Recent comments from SciRate

A nice progress! It seems that the instance generation is really a bottleneck of the peaked circuits protocol. Using postselection, the success probability is exponentially small. Using the variational search, computing the loss function reduces to computing the zero-to-zero amplitude of a quantum c

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A welcome result!

Great, that does clear a few things up. I’m somewhat on board now.

Great, look forward to reading that.

Thanks! No, we purely focused on the decoding problem here without much regard for the associated dual optimization problem.

Hi, thanks for your interest in our paper and your question. The pseudo-thresholds for independent errors and erasures for the 72 qubit code are lower than the other codes presented. It also has logical error rate scaling suggestive of a lower distance code in the sub-threshold regime as expected. I

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Hi KdV,

To again relay a message for William Zhong.

"I've updated the paper with additional notes on the double-checking circuit in the appendix, and also rescaled the error parameter in all of our numerics to allow for better comparison with the original cultivation paper. Unfortunately,

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I wrote that one *basically* needs $m_i > \log_2 r$ above, and I then described that there are some caveats. In particular if the order is even. I have not thought it through in complete detail, but right off the bat it should always hold that you need $m_i > \log_2 r'$ for constructive interference

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@Martin: I was able to factor 161 using a maximum block size of 6 for a=3. Since the order here is r=66, your claim that each block size $m_i $ must be larger than $\log_2 r$ does not appear to hold. It seems the effect of the shift in the unitary for all blocks beyond the first was not accounte

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This is great progress on BPQM! Did you consider the difficulty of the optimization problem dual to decoding turbo codes?

> a common drawback for concatenated codes is their syndrome check weight,
which can grow exponentially with the number of layers `L`

Is this still a drawback in the wake of [blocklet concatentation][1] which claim to only rely on the syndrome measurements of the base code?

[1]: https://s

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Very interesting. We also worked with a single-shot inference QML model in our paper https://arxiv.org/pdf/2501.02148 and found it to be pretty effective (see discussion at top of page 4)!

Very cool result! This is exactly the sort of idea that seems promising for getting DQI around some of the challenges associated with speedups in unstructured settings.

Any updates on Oscar Higgott's comment from 26 days ago?

Thanks! We're working on optimising the code and will share it.

Congratulations on this very wonderful paper! I would like to ask whether there is a GitHub repo or any code available for this paper ?

Sorry, do you mean you want references about the importance of free energy for thermalization? Or did I misunderstand your question?

The stability of ordered phases at finite temperature is controlled by the free energy, which captures the competition between the energy and entropy of excitations

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Thanks a lot for the feedback! I'd be more than happy to correct that and add references to previous works on the topic, if there are some you'd recommend?

The author has made a significant update of the manuscript in V3: https://arxiv.org/pdf/2501.19375. One major update is the new Section VI discussing how to map the high-dimensional manifold back to a CW complex via deformation retraction, which gives rise to a non-topological code defined on a hid

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Can you comment on why the [[72, 12, 6]] code yields the largest area in the last plot of your [python notebook][1], when considering psuedo-threholds?

[1]: https://github.com/susanxschen/qldpc-fusion-lattices/blob/main/Phenomenological%20noise%20simulations/Get%20BB%20lattice%20error%20rate

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Did you catch the discussion by Gidney, VicQ, Pattinson, and squiggles on quantum computing stackexchange, which highlights the substantial overestimation of stabilizer decomposition costs? Your work appears to significantly surpass the numbers discussed [there][1]. Gidney appears to deprioritize ex

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Very nice work!

A quick semantic comment: it is a bit odd to say in the abstract that you "introduce the more general notion of a free energy barrier, whose absence is also demonstrated to guarantee fast thermalisation". The concept of a free-energy barrier, and its connection to slow dynamics has

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Wonderful, I look forward to reading it.

Hi KdV,

I have uploaded a new version of the manuscript, addressing your main concerns.

Please refer to arXiv version 2 for additional simulations and strategies to further reduce runtime, for example using Pauli webs.

Best,
Zhenghao

A few points related to the above:

1. When I briefly reviewed this pre-print as it appeared on the ArXiv I interpreted the authors to say that they perform a number of independent runs, and that the length of the control register (before reycling) is $m_i$ qubits in the $i$:th run.

If so, Crai

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Hi Noah,

Sorry for the late reply, I've been traveling.

