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Why didn't I see the exponential quantum advantage from your PhD supervisor's citations?

The brilliant application of reductio ad absurdum!

Dear Bori,

thank you for your comment. Regarding your final question, please see my answer to Zhiyuan above. We will clarify this some more in version 2 of our paper.

Best wishes,
Markus

Dear Zhiyuan,

thank you for this, I agree this is a natural follow-up question to ask. And I agree that the answer should be “no”. In addition to the local-versus-global invariance that you have pointed out again, let me give another view on this.

Our starting point is the postulate that two (

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Hi Kishore,

In your paper $z=xy$ so it might have been a better way to describe the codes as polynomials in two variables. The $[[30,4,5]]$ code in Nicolas's paper would be : $$[1+x|1+y+x^2y^2],l=5,m=3$$ which is different from your $$[x+x^4y^4|x+y^2+x^2y^2],l=3,m=5$$ these are small enough codes

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Just wait until a quantum AI has found our universe. It will mine all the online text data from all the other universes to write a better paper.

typo, bottom of pg 5: "you clearly cannot have quantum advantage with an imaginary number in there somewhere" shouldn't it be _without_ ?

Excellent paper otherwise. As the saying goes, the real multiverse were the samples we made along the way

Hi! To chip in. For the codes from https://iopscience.iop.org/article/10.1088/2058-9565/ad5eb6/pdf , we also found a small number of BP Iterations to perform best. We think it's due to the relatively large number of small cycles and symmetric stabilizers.

Thanks, Nicolas. Since Q_l is a circulant matrix, your A (A1 + A2 in your paper) and B (A3 + A4 + A5 in your paper) matrices are circulant and, hence, can be expressed as multivariate polynomials. Thus, your codes can be captured by our multivariate formalism. I explicitly calculated the parity-chec

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Thank you Kishor! The parity check matrices of our [[30,4,5]] and [[48,4,7]] codes are described in Table II.

Thanks, Nicolas. I loved reading your work yesterday. In our paper, we’re working with the multivariate polynomial quotient ring to pick out matrices A and B. I noticed you go with an exhaustive search to select permutation matrices, then tweak the number of terms in A and B to find low-weight codes

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interesting data point! it's not what I usually see but I'll take a look at your results to see why. I don't use the python BP-OSD package (I have a homegrown c version) and I might select the candidates differently. Anyway it's worth looking into this in more details. As far as practical implementa

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R.e. the large number of BP iterations, my coauthors and I observed something similar when studying a different code family with comparable parameters https://arxiv.org/abs/2406.14445. In appendix E you can see that the decoder performance continues to increase all the way up to 10000 BP iterations.

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Thanks for the clarification.

The parameters seem a bit unusual : 10000 iterations is huge (normally you get to diminished returns after ~20 iterations); also the osd_order seems low. Most other papers use ~50. Although not all sources define "osd_order" the same way; the number of candidates con

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Hi @qodesign,

Thanks for pointing out that the parameters of BP-OSD are missing. We will include them in the next version. For convenience here they are:
max_bp_iters = 10_000
bp_method = ''min_sum''
osd_order = 5
osd_method = 'osd_cs''

As a sanity check to test our simulator, we reproduced the s

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What are the parameters of BP-OSD?

I'm familiar with the paper in the first comment; it contains a lot of results but again the BP-OSD parameters are not given and the noise models are not clear. I couldn't verify much of the claims there.

Also it looks like one paper reports logical error rat

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Thanks Kishor for letting us know. We will add a ref to your paper in the next version.

Edit: A few comments after having a closer look at your paper. First it's a nice paper, congrats! These variants of BB codes are indeed similar and we will add a link to your paper in the next version of ours.

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Congratulations! Just wanted to mention that we had proposed the weight-5 [[30,4,5]] code and several other such codes in https://arxiv.org/abs/2406.19151 (Page 3, Table 1 and the supplementary material.)

