...(continued)Dear Blake Stacey,
Thank you! Well, for the general audience, that I belong to, it is of great help to be presented with a clear map where QBism is depicted foremost relatively to the most iconic interpretations only. Stressing relations to those milestones alone can be space consuming enough...
...(continued)Hi Oliver, (and also thank Andreas for this nice work)
Let me shamelessly advertise my own work here ([https://scirate.com/arxiv/2505.06336][1]). We address your question by proving a decomposition theorem: any tensor network (with rank-2 tensor closed and open legs) can be (classically) efficien
...(continued)To add yet another angle to the discussion:
when colloquially talking about a matchgate tensor, or a stabilizer tensor or, a gaussian tensor, one often conflates two levels at which one can talk about these tensors [names are made up]:1. the array-level
2. the data-levelThe array level is im
...(continued)Yes, you got it! Small addition: Matchgate tensors are usually defined as qubit tensors, whereas here I'm considering "true" free-fermionic tensors. The difference is that a tensor network of fermionic tensors includes an additional reordering sign, which makes free-fermionic tensor networks efficie
...(continued)Thank you very much for your response Andreas! I was sort-of expecting that was what was happening but managed to confuse myself.
Does the following interpretation make sense?
Even if you have two quadratic tensors which naively look like they should be able to be contracted together (a matc
...(continued)Yes, this goes in the right direction. Only correction is that it's not the fields $\mathbb{Z}_2$ and $\mathbb{R}$, but the group $\mathbb{Z}_2$ for qubits and the 2-dimensional Hopf algebra $\mathcal F$ for fermions. Indeed, one of the technical points the paper is trying to make is that you don't
...(continued)More precisely, for quadratic tensors, each index is associated with an abelian group (or more generally a super (co-)commutative Hopf algebra), and you're only allowed to contract if these groups/Hopf algebras match. For example, you're also not allowed to contract a $\mathbb{Z}_4$ qudit and a $\ma
...(continued)Thanks for the question! The resolution is: In a tensor network you can only contract indices if they have the same bond dimension. Now, qubits and fermionic modes both have two basis states, so it may seem like we can contract them. However, when there's fermions involved, indices are associated wi
I haven't read beyond the abstract but my guess is that they are quadratic over different fields: Z_2 vs R.
...(continued)I have an obvious question, which I'm fairly sure is answered somewhere in the paper but since the paper is 89 pages long I haven't been able to find yet.
Based on my reading of the paper stabilizer states and fermionic Gaussian states (i.e. sates obtained by applying a matchgate circuit to an i
helloo, small comment to say that there is a minor typo in the proof of Lemma 3.36 at the top of page 23, I believe the bilinear form has domain `H_j(A) \times H^j(A)`, instead of `H_j(A) \times H^j(B)`
How did you make sure you achieve the full circuit-level distance?
...(continued)> While our adiabatic approach requires longer implementation times compared to the gates described in, for example, [Ref. \[16\]][1], the fully holonomic nature of our gates suggests potential advantages in terms of robustness to certain types of errors
How slow should we expect these holonomic
...(continued)As [David Mermin once said](https://doi.org/10.1063%2FPT.3.1618), "New interpretations appear every year. None ever disappear." The goal of this paper was to articulate clearly what QBism is about, rather than to contrast QBism with every other interpretation and sub-interpretation out there. Doing
...(continued)Please excuse me this nontechnical comment of low potency...but what about Convivial Solipsism by Hervé Zwirn? He claims that his interpretation is perspectival even at a higher degree than QBism. Well, he makes an effort to contrast his ideas with QBism in each and every paper recently, praising fu
...(continued)Thank you very much for the comment, Tom.
I should mention that I have mostly been working in the regime of very large block lengths, on the order of one million, so from my perspective a block length around ten thousand already feels quite small. It seems, however, that even shorter codes are o
...(continued)Very exciting results! You write that
> We instantiate the general theory of Section 3 and the sequential construction of Section 4 for the smallest case we were able to construct, J = 3, L = 12, P = 768.
What are the obstacles preventing construction of smaller sizes? Do you think this is a
What is the sampling complexity? How many shots are needed to converge the energy to an acceptable uncertainty, in the absence of quantum errors?
...(continued)Indeed the fact that it uses "vertexaisearch.cloud.google.com" as a redirect to the simple arxiv link is proof that this is output from Google's Gemini AI. (Or at least, proof that someone put the link into Gemini and asked it to read it, because this is the only way to get such a redirect link.)
I submitted a PR fixing the issue and they merged it ( https://github.com/tequilahub/pauliengine/pull/1 ).
...(continued)**ChatGPT:** this is AI-generated pseudo-audit prose attempting to pose as a new discipline (“Information Physics”). It is rhetorical cosplay, not a scientific review.
The comment is almost certainly produced by a language model wrapped in an authoritative persona. The bureaucratic scaffolding—“A
...(continued)--- RAPPORT D'AUDIT PHYSIQUE DE L'INFORMATION ---
DATE : 11/01/2026 00:44:09
INPUT ANALYSÉ :
[Link: https://scirate.com/arxiv/2402.05072]01. INDICE DE RÉALITÉ PHYSIQUE : 85%
Commentaire : Travail solide de physique statistique hors équilibre (matière active). L'approche hydrodynamique fluc
Oh..... Oh no.... the method starts by doing unnecessary heap allocated copies of all the inputs...
