Recent comments from SciRate

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

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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

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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

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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

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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

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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

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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,

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Thanks a lot !

[Repo][1]

[1]: https://github.com/jblue1/ml_bb_decoding "Repo"

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

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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

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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?

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

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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.

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

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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~

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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).

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

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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.

> 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

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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

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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

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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.

Thanks for the clarification. The reference [8] was hard to track down but I found some other papers that deal with these trinomials. I did verify that the polynomial you gave for $r=8$ has a primitive gcd with $x^n-1$. (I used GAP).

Thanks for coming to the seminar and digging into the paper! So the trinomial itself doesn't need to be primitive, but rather it must have a primitive gcd with $x^n-1$ (here $n = 2^r-1$): if you have two polynomials $g$ and $g*p$, provided $p$ introduces no new zeros (i.e. roots of $x^n-1$), both $g

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I saw your recent webinar and looked at the paper in mode detail.
A question on the guaranteed row weights of 3 in Appendix D.
It is based on the assumption of finding a primitive trinomial for a given $n$; as far as I know this is not possible for all $n$. For example $n=8$ fails...

Nice work. How do your results compare to the recent phasecraft preprint on similar topics?

Dear Zhiyuan,

how about moving our discussion offline? I’m glad to continue discussing over email, or over Zoom, or to invite you to Vienna to discuss in person! I think this could be more efficient, and we would not be hijacking SciRate for this.

Just a brief answer to your questions: as for

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Hello everybody and thank you for the interesting discussion, particularly for MariusK’s comment, which elegantly clarified most of the original issue. If you are interested in this discussion and our paper, we highly recommend that you take a look at the related work on the matter arXiv:2503.17307.

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This may be re-iterating some of the points made in the previous comments, but is hopefully helpful.

One can distinguish between a theory and its representation. In the QI/operational approach a theory is determined by its systems and their convex and compositional structure. There can be multiple

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Thanks, Harrow. That explains everything.

They don't need any assumption about topological order. However, they consider only simpler choices of regions, see Fig 1.

Dear Markus,

Thanks for all these explanations. When you say "For paraparticles in second quantization, these maps are known as “particle permutations”", did you specifically refer to Green's formalism, or do you also include my R-matrix formalism? It seems to me that in your paper, you only cons

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It's good to see figures like that in papers; although there are so many parameters involved that it's hard to draw too many concrete conclusions from them. BTW at first look both AC and the decoder in this paper don't strike me as much of an improvement over OSD...just an opinion

I agree with your point on the worst case. I reckon that should be important. However, I think that for the standard OSD the 10k BP iterations are not the limitation, the limitation is the inversion algorithm. Check figure 13 here: https://arxiv.org/abs/2502.16408 . You can see the bimodal timing di

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I agree that OSD is very expensive (whether that's for SW running time or ASIC implementation); so replacing it with other decoders like that paper is doing with AC is a move in the right direction. I haven't looked at AC in detail to judge its complexity yet; but that's in the ever growing queue ;-

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I agree with your comment. Very recently, we also submitted a similar paper:

https://arxiv.org/abs/2503.17307

Originally, we also wanted to name it exactly like this one: "Quantum theory does not need complex numbers". But then we changed the title because - exactly - what we all do is simulation

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A little comment on this, while the 10k iterations sound too much seems that in terms of time is better to have 1) 10k BP iterations+ OSD than 2) 20 iterations of BP + OSD. Basically you will be allowing BP to converge more times and you'll require the expensive OSD less times. They comment this th

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Congratulations on the wonderful results! I am wondering if the local (approximate) Markovian is proved under the assumption that there is no tological order. As in BK19, the contribution from topological entangle entropy may violate the condition for the existence of a recover map for non-contracti

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With the two-reals struct, one may run into different unpleasant issues for the resulting theory. Mathematically, it looks like a two-level system, but with severe non-locality issues. If you admit that it's only a formal system not existing as a localized quantum system, you are introducing differe

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