...(continued)Thanks for your comments Jacques. We are discussing how to update the article in light of them.
I would prefer not to formulate Completeness in terms of "hidden variables". There were good reasons to rebrand hidden variable theories as "ontological models", and there are a lot of misconceptions
...(continued)Some of us QBists are discussing this article over email. We think that the way "Completeness" is elaborated in the article sits uncomfortably with QBism, possibly also with RQM.
The article frames the issue like this: either QM furnishes us with a "description" of the properties of physical syst
...(continued)Great paper! I've not had a chance to read it over in detail yet so forgive me if I've missed this but apart from a brief mention in the conclusion, you don't seem to have a discussion on the effects of resonator leakage on your gate fidelity. You state an advantage of your gate is that you can driv
Congratulations for this nice work!
We wanted to let you know of our earlier work in : https://arxiv.org/abs/2503.01738 where we consider an ensemble BP decoding method for the Bivariate Bicycle code family under circuit level noise, as well.
We are very sorry for this mistake (and we are confused how that happened). It has been corrected, and the proper reference to your paper will appear in our next arXiv update.
Hi. You left my name off the authors of Ref. 12, [arXiv:1612.07308](https://arxiv.org/abs/1612.07308).
...(continued)This is an interesting paper, and worth reading, but I view the conclusion that there is no exponential speedup for existing quantum algorithms deeply misleading.
Here's the issue: The runtime of the algorithm in ref ZFF19 (of which I am an author) scales polynomially in the condition number (kap
...(continued)If you are only investigating the error suppression capabilities of the code, then why does your abstract specify "on planar architectures with only nearest-neighbor interactions"?
The code you describe is manifestly *not* planar. It doesn't have stabilizers spanning only nearest neighbors. So the
...(continued)Dear Changhao,
thanks for pointing out this relevant reference. I think your iterative integration-by-part method is related to the one we developed in the context of Trotter error bounds (https://arxiv.org/abs/2312.08044), which might be of interest to you. We also use the first-order variant of o
...(continued)Thank you very much for your valuable comment.
We fully agree that the code capacity noise model is not sufficient for a complete assessment of fault-tolerant quantum computation (FTQC), particularly when considering the impact of non-local stabilizer measurements and realistic circuit-level nois
...(continued)What? You can't use a code capacity model to analyze a concatenated structure involving a non-local code while claiming it runs under planar connectivity! Code capacity models don't understand how operations are performed, but because you're embedding a non-planar code into a planar system those ope
Thank you for the answer!
...(continued)Thank you very much for your interest in our work and for the insightful question.
In this study, we restrict our analysis to the code capacity noise model and do not explicitly implement or simulate lattice surgery operations. The reference to lattice surgery is made to emphasize the compatibili
Congratulations on the nice work, good to see more work focusing on stationary distributions in quantum networking. I wanted to point out a typo in Eq. 7, the top-left entry of the matrix should be (1-p)^2+p^2, instead of (1-p)^2+p.
...(continued)Thank you for the interesting paper.
How did you implement the lattice surgery between two distant surface codes? Have you used an ancilla region to directly measure the stabilizers or do you have a logical ancilla per stabiliser and doing lattice-surgery CNOTs between each logical qubit in the s
...(continued)Thank you for the detailed comment. We are aware of the uniform norm condition on implementable polynomials via the QSVT, but length constraints prevented us from discussing this issue in this conference paper; we make no claim that $P_{2n-1}$, appropriately downscaled, is optimal. Instead, we view
...(continued)The polynomial approximation to $1/x$ here is elegant and optimal, according to its definition Problem 1, which is to minimize error w.r.t $1/x$ on $[-1,-a]$ and $[a,1]$. However there seems to be an issue in its application to QSP/QSVT methods - Problem 1 does not constrain the maximum value of the
...(continued)Hi Alexander, we’re glad you found the paper interesting.
Thank you for kindly pointing out the issue of vanishing $q$. We will include the following clarification in the next revision of the manuscript.
We note that constant qubit overhead is achievable only when $d = O(k/f)$; otherwise, $q
...(continued)Hello, congratulations on this interesting paper.
I do not think the analysis on p2 in the paragraph starting "In addition to encoding overhead…” is correct for all constant rate codes. In particular, from the references it seems that asymptotically good qLDPC codes are the intended choice of ini
...(continued)There is often criticism that quantum models are compared to badly-optimised classical alternatives (see e.g. https://arxiv.org/abs/2403.07059). This paper particularly made me curious why the classical benchmark only achieves 72% accuracy (compared to 50% random guessing!), on an extremely simple t
...(continued)Fascinating work! I have a question on how one should interpret these results.
In what sense do the authors mean that permutation unitaries act classically?
E.g. the Toffoli gate is a permutation unitary, it is non-Clifford and can generate quantum resources (indeed this manuscript is about e
...(continued)Hi, congrats on the interesting preprint! Related to a part of your paper, you might want to check out the connection to the notion of the entangling power of unitary gates -- the average entanglement created on an ensemble of separable states. It was introduced in the bipartite setting by Zanardi,
Thanks a lot !