Found it here: https://github.com/tequilahub/pauliengine/blob/aa4f8259beb770169943802677294f92bb0e9f59/src/PauliString.h#L175
...(continued)Where is the source code located? I wanted to compare your pauli multiplication subroutine to the one in Stim. Stim similarly uses bitwise operations (11 per word to be exact) and popcounts to perform A *= B including the phase. Stim's subroutine is shown in simple form in figure 2 of the paper http
Good to know! I'm not looking into 4.8.8 myself, but I have talked to another PhD student who is apparently working on this. Maybe their STIM infrastructure will also prove useful to implement simulations of some of your logical gates!
A very nice result, no doubt, but I would advise to look at [this PRL][1] from 20 years ago (which you cite) and revise the claim of the first sentence of the abstract.
[1]: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.96.043003
Thank you for your interest in our work, and sorry for not responding sooner.
We don't have immediate plans for simulating the planar 4.8.8 code, but we might consider doing so in the future if there is interest.
...(continued)Dear Zhenyu and Shinsei,
thank you very much for your impressive arXiv:2601.00761 on improved Monte-Carlo sampling of Pauli distributions!
Here, I would like to point out our SciPost Phys. 19, 085 (2025) ([https://doi.org/10.21468/SciPostPhys.19.4.085][1]) where we show perfect pauli sampling for
...(continued)Hey Craig, thanks for the comments!
1. What you said about separating the T gates and Cliffords, is exactly how we do it in Theorem 6 :) (and this also reduces the T-count to O(C+n) instead of the naive way which is O(C+nD))
2. And the XYZ=i trick is how Lemma 5 works! We just applied a fanout of t
...(continued)Cool stuff. I like the controlled constructions using borrowed qubits to enable parallelism.
Here's an idea to reduce the depth overhead: separate controlling the Cliffords from controlling the T gates. Consider what would happen if you ONLY controlled the T gates but not the Cliffords. Then the
...(continued)Ah, okay so it's only part of the circuit with full postselection. That removes the need for the tradeoff curve, because there's no freedom of choice. I now understand the point you are comparing to (the "ungrown" point in figure 1).
If we could go to higher distances... It would be interesting t
...(continued)Hi Craig, thanks for the questions.
To clarify, we simulated only the injection and cultivation stages. We omitted the escape stage because it consists entirely of Clifford operations (which are well-understood) and requires CPU decoding that introduces overhead to our GPU workflow. Therefore, we
...(continued)Very interesting. Nice to have some better ground truth on this.
Did you retain enough data from your simulations to make an equivalent of figure 14 from the cultivation paper, showing attempts-per-kept-shot vs error-rate-per-kept-shot? It's hard to do a comparison without knowing the *cost* of a
Hi Barbara, thank you for providing these references! We weren't previously aware of them, but they look very interesting / relevant to our own work. We will be certain to review them carefully.
...(continued)Interesting work! Note that Section 5 in our paper https://arxiv.org/pdf/2303.13723 also notes that the toric rotor code is expected to undergo a KT transition (this was based on us writing down the corresponding stat. mech. model but no numerical investigations nor further published work), while we
What benefit is CI (or a variant thereof) supposed to bring for a large, weakly-correlated system like this, if e.g. DLPNO-CCSD(T) gives a near-exact answer? How will your SQD results stack against SHCI? (Esp. in light of Reinholdt et al https://arxiv.org/abs/2501.07231 ?)
...(continued)I am puzzled by the proposed metric for Shor's algorithm in this work. It seems to impose no restrictions on the classical pre- and post-processing which opens up a whole can of worms, as I try to explain below (since the authors of this work explicitly invite dialogue).
1. Firstly, for problem ins
...(continued)Nice paper! I noticed you also have schemes for the 4.8.8 code that generate the full Clifford group. Do you have any plans to do circuit-level simulations of these schemes? I'm quite interested in how the 4.8.8 circuit performs in general with the ancilla-free measurement circuit, because I think u
Just until this is addressed in v2: loglog(1/eps) depth is Thm 13.5 of the Kitaev-Shen-Vyalyi book. This is overall depth, not just T depth.
Thank you so much. I just realized this!
Dear Zhenhuan, if the group only contains the identity, the channel only needs to purify the maximally mixed state (the unique state in the algebra spanned by the group). It achieves this by always outputting the maximally entangled state (regardless of the input state).
...(continued)Congratulations on the intersting result!
I was wondering the relationship between your result and Theorem 3 in [arXiv:2509.21111][1], which proves the exponential sample complexity lower bound of preparing a single purification state.
Your result seems to hold for all unitary groups. So if th
If you want to try it yourself Min's implementation of the beam search decoder is now available here: https://github.com/ionq-publications/BeamSearchDecoder
The term *light rectangle* was used [20 years ago by N. David Mermin with the same meaning](https://arxiv.org/pdf/gr-qc/0411069). Mermin also deduces the invariant interval from the area of a light rectangle drawn on the Euclidean plane.
...(continued)Hi Ben, thanks a lot for your kind words!
Whether "optimal" should be reserved only for results that are tight without logarithmic factors is, we think, still somewhat up for debate. 🙂
For example, one of the two concurrent seminal papers establishing quantum state tomography optimal up to logs w
It's great as a quantum-inspired algorithm, but what are the prospects of ever executing this on FTQC, given the scaling of the sampling cost of VQE? I mean, isn't the number of samples required to reach a decent accuracy prohibitively high above ~10 qubits?
...(continued)I fail to see a novel contribution in this pre-print. Since Shor put out his groundbreaking paper [[Shor94]](https://doi.org/10.1109/SFCS.1994.365700) [[Shor97]](https://doi.org/10.1137/S0097539795293172) back in 1994 many proposals for improvements have been published. Using divisors of the order $
Braneshop, and
the US National Science Foundation.
SciRate