Isn't the concept of boosting usually known as pumping? Or am I misunderstanding something?
...(continued)Thanks for the reach out, and we enjoy reading your work with Prof. Dakic. Actually, we have cited it around Eq (16) (very nice formula). And we will also cite your work in Sec. V in the revised version.
In my opinion, it is very unfair to say “shows a strong degree of overlap”, and our work is dis
Very similar to the recent publication Phys. Rev. Lett. 131, 083601 (2023)
...(continued)Thank you! Yes, in Proposition V.2 we explain how the spacetime graph for the overlapping window decoder can be constructed by taking the hypergraph product of the QLDPC code with a repetition code. Our understanding is that your result from Ref. [93] implies that all circuits constructed using this
...(continued)Enjoyed looking through this paper! I had a basic question about 3D surface codes, as they relate to my work on distance-preserving stabilizer circuits. You write "recent work suggests that the ordering of operations in the syndrome extraction circuit does not affect the
effective distance of the c
Hello, I believe this result shows a strong degree of overlap with [a previous work][1] of my group, particularly the estimation of off diagonal elements (one of the main results given in the latter half of the paper).
Best,
Joshua Morris[1]: https://arxiv.org/abs/1909.05880
...(continued)In a follow-up research, I found out that even if just a single known qubit of query registers is affected by the depolarizing noise of rate p, quantum search among n elements cannot be done any faster than in O(np) queries. This holds both when the affected qubit is one of the log(n) index qubits a
I see. Thanks for mentioning this point and your paper to us!
...(continued)This isn't really core to the paper or anything, but the CX*H*CX*H circuit in fig 16 can be optimized into CX*H*CX*Z because Z has the same action as H on the |Y> state ( as in https://arxiv.org/abs/1708.00054 ). Z is cheaper than H because it can be done in the classical tracking instead of on the
This is a well presented, innovative algorithm.
Agreed - really informative and well organized. A maintained version of this would be a very welcome resource for the community
A really impressive work. It would be better if this is uploaded to a website so that the information can be updated.
...(continued)Thank you very much, Eric! Our model (depicted in Fig.2c) is defined by coupling Alice's input signals to environmental systems through unitary interactions. Consequently, this model is consistent with quantum mechanics and, in particular, it does not violate the quantum no-cloning theorem. Once inf
...(continued)Hi Francesco, this is excellent work! I'm always excited to see more ways to carry out QI transport. I have one conceptual question that may be answered in your paper in a way I did not fully understand. By thermal noise, one usually means phonon interactions. If a photon's QI is lost to the system
...(continued)Very interesting paper and good comment by Jason. I agree that such insights should be clearly written up and simple to find in the literature!
I want to add that the fact that the Pauli group is not complemented within the Clifford group (i.e. there's no group $G$ in Jason's comment) is known from
...(continued)This is very interesting! I am sure the explicit character tables will be helpful in the future.
I just wanted to point out that Conjectures 5.4 and 5.5 are known (or follow directly from known results). In the below, always take $n\geq 3$. The main facts being used are the observation that $\ma
Is it clear if this protocol works for noise models where different Pauli errors occur with different probabilities? My understanding right now is that you have to assume each fault occurs with the same probability *p*, but maybe there is some way around that?
Ah, true, the hermitian conjugate is only equivalent to the inverse for unitaries, simple mistake. Thanks!
...(continued)Yes the EM3 distance does usually match the embedded distance, although we found one case where they differed (for n=320, k=18 with EM3 noise the minimum-weight error included Pauli errors that caused time-separated detection events). Thank you for pointing me to your updated GitHub repo, and I agre
...(continued)The spectral decomposition you use in Lemma 1 is only valid for normal matrices, not all diagonalizable matrices. Of course, the lemma (trace = sum of eigenvalues) is true for all diagonalizable matrices, but for diagonal matrices that are not normal, the proof of that fact requires more than just a
...(continued)Thanks for your comment, Oscar! Yes, the DP1 distance the way you defined (and is equivalent to the code distance defined in our paper) equals to the lesser of "the embedded distance of the superlattice" and "twice the embedded distance of the dual of the superlattice". It is still interesting to me
Thanks a lot for the hints! I'm now surprised I haven't found them earlier in my own searches. I'll soon upload another version of the manuscript crediting their work appropriately.
...(continued)Very interesting work, congratulations! Where you compare to our work you say "At similar encoding rates, the codes shown here have a larger relative code distance". The reason for the discrepancy is that we report the distance of our circuits, which include two-qubit errors, whereas you are reporti
Thanks for the references Josu. I see that what we called single-qubit site-dependent Pauli noise is something you have studied and called i.n.i.d noise. We will make sure to reference these works in the next version.
...(continued)Very interesting manuscript. I see that you have considered Pauli noise that shows different probabilities for each of the qubits of the surface code, which I see that you named single-qubit, site-dependent Pauli noise. I attach here a couple of references regarding studies of surface codes with suc
...(continued)The numerical efficiency of computing the fidelity in this way was previously pointed out in https://arxiv.org/abs/2211.02623.
