Recent comments from SciRate

Indeed, I agree. To be honest, when we started this project we thought there would be obvious instances that work this way, but it turned out there weren't. We discuss this more explicitly in section 5. Perhaps some of the confusing parts are leftover from earlier drafts and should be reworded, than

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Thanks Tuomas. I don’t doubt that there exist classically intractable instances of the Jones polynomial problem (the worst case complexity results you mention are sufficient for establishing that). The trouble is actually finding those hard instances without requiring inordinate quantum resources to

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Thanks for the kind words! I am interested in adapting this kind of approach to the Khovanov homology, and I have some questions about your quantum algorithm for this (I might email you about it, if that's alright).

Hi Ryan - I'm not aware of any explicit instances of this type, except those arising from the BQP/DQC1-completeness proofs of the problem, which seems like 'cheating' to me. So they certainly exist, conditional on P != BQP, but I'm not sure they are natural or interesting. On the other hand, it migh

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Dear Zhiyuan,

thank you so much for your interest and your explanations! We agree that a key distinction is whether one demands invariance of *all* observables or just the local ones, and your interesting results are not in contradiction to ours.

Let us add a few clarifications; we are still t

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Very interesting paper. You discuss that for random instances of the problem the coefficients of the Jones polynomial will exponentially concentrate, which prevents the quantum computer from efficiently providing a non-trivial estimate of the Jones polynomial. You also discuss instances of the probl

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Dear Zhiyuan,

Thanks a lot for the clarifications!

Best wishes,
Marius

Congratulations on this excellent paper! It’s exciting to see that quantum algorithms for knot invariants are a promising tool for benchmarking and potentially even for near-term quantum advantage.

Ok, Thank you for the reply!

Thanks for the question. Weak physical measurement will become weaker logical measurement if the logical measurement is performed by destructive measurement of all supported physical qubits. We focused on the destructive case because in MSD the measured logical qubits should be discarded and only th

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Dear Marius and Thomas,

I just briefly read the first few sections of this interesting paper, and let me share my thoughts on this. While this paper probably rules out parastatistics in all few body systems, it does not rule out the emergent R-matrix parastatistics in topologically ordered system

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Thank you for the interesting read.

One thing that baffled me is the claim that weak physical measurement translates to weaker logical measurement. It sounds like this leads to quantum error correction becomes ineffective against weak physical measurements. How is this possible and what am I miss

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Dear Manuel, Thomas, and Markus,

Thanks for the clarification! From just skimming through the paper superficially, I was indeed under the impression that Eq. (1) is a constant requirement.

Best wishes,
Marius

Dear Marius,

thanks very much for your interest and your thoughtful comments!
We agree that the paper by Wang and Hazzard is interesting. Indeed, we cite it and consider it as part of the motivation for our work. We think our results should apply there because all we assume is that there is *som

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This is a very nice overview, but it does QBism a bit of a disservice. Specifically, the motivation for QBism comes from interpreting quantum probabilities, not states, hence the connection to Bayes and a subsequent quantum Bayes theorem. The collapse problem as explained here doesn't distinguish cl

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Great work!

There is one promising approach to parastatistics of which I am unsure whether it is covered by your framework. See e.g. this paper by Wang and Hazzard:

https://www.nature.com/articles/s41586-024-08262-7

They use the trick that guides us from Abelian gauge theories to non-Abelia

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Wow! This is quite the break though! Looking forward to reading it in detail!

fantastic work!

Hi Anqi! Thank you for your comment. It's technically all-to-all, but with distributed entanglement systems as outlined in [Scalable Fault-Tolerant Quantum Technologies with Silicon Color Centers][1] it is possible to break the all-to-all scaling. Ultimately, there is a tradeoff between IO scaling a

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Thanks for the second question. Corollary 2 applies to a general matrix with a norm greater than 1, resulting in an exponential additive error. However, in GBS cases, the norm of the corresponding matrix is strictly less than 1. For more details, please refer to S4 of the supplemental material.

Thank you for your reply. Can you elaborate why your Hafnian approximation is efficient regardless of the matrix norm? I ask this, because in Corollary 2, the additive error does scale exponentially with the norm of the matrix. If I absorb this into the error epsilon, does the run-time then have an

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Thank you for your interesting question! In general, the norm of a matrix is important, and approximating the hafnian of a matrix with a large norm naturally leads to a large additive error. However, specifically for a GBS circuit, we can efficiently approximate the corresponding hafnian regardless

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Hi, exciting paper! In your Corollary 2, the efficiency of estimating the hafnian seems to also assume that the norm of the matrix needs to be inverse-polynomially bounded. Is that generally true for a GBS circuit that you propose to estimate the Hafnian with?

We have updated the manuscript to v2 (https://arxiv.org/abs/2501.19375). In particular, we have added a conjecture about the constant-depth equivalence between the skeleton and thickened qLDPC codes in Sec. VD, which will allow a direct implementation of a logical gate corresponding to a constant-d

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Congratulations on this wonderful result!!

