Recent comments from SciRate

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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Ah yes, we're slightly abusing notation there. If a basis of chains is chosen (in this case simplices) then one can define a basis of dual cochains for each simplex which is a kronecker delta on that simplex.
So Eq.3 means that the cup product of the function that is only non-zero on [ab] and the fu

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Ahh, I see. Thanks. A quick follow-up question then. In the next subsection the cup product is defined in terms of a product of R-valued functions on arrays, but in example 2.1 it seems to act directly on the arrays themselves. How should I understand the functions and the ring in this case? Is ther

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f acts on p things, while δf acts on p+1 things, so it is correct. We're defining the coboundary in terms of its action on chains. We're not mapping a function acting on p+1 things to something that acts on p things.

A very minor question where I'm probably missing something basic, but it seems like the coboundary operator at the top of page 8 is mapping a function on a length p+1 array to a linear combination of functions on length p arrays. Wouldn't this make it a boundary operator rather than a coboundary one

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Just FYI, if you've got a BSM that works >66% of the time, you can do fault-tolerant quantum computation with *unencoded* 6-ring resource states, which are a lot more feasible to generate, see https://arxiv.org/abs/2301.00019.

There's also some subsequent discussion of this construction (and a few

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Congratulations to the authors on a very nice result!

I'll also use this as an opportunity to note that, following discussions with the authors of this work, my coauthors and I have updated our related work (arxiv.org/abs/2408.13130) and modified our claims r.e. achieving $\gamma \rightarrow 0$

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We have updated this paper to v2, with the title "Improved QLDPC Surgery: Logical Measurements and Bridging Codes". The abstract, introduction, and some technical components are augmented.

Looks like the pdf links aren't working on arXiv today.

You can see the pdf by adding a v1 at the end - for instance: https://arxiv.org/pdf/2409.18175v1

Aram is correct: we roughly prove that if you can show a slower than 1/n^2 lower bound to the gap, you can bootstrap it to a constant bound. But if the gap closes faster than you don't get any improvement.

The gap can vanish faster than 1/n^2. Their theorem just says it can’t vanish more slowly. See eq 8.

Nice result! I am wondering how to reconcile this result with this example of the 'area weighted Motzkin chains' https://arxiv.org/abs/1611.03147 where the model is frustration free, the Hamiltonian is a sum of projectors, and has short range interactions everywhere (even at the boundaries where the

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Thanks for the interesting paper!

I would like to ask whether the condition in Theorem 6 should be $PE_i^{\dagger}E_jP=\alpha_{ij}P$?

Thanks for your reply and for your comment.

Indeed it is true that the mentioned papers do not use the phrase "superchannel", which could lead to one missing these references. They instead use the phrase "bipartite operation", which is a less fitting term.