.e. when you say

> we establish the existence of asymptotically good CSS codes

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Dear Markus,

The more provocative, athwart my intuitions and mentally demanding your idea is, the more I sympathize with your efforts and the general program. Especially having realised that your Postulate 2 is a far kind of the forementioned "totalitarian principle" by Adan Cabello, but much mor

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Hi! This is just a comment.

In the work (https://scirate.com/arxiv/1908.01020), the authors consider query algorithms with "abort" and show a version of Yao's minimax theorem within that framework. This may be related to your work.

Hope this may help in anyway.

Dear Kryszak,

thank you for your reply and your continued interest. You have been mentioning very many different things in your post. Let me just give three brief comments.

(1) You wrote you "cannot feel how inverse Solomonoff induction... can save the appearance". Note that this only applies to

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Interesting work! But I am concerned about the density operator you assume: in Sec. IV, you seem to assume the one-photon density operator and there's only one photon, whereas in all practical problems, one can receive many photons in many temporal modes. The correct density operator to assume is th

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Dear Markus,

Thank you so much for your reply!
So glad am I! - glad, that my problems with grasping your idea not uncommon, and my articulation of them can be perhaps helpful.

To be honest, I still can not tell that I can feel how the "inverse Solomonoff induction" reasoning can "save the app

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Dear Wojciech,

thank you for your interest! Note that ${\mathbf P}_{\rm 1st}$ does not represent what you believe, but what you *should* believe. It is not your expectation, but a notion of objective chance of what will happen to you. I explain this in some detail on page 10.

According to Post

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Dear Markus!

Wait, but why $ P_{1st}(y|x) = M(b|x) $ ? (page 15.)

I guess that by P1st you would like to have my 1st-person expectations (i.e. you would like to interpret this formal object P1st as sth that represents my expectations), am I right?

If I am not plainly wrong here, then it se

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Hi Yufan, yes, I think that is fair to say. We show that if couplings between the flux qubits are weak (they can be inductive and/or capacitive) one can do a canonical transformation, before truncating the state space to qubits, which results in a TIM (of course we don't focus on full rigor and appr

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Hi Barbara, thank you for pointing out the reference! I have a question: can I safely say weakly-coupled flux-qubit Hamiltonians are “StoqMA-complete” in some sense? This is because inductively coupled ones can implement arbitrary TIM and weakly coupled ones can be reduced to TIM based on the result

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Hi authors, congrats with your results! Perhaps you find the physically-motivated (using descriptions of superconducting qubits) discussions on stoquasticity in https://arxiv.org/pdf/2011.01109 of some interest.

Nice work! I'm curious about how this approach would perform for multi-qubit gates other than CNOT, such as SSPC gates, which can implement two-body parity check circuits in a single step (https://iopscience.iop.org/article/10.1088/2058-9565/ad473c/meta). Is your approach suitable for n-qubit unitar

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Hey Felix,

Thanks for the message! I got an email from Carlos a few days ago telling us about his paper. We'll be sure to credit this paper (and apparently several follow up works) in our next version.

Want to make sure I understand the statement of Conjecture 3.2:

It seems that for the conjecture to be true, $\zeta(N)$ must be negl($\log N$). For the setting of T={1}, we have that the substitution distance for $i = 1$ is $\zeta(N)/2$ which we need to be negl($\log N$).

Given this constrai

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Dear authors, the inequality in Lemma 18, that is the generalized uncertainty relation $\sum_i \mathrm{tr}(A_i \rho)^2 \leq \vartheta(G)$, was already shown by de Gois et al. in "Uncertainty relations from graph theory", Phys. Rev. A 107, 062211 (2023), arXiv:2207.02197.

Great work! Your successful implementation of VQE-SA-CASSCF on a superconducting quantum processor to study conical intersections is impressive. In our earlier paper, we also combined VQE and SA-CASSCF to calculate conical intersections using real quantum hardware. It would be interesting to compare

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Great work! Your application of CQE and VQD to compute near-degenerate states at conical intersections is impressive. We also worked on conical intersections on real devices as follows. I hope you are interested in it.

https://www.nature.com/articles/s41524-023-00965-1

Thanks Nat! Yeah, I totally understand your points. You did mention our paper implicitly contains this circuit, so I'm just mentioning that in the updated version it's now explicit.

Thanks Guanyu!

- The most interesting result in our paper is to develop a cup product formalism for general chain complexes (beyond simplicial complexes on manifolds), which we do in Secs. 3 and 5.
- This allows us to expand to more interesting codes, such as hypergraph product or balanced

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Ok, that makes sense. Thanks a lot.

Congrats on the interesting paper and glad to see that more people in the QEC community start using cup products! Just a note: a "copy-cup gate" was also explicitly presented in Sec. III of the recently updated version of our previous paper upon referee's request: https://arxiv.org/pdf/2310.16982

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