...(continued)I just send an email to
craiggidney@google.comThanks for the suggestion!
I agree that unrolling repeat is a bad idea and might cause extra problem.
We do this because it's easier for us to understand how to inject error and compile the QEPG graph without repeat. And I believed that conce
...(continued)Yes, please send the exact circuit.
Incidentally, it is a bad idea to split up the operations the way you are doing. It not only makes the circuit files huge, it *hurts sampling performance*. You're causing entropy to be generated in smaller less efficient chunks and probably causing more branch
If you like, I can send you the exact circuit containing all depolarization (0.0005) instruction (Which is extraordinarily large) through email.
...(continued)We store the bare circuit to save space. As mentioned, above, the noise model is injected by another function before testing start.
To get the exact STIM circuit, you just need to use the noiseless stim program as input of the following code, and you should directly see the output program. The e
That circuit does not contain any noise instructions and so its logical error rate is 0, not 1.51e-11.
What is the *EXACT* circuit that you simulated? Including the noise.
...(continued)Yes! The circuit is stored in the following link:
https://github.com/yezhuoyang/ScaLERQEC/blob/main/stimprograms/surface/surface17
We construct the circuit directly by STIM's interface (Rotated memory Z) with 3*17 rounds of repeated measurements. To make parsing easier for us, we rewrite the o
...(continued)`this are essentially stabilizer states' - in the sense that there is a 1-1 correspondence yes. But, the mapping between Majoranas and Paulis is, of course, not unique. So while everything can be translated back and forth, for certain questions, it is not desirable. For example, one might consider s
I'm interested in verifying the 1.51 * 10^-11 you mention in the abstract. Do you have the associated stim circuit? I couldn't clearly identify it in your code.
...(continued)Your work, to the best of my understanding, is closely related to my paper published in Physical Review Letters. I also sincerely appreciate your citation of my work. However, I would respectfully point out that in your Ref. [26], the listed authors are incorrect, although the paper title and the ar
Ah, I see. I misread equation 24 when I was reading the paper before. I apologise for that! So this are essentially stabilizer states but I write my Pauli operators in terms of Majorana operators instead?
Could you please confirm the correctness of the $[[28,6,7]]_3$ qutrit code listed in Table 1? I ran my own program to verify the code parameters, but obtained a different value for the logical dimension $k$. I would appreciate it if you could double-check this and clarify the discrepancy.
...(continued)Hi, the states are not `a subset of both the set of stabilizer states and that of fermionic-Gaussian states' but are in 1-1 correspondence with stabilizer states. You can see this from the non-Gaussian generator in Eq. 24.
The canonical form used here is analogous to the phase-sensitive CH stabi
...(continued)I think I am missing something with this paper. As far as I can tell the Majorana stabilizer states they consider are a subset of both the set of stabilizer states and that of fermionic-Gaussian states (under the Jordan Wigner transformation).
For the stabilizer states phase-sensitive representa
...(continued)Thanks for your question! The GB codes used have check weights and qubit degrees of six. When performing any given logical measurement, each processing block qubit can be connected to up to four gadgets, meaning that the degree of each of these qubits in any given logical cycle can increase to be be
(Sorry never mind my previous comment; I didn't read the paper carefully enough)
...(continued)Can you clarify what degree connectivity is required by the hardware architecture you propose? The paper says it is "bounded" but I don't see where it provides the bound. This is a critical factor determining the feasibility of a superconducting qubit architecture since it scales both the number of
...(continued)Thank you for your interest! Thank you also for sharing that reference; we will be sure to consider what improvements it allows and to cite appropriately in an updated version of the work.
In answer to your questions:
1. Equation 9 presents the T count, which comes from the cited work by Campbell
...(continued)I believe the following addresses all the remaining issues/questions/concerns in this scirate comment discussion.
Minimally reproducible code available at https://github.com/kh428/accel-cutting-magic-state .
Arxiv versions 6 includes an end-to-end non-Clifford simulation of the d=3 cultivation
...(continued)Thank you for the end-to-end accounting of Trotterization and factoring on your architecture!
I’d like to better understand the Trotterization accounting. As you note, without Hamming Weight Phasing, the T complexity is dominated by RZ synthesis costs. Note that https://arxiv.org/abs/2203.10064 l
Hi Johannes,
Thank you for bringing your work to our attention! We agree there is a close relation, especially to the examples in section VII in your work. We will be sure to cite your work in our next update.
Best,
Joseph
...(continued)Hi Joseph and Daniel,
It is nice to see more works that spread tomography across the time domain. I would like to point out our work on "Tomography of parametrized quantum states" that seems highly relevant: https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.6.020346
In it, we pro
...(continued)Hi Pavel, thank you for the kind words.
