...(continued)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
...(continued)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
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
...(continued)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
...(continued)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
...(continued)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
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.
...(continued)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
...(continued)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
...(continued)@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
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
...(continued)@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'
...(continued)- 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
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.
...(continued)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
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?
...(continued)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.
@craig-gidney What is your take?
...(continued)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
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
...(continued)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
...(continued)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
...(continued)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
...(continued)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
...(continued)Post-selecting in ZX-diagrams is easy: you can add a single-leg spider (with no phase) to the qubit you are post-selecting (in the usual formalism this is like multiplying by $I \otimes \langle 0|$ or $I \otimes \langle +|$). So this doesn't add any extra terms. Sampling the measurement outcomes wou
Nice work! Could you please check if your repository has public viewing access https://github.com/franz3105/GPVQuEst. Thanks
...(continued)Hi, re: PySCF, the docstring for the selected CI module clearly states:
"This is an inefficient dialect of Selected CI using the same structure as determinant based FCI algorithm. For [an] efficient Selected CI program, [the] Dice program (https://github.com/sanshar/Dice.git) is a good candidate.
...(continued)Hi Chignons and Kristel,
I’d like to share a recent work of mine that’s closely related to yours: [Near-Optimal Parameter Tuning of Level-1 QAOA for Ising Models][1]. We show how to efficiently obtain provably optimal parameters for QAOA at $p = 1$ in linear time, without making any assumptions a
Love the title! :D
...(continued)Dear all,
Let me add a few points here.
Firstly, nice work Tim and I really appreciate the retraction of the evidence claim upon re-doing the comparison with proper HCI.Despite the upset our work (arXiv:2501.07231) of pointing out flaws in QSCI might have caused some, to date no real solu
...(continued)Dear Michal Krompiec,
Thank you for your comment.
We actually released a revision to the preprint on 10th September, in which we addressed all of the points you raise here. For example, we included HCI results generated with PyCI and found that while, yes, HCI produces the most compact wavef
...(continued)We've made a significant update for this paper. The new discovery is the transversal CCZ gates on the 5D non-Abelian self-correcting memory using a more general type of cohomology operation (classified in https://arxiv.org/abs/2411.15848) involving the higher cup product, which is able to break th
...(continued)It is surprising to see that QSCI (aka SQD) is compared (just like in the Robledo-Moreno paper) to SCI in PySCF, rather than only to the implementation of HCI in PyCI, or to HCI as implemented in the reference codes Arrow and Dice. In other words, beating PySCF's SCI does not invalidate Reinholdt's
Thanks for the comments! LCHS addresses non-unitary dynamics, and our work focuses on unitary dynamics.
...(continued)It seems that your approach relies on post-selecting the (+1) measurement outcomes. How would you simulate the post-selection or measurement process within the ZX-calculus framework? Presumably, you'd need to introduce errors into the ZX graph, then contract the graph up to the measurement nodes and
...(continued)Thank you, Joseph and Konstantinos, for sharing your really nice works! We will include them in our next paper update.
I also want to mention that our previous theory work https://arxiv.org/abs/2401.10095 has proven that all shallow quantum ML models are efficiently learnable, and are known in co
...(continued)Thanks for reading. Replying on behalf of Zhenghao.
This error model was picked over the circuit-level one, like Boldizsár Poór mentioned: "something like a ZX diagram, where there is no fixed direction of time, this noise model seems like a natural choice". We agree with this.
Operationally, it's
...(continued)Awesome work! Really nice.
I would like to bring to your attention our QNLP paper from our Oxford team [ https://arxiv.org/abs/2409.08777 ]. Of course, the learning tasks, the motivations, and the methods are different. But I claim that the Strategy for bypassing trainability issues is the same: tr
Hi guys, nice work!
In case you missed it, we also developed a method to classically train a class of quantum generative models with hardness guarantees (IQP circuits), and managed to train circuits with up to 1000 qubits.
https://arxiv.org/abs/2503.02934
...(continued)I think the $|W\rangle$ and $|CCZ\rangle$ are in different SLOCC classes, no local operations + CC can convert one to another. It would have to some non-local operations, maybe you can play with H-boxes ($|CCZ\rangle$) and the $|W\rangle$ written as a ZX-diagram, equation 7 from https://arxiv.org/ab
...(continued)Just jumping in to say that in https://arxiv.org/pdf/2506.17181 we studied this exact error model. For something like a ZX diagram, where there is no fixed direction of time, this noise model seems like a natural choice.
Regarding its relation to circuit-level noise, if you use the standard mappi
...(continued)Congrats on the results! Do you know how your noise model in Section 5 compares to standard circuit-level noise?
It seems to omit some $O(p)$ errors after two-qubit gates. On the flip side, as you explain, it has more error locations, which increases some error probabilities.
Why pick this mo
...(continued)Hi! I have a question regarding the noise model considered here. You state that "we performed numerical simulations under a circuit-level noise model", but then, when the model is described, you consider biased noise in the physical qubits and "each stabilizer measurement may independently fail with
Braneshop, and
the US National Science Foundation.
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