...(continued)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
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.
...(continued)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
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.
...(continued)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
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.
...(continued)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
Ok, that makes sense. Thanks a lot.
...(continued)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
...(continued)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
...(continued)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
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.
...(continued)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
...(continued)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
...(continued)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 $\gamma \rightarrow 0$
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.
...(continued)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
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.
...(continued)Dear Mark, thank you for letting us know the papers and sorry for replying late. I managed to create an account. We will definitely cite them in future work if they are relevant on a technical level. My arXiv posting is random. Given my limited knowledge, probably I wouldn't encounter them in the co
...(continued)This kind of theory, thinking of codes in terms of superchannels, was developed previously in https://arxiv.org/abs/1406.7142 , which is not cited in the paper. See also the related work https://arxiv.org/abs/1210.4722 . The paper is now published before the arxiv posting appeared, which is unfortun
...(continued)Your *Better Solution Probability* (BSP) metric reminds me of the concept of *advantage* used in reinforcement learning. There, given a *reward* (or better, a *discounted return*) $R$, the advantage is defined via $\mathrm{adv} = R - \mathrm{base}$. Here, $\mathrm{base}$ is a baseline. It could be a
...(continued)Hi Seiseki, thanks for the comment! Indeed, as our desired map is not trace-preserving, we prove Lemma 2 in order to apply randomized compiling to QSP. This offers a quadratic suppression of error in general.
As you mention, your lemmas 4.1 and 4.2 upper bound the error of a randomly-compiled chan
...(continued)Congratulations on successfully expanding the use case of randomized compiling. Thank you for citing our work in your research. It seems that you are applying randomized compiling to channels with projection. This requires the extended version of the mixing lemma, such as Lemma 2. Since your target
...(continued)Hey Yue, thanks for bringing this work to our attention! Indeed, the idea of using the mixing lemma to improve performance is quite similar. We’ll be sure to cite your work accordingly in an updated draft. It’s super neat that you were able to observe such good performance by simply mixing over two
...(continued)I found this paper very interesting and would like to draw your attention to "Faster Quantum Algorithms with 'Fractional'-Truncated Series" (https://arxiv.org/abs/2402.05595). I noted some similarities, particularly in performing randomization on polynomials with modified coefficients. Both your and
...(continued)Is SciRate really the place for these types of comments? Is it not more constructive to communicate such feedack privately over an email?
I always felt that SciRate comments were for public discussion that could benefit the authors and also the whole quantum community that might see the reply. Thi
Hi Jahan,
Thank you for informing us about the general opinion that the referees had regarding the partial dot product notation! We will be sure to update our paper with notation that is consistent with yours!
...(continued)This looks great, looking forward to reading it in more detail!
Just FYI, the partial dot product notation Argyris and I used in our proof was generally disliked by referees, so we've updated our paper to not use it (will be updated on arXiv at some point).
Instead of partial dot products, you
The authors agreed with the above comment in a private correspondence.
...(continued)**Long story short:**
Use $Tr(U_B \rho_A)$ instead of (for instance) standard Hadamard test for $\langle B|A\rangle$ amplitude estimation.
**What do we know?**
$\vert B\rangle$, not $\vert A\rangle$.
**What do we need?**
Diagonal (Unitary) Block state Encoding (UBSE) for $\vert B\r
...(continued)Hi Anqi,
Thanks for your detailed comment! You are indeed right that the resultant 189 qubit code would not have all stabilizer weights divisible by 8 and not satisfy the triply even code definition mentioned in the paper. This was an oversight on our part and we will clarify this in an updated ver
...(continued)Dear authors, please correct me if I am wrong. When applying code doubling using a doubly-even code of length m and a triply-even code of length n, from Eq. 60 of arXiv:1509.03239, for the last row to have weight divisible by 8, don't you need (m+n) to be divisible by 8? For the first code you const
...(continued)Nice paper! I do miss some references on coherence time drift and fluctuations which seems an important part of it though, including a couple of our team. I leave them here as a reference:
- https://www.nature.com/articles/s41534-021-00448-5
- https://journals.aps.org/prresearch/abstract/10.1103
...(continued)Hi Lorenzo,
Thank you for pointing us to your paper on pseudomagic quantum states. We’re glad to see that there has been progress made in this direction! We’ve updated the manuscript and have mentioned your results. Thank you again and we look forward to your future work!
Best,
Roy on behal
...(continued)Just for the record (as I have already mentioned to Aleksei via email), a similar algorithm was presented in [arXiv:2311.01362][1], specifically in Appendices A and B, while we were also unable to find any prior literature explicitly discussing this approach.
[1]: https://arxiv.org/abs/2311.0
...(continued)Hi Craig, thanks for the comment. We were searching the literature for the simple and explicit equation for Pauli decomposition but to our surprise we could not find any. This is why we derived and proved Eqs.(6)-(9) ourselves. Algorithm is just a direct implementation of those equations. I will inc
...(continued)I can't find the original citation, and probably that's a sign that it's useful to have it pointed out to the community another time, but this transformation *is* known. For example, although I don't remember where I learned it, I described it and gave working source code for a stack exchange answer
Yes exactly, thanks Oliver for your response!
...(continued)Hi Roy and coauthors,
Congratulations on this interesting piece of work on magic-state resource theory!
I would like to comment a bit on Conjecture 1, bringing to your attention some new results from our team that you may not be aware of. The observation that a magic monotone cannot be accurat
...(continued)Others can probably answer this better than I can, but quoting from the introduction
> A series of recent works [15–22] have provided unconditional results
> addressing a more limited notion of quantum advantage. In these
> works, a computational problem is introduced that can be solved by
> g
...(continued)Apologies for what I'm sure is a very naive question, but what exactly is meant by the claim of "unconditional quantum advantage" in cases such as this? As someone who is fairly ignorant of complexity theory I would have thought that an unconditional proof that a certain problem can be efficiently s
...(continued)I am one of the authors, I think it is a very interesting work, in fact I think it is my best work in these years, so I am excited, and want to share this paper with my friends (they are all studying quantum information), and some of them give comments about it. I wish more people to pay atten
note that a large number of the scites (and most comments) for this preprint come from otherwise inactive accounts that were created within the last month...
Dear Michal,
Thank you for your pointing out this work, which we were not aware of. We have noted that efficient learning has already been established in an updated listing of our paper.
Best wishes,
Josh
Braneshop, and
the US National Science Foundation.
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