We are certainly aware of your paper, but completely missed that you had studied the same family of codes. We'll make sure to properly cite your paper, as well as the other references you listed, in an updated version.
Regarding the conjecture, I agree t
...(continued)Fantastic results! Very cool architecture-level analysis. My sincere congratulations to the authors.
I would like to mention our joint paper with Gleb Kalachev from 2019 (arXiv:1904.02703), which you may have missed. In that work, we studied **Hamming-** and **BCH-based** generalized bicycle (GB)
The figures are incredible!
...(continued)Hi Scirate! Just wanted to highlight the v1 release of QUITS. Additional to the cardinal circuits in this paper, the package now also supports depth-7 circuit of BB code and ZXcoloration circuit of bring-your-own code, all in a modular fashion. There are many example notebooks in docs folder, so hop
Wow! I guess this is just the tip of the Iceberg :-)
nice!
...(continued)Definitely agree.
The current method is limited to a **uniform noise model** and depends on several simplifying assumptions. In contrast, **brute-force Monte Carlo** provides an **unbiased estimator** and applies naturally to **non-uniform noise models**. Extending our approach to non-uniform noi
...(continued)Hi Craig,
Thanks for your comment! First, I definitely agree with you that single round circuits cannot represent real world circuits (They are not fault-tolerant due to Hook error)In our paper, we always use 3d rounds of repeated syndrome measurements, so we are confident that they are fault-
Hi Yijia, thanks for pointing out your very relevant paper! I'll look into it and include it as another example of "generalized Clifford operations" in the next arXiv version.
...(continued)We have updated our paper to give a streamlined proof of our main result: constructing approximate unitary designs in circuit depth scaling logarithmically in the system size. Our paper is now [published][1] in the Communications in Mathematical Physics.
[1]: https://link.springer.com/article/10.
...(continued)Given how negative this paper is about Monte Carlo sampling, I feel compelled to defend it.
The benefit of Monte Carlo sampling is not its speed. Its benefit is *being bullet proof*. There's no hyper-parameters for me to misconfigure, no tricky approximations to fool me, no subtle preconditions f
...(continued)How many rounds long were the circuits being tested? The prose reads like they are all single round circuits, but single round circuits are known to not be representative of real world circuits (e.g. the code capacity threshold of the surface code is 10x higher than the actual threshold). This is si
I don't see why the inequality $\sum_x \lambda_x^{\alpha} \geq (\frac{1}{rank(\sigma)})^{\alpha-1}\sum_x\lambda_x$ in lemma 5.3 would hold true. It holds untrue for example when $\lambda_x=\{0.02,0.03,0.04,0.45\}$ with $0.76<\alpha<1$.
...(continued)Dear Andreas,
Very nice work, I really appreciate the illuminating results on unifying Clifford circuits across different physical degrees of freedom.
I wanted to draw your attention to our earlier work on the rotor Clifford group, where we considered non-CSS Clifford circuits for rotor system
Hi Craig, thank you for pointing this out. We are currently working on upgrading this part, and we will let you know once a revised version is available.
...(continued)The end of Figure 13 would be more efficient if it only had one pipe touching the target wordline:
in--Z--out
|
|
T------Z-----(X or Y)In the above, "X" is an X type spider and "Z" is a Z type spider and "T" is an input state |0> + sqrt(i)|1> and "Y" is a p
...(continued)Part 2:
The first tenet of QBism is that quantum states are doxastic quantities. This is an interpretation that one can also apply to density operators on a Fock space, to states in a Type II von Neumann algebra, etc. The arguments for giving these entities a doxastic reading work just as well (or
...(continued)The paper states that QBism "requires a [probabilistic] representation that is not overcomplete". This is inaccurate. See, for example, [arXiv:2312.12790](https://arxiv.org/abs/2312.12790) and [arXiv:2412.13505](https://arxiv.org/abs/2412.13505) by Matt Weiss, or going further back, section 4.1 of F
...(continued)Additional note: We've very recently updated [our paper (v4)][1]. Specifically, I think you might be interested in our various attempts for approximating logical gap from a subset of logical classes, which was not very successful. New data for 'BP+LSD logical gap' and 'logical gap proxy' are added t
...(continued)Really interesting work! I'm glad to see an efficient, effective, and general post-selection strategy for qLDPC codes developed so soon after our work [18]. I think it is also worth trying to integrate cluster-stat-based and argument-reweighting-based strategies in some way (given that a clustering-
...(continued)Is there an introduction to the introduction? Newcomer here with just knowledge about Clifford circuits (without tensor language) and free fermions Hamiltonians. Seems very interesting to me from the point of view of the quantification of "something" that is hard to simulate efficiently (like non st
...(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
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