Reminds me of a Nirvana song called "Smells like Quantum Advantage".

How can emerging physical-layer security strategies be systematically integrated into 6G ISAC networks to simultaneously safeguard both communication data and sensing information, while preserving the ultra-low latency and dual functionality that define ISAC’s commercial appeal?

How can the 6GStarLab mission, envisioned as an open, flexible in-orbit platform, enable experimentation of future 3GPP NTN standards across multiple frequency bands and optical links while ensuring reliability, scalability, and adaptability for diverse use cases in dynamic orbital environments?

How can a networked ecosystem of autonomous and embodied AI agents, each potentially possessing distinct goals, learning algorithms, and generative foundation models, maintain consistent, coherent, and up-to-date shared knowledge while operating under dynamic network conditions and diverse task requ

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Ludovico didn't let me do this :(

Shouldn't it actually be denoted by Ü, or would that be the umlaut umlaut information?

No problem, thank you!

Oh that's so cool! Sorry I missed it. I'll add a reference to your work in a future update :)

Hi Nouédyn,

Congrats on your result! With regards to the open question that you stated about self-correcting memories in dimensions less than 4D, we wanted to share our [work which discusses self-correcting memories on fractal lattices][1] with Hausdorff dimension $D_H=4-\epsilon$, obtained by punc

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Thanks to both of you for your explanations. All this makes sense except that I am not fully convinced that we even know for which instance *sizes* quantum advantage is expected. It is plausible to me that at the sizes where random instances become classically intractable, all instances either conce

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Dear Markus,

Thank you for your explanations. I haven't yet read the full details of your paper, but I'm curious if it is possible to generalize your results from the symmetric group S_N to the braid group B_N, and also "rule out" non-Abelian anyons in 2D? Does it make sense to talk about "invar

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Ah, duh, it's not a 1d stabilizer code. It's local at each level, using only adjacent logical qubits, but each level is zoomed out so the global picture is not made up of local stabilizers.

Doesn't Jones et al's concatenated 1D construction from https://journals.aps.org/prx/pdf/10.1103/PhysRevX.8.021058 have a growing distance?

The paper reads well but it is missing relevant secure ISAC works such as [R1]

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References

[R1] A. Bazzi and M. Chafii, “Secure Full Duplex Integrated Sensing and Communications,” in IEEE Transactions on Information Forensics and Security, vol. 19, pp. 2082-2097, 2024, doi: 10.1109/TIFS.2023

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The paper introduces a dynamic array partitioning framework for monostatic ISAC systems to enhance sensing performance while supporting communication requirements. In particular, the paper formulates a joint optimization of transmit beamforming and array partitioning to minimize Bayesian Cramér-Rao

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Indeed, such methods are especially crucial in 6G networks, where the importance of achieving high bandwidth efficiency and sustaining the connection in adverse conditions is significan. A significant adversity can come from satellite incumbents [R1] and coexistence which is of paramount importance

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Thank you Ryan for the comment. As Tuomas says, we do make it clear in Sec V that we have only identify the instance *sizes* for which advantage is expected. I still think this is cool, though, and takes a non-trivial amount of work to benchmark this end-to-end quantum algorithm. This project is mos

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Dear All,

I would like to call attention to our paper [https://arxiv.org/abs/2306.05919, also Ref. 11], which appeared slightly before Zhiyuan’s paper and presents a very similar classification of generalized statistics, termed transtatistics. I am still reviewing the work by Manuel, Thomas, and M

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sure!

The explicit expression appeared even earlier in Eq. (4) of

https://arxiv.org/abs/1310.7178

for the special case of α = z = 1/2 .

Thanks for pointing this out, we’ll update the paper with this information in the next version. We used 30 iterations of parallel sum-product BP and OSD combination sweep with order 60 (all using the ldpc library).

BP-OSD has a lot of parameters which can have a big affect on performance and complexity. It would help if you explicitly specify these parameters; otherwise it's hard to compare decoders.

+1 !

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!