Recent comments from SciRate

Thank you very much for these detailed and helpful comments. We will carefully consider them and make the corresponding clarifications and updates in the next version.

Congratulations on this very nice review! It is glad to see that many of our works are introduced in this paper :) I would like to kindly point out some improper statements in the review, especially in the sections of quantum learning and randomized measurements. I hope these can be helpful to impro

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Thanks for the clarification.

Good to see that all reported performances are based on the same hardware architecture and parameters. I usually interpret "Real-Time Decoding" as one where the latency is guaranteed (as in the case of classical communication for example); so the worst case latency

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Hi, thanks for your comment.

The value 400 represents the maximum number of decoding iterations and is rarely reached (with probability less than the logical error rate). Our decoder uses an early-stopping criterion: at each iteration, it computes the syndrome of the estimated error and stops whe

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Nice to see hardware implementations with fine details on performance and latency.

In Fig.1 you show that for the $[[144,12,12]]$ code you get logical error rate of ~6e-9 at physical error of 0.001 (GARI decoder); but that's with 400 iterations. The FPGA implementations seems to be using 10 itera

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Happy to hear about careful reading of the technical parts! Indeed, you're right about this. Actually this is a surprisingly meaningful correction, since it implies the number of resource states for distillation is $o(N)$, even if it's not poly-log in the address size.

Great job, finally we have a proof!

Hi! Nice work. What do you think on the resource estimates for entanglement and real hardware performance donated to our work https://scirate.com/arxiv/2408.02837?

**Update**: The [ldpc-post-selection repo](https://github.com/seokhyung-lee/ldpc-post-selection) has been made public. Feel free to leave any issues, comments, or pull requests!

Maybe you can call it "fast mixing"

Thanks for the feedback, we will try to clarify the terminology in an update to avoid confusion across fields:)

Thanks, makes sense! Maybe some other phrase then like “quite rapid mixing”? :-) Since thermalization also has a technical definition, the title could be misleading to a different community.

Hi Vedika, Thanks for the clarification! As you said, we are indeed focusing only on "mixing" in the open system/Markov chain setting. We also fully agree that our result does not apply to closed-system thermalization in the context of MBL. Perhaps a technical reason we did not explicitly say "rapid

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“Thermalization” is a distinct concept from Gibbs state preparation / mixing. Thermalization refers to the ability of a system to bring its subsystems to thermal equilibrium under its own unitary dynamics. Rapid mixing is about the ability to prepare Gibbs states when the system is coupled to a bath

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We adopted the naming convention used in Jones and Montanaro's but I also found it initially confusing because "bipartite product testing" actually refers to this more general question about testing states on $(\mathbb{C}^{d})^{\otimes n}$. That said, we couldn't think of a better name, so we just d

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We are thinking about how to approach this best. Completeness will be a secondary goal, and an interesting starting point would be to try extending fault gadgets to non Pauli noise / generalising Pauli Boxes. After this an extension to full non-Clifford diagrams might be easier. Considering universa

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Thank you Jacob! I now understand that the difference between our results is that you are considering the case where the bipartition is unknwon, while we were considering that the bipartition is known. Sorry for the misunderstanding. It is amazing that the lower bound results we derived are the same

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Thanks for your interest in the paper! The resolution is that each component of the circuit is considered to be noisy and Clifford. This means that you can not perform syndrome measurements throughout the circuit and store the results in noiseless classical memory to be post-processed at the end. In

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Hey Zhenhuan, thank you very much for your comment. I am so sorry I overlooked your prior work. I just took a look at the first paper and, indeed, your lower bound in Theorem 2 is quite similar to our Theorem 1. However, unless I am misunderstanding your work, you were considering the case of testin

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Nice title ;) (prepare for weird emails though)

I believe that most simulations of Clifford error correction circuits so far involve offline syndrome decoding.

Their model doesn't include fast classical processing of the syndromes.

Thanks for your response! Would running a truly non-Clifford simulation (or its proxies) lead to any additional surprises?

Are there any plans to extend this framework to include non-Clifford ZX diagrams?

Fascinating results! I’m curious how this compares to, or perhaps even contradicts, the numerous studies on Clifford error correction circuits, especially those numerically simulated to very low logical error rates, some even down to $p_{\text{logical}} = 10^{-9}$. What's the catch there? Am I missi

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Very interesting work!