For QAOA and AMP we can prove explicit bounds for any $k$ and $\lambda$ someone gives us. [This has actually already been done for depth-1 QAOA][1], all we do that builds on this is pick some explicit choice of parameters and look at the scal

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Each block’s measurement is not just a random sample, it is an estimate of a specific segment of a true eigenphase. While it’s true that Shor’s algorithm can involve as many as 2^{2048} eigenphases (“colors”), there is no need to see the same color twice. Because two different colors can still share

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And does it continue to work when there are 2^2048 colors, instead of 2 colors? Because when there are 2^2048 colors, you'll de-facto never see the same color twice.

Dear Namit,

Thank you for the quick review of our preprint. We appreciate your feedback and hope our reply will address any misunderstandings or shortcomings in our work.

‘Utility’ is usually defined as a demonstration of the ability to solve problems at a scale beyond brute force classica

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Are you able to prove any explicit bounds for finite k?
Eg, for the (3,6) Gallager ensemble, what is the maximum achievable satisfaction fraction of DQI, AMP, QAOA?

Do you have any results on stability when the value of \ell is beyond half the minimum distance?

Also, have you considered bound

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@Craig Gidney - It seems we agree that the authors’ method works when the given state is an eigenstate. The authors then extend their method to the case of a superposition of two eigenstates in https://arxiv.org/abs/2508.05805
and use it for modular amplitude estimation. That part looks correct to

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Really nice work!!

I think this would be a great tool to have in the community. Do you have any plans to release a public version of your software?

@Q_cat_1729 It looks their proof only considers the case where the given state is an eigenstate of the operator, which isn't true in Shor's algorithm. When the state isn't an eigenstate, step 13 of algorithm 1 will fail to converge.

Thank you very much for the answer and the references. I was not aware of those works.

Cheers,

Raf

@Craig Gidney - You may want to check out this paper https://arxiv.org/abs/2507.22460 where the authors provided a method for performing phase estimation with fewer qubits. The paper contains the mathematical proof and the quantum circuits for verification. They have used the same ideas in the Shor'

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- Am I missing something or there is no "quantum utility" in this work? In which case, the authors should consider changing the title?
- More generally, a *constant-depth* simulation of the 1D Fermi-Hubbard
is unlikely to yield any serious utility (happy to debate that).
- Regarding MPS sim

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Great paper, very thorough Trotter analysis

In short, (exact) Majorana zero modes may not exist in number-conserving systems, but the universal properties (e.g. braiding statistics) of the topological phase predicted by Bogoliubov MFT still has a chance to be exactly correct at long distance.

Thanks! Yes, that's correct. Your second question is highly nontrivial and the quantum complexity theory community is still working on answering that. A closely related question is when can shallow quantum neural networks (which is always quantumly easy) produce distributions that are classically ha

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Hi Matthew, thanks for this! Definitely a typo, will acknowledge and correct it in the next version. Please also check the short follow up to this @ https://scirate.com/arxiv/2509.08658 . Cheers!

Very nice paper! However, I noticed in table 1 / footnote 9, it suggests 7^{53/6} ~= 29,176, though this seems to be a mistake in its order of magnitude and should be 29,176,466?

Dear authors,

I fully agree with you about the seriousness of this number-conservation issue--indeed, I questioned this point very seriously during my PhD, and only left this field because most physicists do not seem to care about this. Now I'm glad to see that you bring up this issue once again. 

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@craig-gidney What is your take?

Cool results! The trick in the Instantaneously-deep quantum neural networks is basically keeping the depth constant by paying a polynomial increase in the number of ancillary qubits, right?

What kind of properties does a classical distribution need to have in order to be classically hard but easy

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To clarify there are two "Yifan Zhang" at Princeton ECE. One also goes by Frank. This paper is written by Yifan Zhang not Frank Zhang

Hi KdV and Tuomas,

I am relaying this message again on behalf of Zhenghao. Thanks. Personally, I am happy that this short note is receiving some attention on scirate.

We don’t think the number of terms will go up, but we don’t have any solid evidence right now. One argument is: you can contract th

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I understand that you just add a phase-less single leg spider for post-selected measurements. However, in an end-to-end simulation, a measurement outcome can return a -1 value and would still be considered an acceptable shot if the specific detecting region/check/"closed" pauli web (defined in Boldi

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Thank you, Enrico!

We were in touch with the authors of the first paper you mention. They use quantum relative entropy as the loss function to obtain a good optimization landscape. To run their algorithm, one needs to be able to prepare Gibbs state for all the Hamiltonians traversed along the train

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Still reading the paper and it has some very interesting constructions.

I wonder if this paper https://www.nature.com/articles/s42005-024-01763-x should also be considered in the category of _generative quantum advantage_. It seems to fit "generative quantum models that are hard to simulate clas

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