(The expression itself appeared earlier; the similarity of the matrices was noted already in https://arxiv.org/abs/0805.2037, and I can find an explicit expression e.g. in
...(continued)Hi Pavel, thanks a lot for your comments and suggestions. Most of our results are extensions of your BP-OSD work so I am really glad to get a feedback from you. The generalized bicycle code [[126,12,10]] is indeed very close to codes from our paper in terms of the distance and encoding rate. It is a
https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.4.030335
...(continued)Dear Yiren,
Thank you for bringing this serial CPU-only Python implementation to our attention. We added a reference to it, as well as a note thanking you for pointing it out to us, in a v2 version that will appear on arXiv shortly.
We note that the mixer implementation in (Sack & Serbyn, 2021) re
...(continued)Hello, I think similar idea seems to have appeared in the [source code](https://github.com/shsack/TQA-init.-for-QAOA/blob/master/TQA_QAOA.ipynb) of (Sack & Serbyn, 2021), which might be better to be included as related work.
Sack, S. H., & Serbyn, M. (2021). Quantum annealing initialization of
Sure. Should I have any further comments/queries, I'll reach out via email. Thanks.
...(continued)Hi Kishor,
Thank you for your very kind words regarding our paper and for your helpful feedback!
1. Regarding your first comment, we are indeed aware of your nice paper on pseudo-random unitaries, which we cite in our work. Our work complements your discussion of other pseudo-resources, by con
Understood! Thanks a lot for the clarification!
...(continued)Hi Yiren,
Thanks for the question. This is indeed a bit implicit in the literature, but well-known. One can for instance recover it from the lower bounds by Beals et al in \[1\]. Here is the short additional argument: Let $x \in \\{0,1\\}^N$ be a bit string and assume the Hamming weight of $x$ is e
...(continued)Beautiful work! My congratulations to all the colleagues involved in this work.
Upon a quick glance, Tobias, Dax, and I wanted to respectfully bring a few points to your attention:1. In our recent paper on pseudorandomness ([https://scirate.com/arxiv/2306.11677][1]), we explore the concept of pseu
I have a simple and basic question: why the $\sqrt {Nk}$ query complexity is optimal? It seems to be a well-known result but I fail to find a reference.
...(continued)Very impressive and unexpected results! My congratulations to the authors!
I noticed that you mentioned our [[882, 24, ≤ 24]] code. I want to point out that in the same paper in Appendix C we also constructed a family of weight-6 generalized bicycle (GB) codes, which are obtained from two weight
Probably contributions section of the year as well.
Hi Oscar! Thanks for letting us know about your work. It looks very nice and relevant, and I'm sorry we missed it. We will be sure to cite it in the next version.
...(continued)In the [[10,3,3]] code (Fig. 8), let us write two sets of paths for 𝑋̅ – one with weight two and one with weight three. The operators of weight two commuting with the stabilizers are {𝑋1 𝑋3, 𝑋2 𝑋4, 𝑋7 𝑋9, 𝑋8 𝑋10}. The operators of weight three are {𝑋1 𝑋5 𝑋7, 𝑋3 𝑋5 𝑋7, 𝑋1 𝑋5 𝑋9, 𝑋3 𝑋5 𝑋9, 𝑋2 𝑋6 𝑋8, 𝑋
...(continued)Congratulations on this very nice result! On page 6 you say "To the best of our knowledge, this provides the first example of high-rate LDPC codes achieving the pseudo-threshold close to 1% under the circuit-based noise model." In https://arxiv.org/abs/2010.09626 and https://arxiv.org/abs/2308.03750
...(continued)Thanks for bringing this interesting article to our attention! There does seem to be a comparison between the thermodynamic algorithms we presented and these Monte-Carlo algorithms, because 1) both are nondeterministic, and can be seen as Markov processes, and 2) both can achieve O(d^2) operations a
...(continued)Hi Alex,
Thank you for your very important question! Though we do think a lot about this, we do not have a good theoretical handle on the QAOA behavior. Let me say two things.
First, the speedup we observe is not unique; Boulebnane and Montanaro ([arXiv:2208.06909][1]) observed a similar speed
...(continued)I am curious about how your results relate to the various Monte Carlo algorithms for matrix inversion and linear algebra. From a superficial skim, your algorithms seem to be a continuous time formulation of an MC algorithm for Matrix inversion.
See for instance
https://link.springer.com/conten
...(continued)Reaching+beating state of the art performance is great and certainly the most important metric, but is there a deep theory here *why* QAOA would be expected to do well here? Something about the geometry of the Hilbert space to naturally reflect the problem? I'd be curious to know, in the authors' es
The circuit qftentangled in Table 3 has 279 2Q gates, (typo in paper says 0). This will be fixed in next version.
:)
Hi Kishor, many thanks for highlighting this, we're looking forward to seeing your upcoming work.
Braneshop, and
the US National Science Foundation.
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