I hope this comment is helpful—I would like to kindly point out that in our previous study on the complexity of entanglement detection (**Phys. Rev. Research 7, 033121 (2025), Theorem 2, D2**), we explored a closely related problem, and the results seem to align with **your

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Hi Allan,

Thanks for reaching out, and for bringing your work to our attention.

Regarding how our methods compare, the key difference is our use of a qDRIFT-style randomization combined with extrapolation. This combination is what allows us to achieve short circuit depths, eliminating the need for

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Thanks for pointing it out! we will update it ASAP.

Congratulations on the nice paper. Your approach to randomization that allows forgoing the use of a block encoding is particularly interesting. I want to bring to your attention our paper "[Randomized semi-quantum matrix processing][1]" where we randomize the QSVT protocol by sampling from the distr

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It seems that the discussion section is incomplete - the last sentence "This is consistent with o" suddenly ends. Perhaps some sentences were omitted?

thank you!

Thank you for the helpful feedback! In our setup, the magic states are transferred from the small color codes into the BB code, and our simulations focus on this transfer process, which is significantly noisier than the initial states. Rather than simulating directly from magic states, we perform Cl

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Something that I found in [my own work][1] on the Floquet code (your ref 15) that was not obvious to me: If you do $d$ rounds of $(XX\rightarrow YY\rightarrow ZZ)$ measurements on the original Hastings-Haah code, you end up with a timelike distance of $3d/4$ rather than $d$. This is because, e.g., t

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Are your stim circuits open source? Appreciate it.

Interesting work! I had a question—it's not entirely clear to me what exactly is being simulated. From the appendices, it seems like the simulation involves a Clifford surrogate for logical performance rather than a full implementation of a non-Clifford scheme or a direct replacement of T gates with

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Banger, very interesting work!

Note: The [ldpc-post-selection repo](https://github.com/seokhyung-lee/ldpc-post-selection), which implements our soft-output decoder and post-selection strategies, will be made public in a few days.

I was worried about the interface between the lattice surgery round and the memory rounds before/after it, akin to how surface code lattice surgery needs d rounds before & during & after the surgery for fault tolerance. But in this case the memory is also single shot so it seems there could be no pr

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thanks a lot!

I'm not entirely sure I understand your question. The point of the fast surgery is to reduce the number of rounds of measurements from `d` to `1` fault tolerantly. Which is why we simulate a single round for that protocol and the curve shows that indeed the logical error rate remains

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hahaha

Your (and Craig's) argument mainly appears to rest on the premise that "sampling small parts of the output is equivalent to sampling a uniformly randomly generated number.'" However, if the initial target state is not $\langle 1 |$ and is perturbed, the initial state effectively becomes a non-unifor

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Congrats on these nice results!
I was surprised to see that "fast 1 round" curve was below the "standard 3 rounds" curve, but then read that "For the fast scheme we simulate only a single round." Wouldn't simulating only a single round be unable to check the fault tolerance of the protocol?

I stand by what I already wrote above, and I therefore see no reason to continue to spend time on this thread. Based on what I already wrote above and the arguments presented, I see no reason for why the algorithm would scale efficiently. I note that Craig also wrote that he ["thinks it's wrong"](h

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It seems that to acheive a lower number of T gates, a larger number of ancillae are needed. 

Your conclusion that the manuscript updates constitute an “acknowledgment” of your claims is unconvincing. The preprint v2 already stated:
"Although not presented here, we also considered factorization of larger integers (using $m_{\max} < n$) and found that our proposed modular approach works succ

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I just became aware of a significant overlap with arXiv:2403.14416
An updated version with proper references to related results will be posted soon.

Hi Tom, sorry for the late response. Yes, Nouédyn is right: As it stands, this paper is purely a bound on classical codes. With that said, it does capture certain types of unitary quantum logical gates.

It breaks down when generalizing to CZ and CCZ and the paper you linked to is a counter exampl

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banger

No, my claim has not been refuted. You can see that it holds by analyzing the quantum algorithm mathematically, or by simulating it.

1. I note that after I first commented that one cannot pick the $m_i$ very small (for instance, fix them to $3$ or $4$, see also [this comment](https://www.reddit.com

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Very useful feedback, and we'll add a mention to that paper, tysm :)