[Repo][1]
[1]: https://github.com/jblue1/ml_bb_decoding "Repo"
...(continued)Hi Scirate, in discussions with others, a common feedback I’ve heard is: "There have been so many papers on code surgery recently — it's hard to keep track of what each one is doing and how they differ.” So for everyone who share this thought, section 3.2 of this paper is a high-level, 2-page summar
...(continued)A few years ago I wrote a similar algorithm for the log-determinant, which can be found here: https://arxiv.org/abs/2011.06475 . It seems to me that it is more general and faster: we have a linear dependence in the approximation error (instead of cubic) and we are linear in the sparsity (instead of
Great figure!
Funny, our paper from 2018 (https://scirate.com/arxiv/1803.10520) which contained essentially the same algorithm only got 9 scites. I guess I need to get better at selling results.
Dear authors: I would like to introduce our previous paper https://arxiv.org/abs/2409.18369, where generalized iterative integration-by-part method is also used.
If you're using a fault-tolerant CCZ gate to perform distillation coherently, is the intended future direction to distill Clifford states, to, for example, perform a logical Hadamard instead of the non-Clifford T states that you're distilling here?
...(continued)Hi Craig, thank you for your helpful and constructive comments. I do agree, of course, that suppression O(p^d) is better than O(p^ceil(d/2)). In the long-term, this should be the ultimate goal. My take for the near-term however is more in the direction of trying to find circuits that you CAN actuall
Note also that the quantum Fisher-Yates method introduced in arXiv:1711.10460 is in Appendix C, rather than in the main text, because in the main text we introduced an even more efficient coherent sorting method for preparing those sorts of states.
...(continued)Gah, and of course that also saves another factor of 2 on the depth.
So in total: the unitary circuit should have 4x less depth and 2x less gates compared to what's shown in the paper.
https://algassert.com/quirk#circuit=%7B%22cols%22%3A%5B%5B1%2C1%2C1%2C1%2C1%2C1%2C%22H%22%5D%2C%5B1%2C1%2C1%2
...(continued)Actually, because the intermediating qubits are known to start in 0, you can also reduce the gate count by 2x:
https://algassert.com/quirk#circuit=%7B%22cols%22%3A%5B%5B%22H%22%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C%22H%22%5D%2C%5B%22~t6gb%22%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C%22~knev%22%5D%2C%5B1%2C%22~
You can cut the depth of your unitary entangling circuit in half by pipelining the CX gates: https://quantumcomputing.stackexchange.com/a/38464/119
Many thanks for pointing out that this reference is missing in our list of prior constructions! We will append it in a future version. Note that this also aligns well with the method introduced by Barenco et al. (https://arxiv.org/pdf/quant-ph/9604028).
For the interested reader, it might also be worth mentioning the prior work of https://arxiv.org/pdf/1711.10460 (see Appendix C for a quantum variant of the Fisher-Yates shuffle).
...(continued)When I explain to people why magic state distillation has remained better than other techniques, despite substantial effort to displace it, I consistently find myself explaining two things:
- Distillation gets O(p^d) suppression instead of O(p^ceil(d/2)) suppression because you can use error dete
hey noah, thanks for pointing this out! in the conclusion I refer to a FT construction of these multi-qubit-controlled gates, which one could maybe use to circumvent this problem. with some extra tweaks in the CFN, you might also be able to tolerate more noise there. happy to discuss!
Because the coherent feedback network requires multi-controlled gates, wouldn't this circuit end up consuming more magic states than it generates? Apologies if I have misunderstood something simple.
...(continued)> had complex numbers never been invented (or used, due to some other
> reason...In the Schrödinger equation, there is an "i" prefactor. It's fundamentally tied to the complex number system. For a time-dependent Hamiltonian, I think the real-number representation of a complex number might be so
...(continued)Interesting and a strong conclusion. Sorry to interrupt. I would like to take this opportunity to humbly promote the reading of this work:
https://arxiv.org/abs/2502.06311, which discusses (possibly) related concepts, including analysis of time-dependent Hamiltonian drives, dynamics, and *n*-qubit
...(continued)Interesting and nice. Sorry to interrupt. I would also like to humbly promote the reading of this work ["[Analog classical simulation of closed quantum systems][1]"], which discusses (possibly) related concepts, and also includes analysis of time-dependent Hamiltonian drive, dynamics, and n-qubit co
Awesome, really looking forward to it !
Hi Zhide - thank you! We're working on getting the repository in sharable shape, and I'll make sure to comment here with a link when we post it.
**Major arXiv update**:
We make our efficient method to engineer arbitrary many-body Hamiltonians robust against various dominant errors.
See updated abstract above.
very nice work! Is there a GitHub repo or any code available for this paper ?
We have made a major update with an author (Zhi Li) added in v2. Improved bounds with new results on local operation (LO) distillation and logical operators.
Braneshop, and
the US National Science Foundation.
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