Could you please comment on your depth-one assumption for implementing $\Pi_i CNOT_{i,\pi^{-1}(i)+n_r^2}$ for arbitrary permutation $\pi=\sigma_1\otimes \sigma_2$ (page 15)? For the physical implementation time to be independent of the size of the simplex

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Super work! @Giulia Mazzola

Indeed, the authors say "Ideally, such a state should provide a probability distribution that closely matches the exact FCI solution" and some of the results are based on states prepared with CASCI. However, they have also tried UCJ and LUCJ ansatze, purported to reproduce the circuits in previous w

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Thank you Alvaro!

Thanks you very much for the circuit and reference!
This looks more economical than what we had in mind (full CH + CSWAP similar to the CCZs here). We'll have to take a deeper look and report back, should be very interesting!

Thanks for reading our paper! I completely agree that X_1 CX_23 would work just fine and has the ~1/3 rate advantage here. I'll note that when 2CX->Toffoli fails, you can still recover one CX which should also be counted in the rate. I'm honestly not sure which of CX/XCX would be best in terms of qu

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Congrats to the authors on this super nice result!!

Hey Renato, thanks for your questions. I think of this method as belonging to a very general class I would label "ensemble methods". In short, they let you replace the execution of one circuit for one expectation value with a weighted sum of different (circuit, observable) pairs which are easier to

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I mean control this: https://algassert.com/crumble#circuit=Q(0,2)0;Q(1,1)1;Q(1,2)2;Q(1,3)3;Q(2,0)4;Q(2,1)5;Q(2,2)6;Q(2,3)7;Q(2,4)8;Q(3,1)9;Q(3,2)10;Q(3,3)11;Q(4,2)12;POLYGON(0,0,1,0.25)9_10_6_5;POLYGON(0,0,1,0.25)4_5_1;POLYGON(0,0,1,0.25)6_7_3_2;POLYGON(0,0,1,0.25)1_2_0;POLYGON(0,0,1,0.25)11_8_7;POL

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Ryan: thanks for engaging. This is a new framework and we are trying to understand and characterize its power. As mentioned before, we believe that any claims should be based on proofs or extensive benchmarks, and we welcome open discussion of such explorations. To the best of our knowledge, in the

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Nice paper! Could your scheme be adapted to measure X_1 CX_23 instead of CX? I think so but maybe I missed something
Because it seems you pay a lot to just measure CX, you need 2 magic states instead one, there is the 4/9 probability, and the sqrt(3/4) first projection. Wouldn't it cost less to add

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I am not sure if this is the best place to ask this, but is your method in the same class of methods as "circuit knitting", "randomized measurements" (including "classical shadows"), and other "quantum-classical interfaces" such as arXiv: 2112:11618 and arXiv:2203:04984?
If so, what is the main diff

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Antonio: in addition to polynomial overlap (a phase-estimation-like assumption) your proof also seems to require ground state sparseness. That seems like a very strong assumption. If you have both polynomial overlap and ground state sparseness then wouldn't many classical methods, e.g., perturbation

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Thanks, Marcin. I understand the limitations of the mirroring approach, but as a reader, I would still appreciate a note about the differences between the two methods.

Thank you for your comment and for pointing out the reference. The mirror circuit approach indeed addresses the scalability problem of the Quantum Volume. However, this method primarily evaluates a machine’s ability to invert its own operations, which does not necessarily provide a reliable benchmar

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I'm not 100% sure I follow this construction, but we did think about measuring H on a single surface code. For a rotated surface code, we think it requires 5-body operators that would reduce the distance considerably. But we think we found a way to get it to work on the non-rotate surface code with

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I haven't read the paper yet, but it seems odd to me that the authors don't cite https://scirate.com/arxiv/2303.02108, which aims at solving the same scalability problem of the QV benchmark.

Did you consider using the non-local gates to implement a GHZ controlled gate on a single surface code, instead of two? For example, do an H_XY (= S*Y) by controlling a folded S gate + Paulis. The GHZ state would also be smaller, since there are half as many two qubit gates to control.

ah thanks! I think I can understand it now better.

The conclusions of this manuscript are based on a wrong assumption: that the best distribution one can draw samples from is the ground state, or powers of it. This is wrong in general. In fact, the optimized LUCJ circuits we have used in Sec IV of the supplement of https://scirate.com/arxiv/2405.050

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There is one qubit on each edge in each copy. So on the simplicial complex, there are indeed two qubits on each edge if you view it in this way.

Thanks for your response! Just to confirm that I understand, in a 2-copy identital code setup, are there two qubits on each edge (1-cell)?

Thanks for your question! In the simplest case the two or three copies of CSS codes are identical (it can also be non-identical in the case of higher gauge theories when qubits are allowed to be put on higher-dimensional cells). However, the CZ gate do not act on the qubits on the same edge of t

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when the paper says put "two copies" or "three copies" of CSS code, do you actually put two or three qubits on each edge?

From equation (14) they were two copies (one with prime and the other with out prime) $a[v_0v_1]\cup a'[v_1v_2]$, but from equation (15) they become $CZ([v_0v_1],[v_1v_2])$,

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This is a very nice work! Just as a heads-up, we've been doing graph code constructions based on graph states (See your Ch. 4) back in 2007 (including higher dimensional systems, D>2), see https://arxiv.org/abs/0712.1979 Those encompass stabilizer codes, as well as non-stabilizer (non-additive) ones

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Hi Simon, thanks for the comment! This is noted in footnote [2] ("More precisely,...") , but perhaps it would help avoid confusion if we moved it to the main text.