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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.

S_6 is isomorphic to Sp(4,F_2) which is not the Clifford group on two qubits, only a quotient thereof.

Hey! Thanks for engaging!

Let me jump in on the fun.

In terms of Chae-Yeun's point 1 and Alex's point. I fully agree that "in a sense" is doing a lot of work but the aim of *that* paragraph was in a large part to point out the positive side of being able to often classically simulate/surroga

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Yay, I also want to join to the party and drop my opinions :D

Re-Re point one: My general feel is that we as a community should aim at being as transparent as possible. In the present case, we should do our best to not -- not even unintentionally -- sweep implicit assumptions under the carpet. C

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Hi Andrea, thank you very much for your message. We will acknowledge this work in the next version of the manuscript.

I would like to mention that ZNE on logical qubits was theoretically and numerically studied in this work: [https://arxiv.org/abs/2304.14985][1]

Having said that, it's great to see a real experiment! It shows that error mitigation will continue to help beyond NISQ.

[1]: https://arxiv.org/abs/2

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There's a nice paper addressing your first point on warm-starting [here][1], see, e.g., around Eq. (12); the authors show in a certain setting that where one has provable guarantees on good gradients in a warm-started region, you also can construct a classical surrogate model in that region.

For

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Thank you for sharing your nice perspective.

Here are some of my comments on Myth 4:

1. "While there have been a number of approaches that have been proposed to avoid barren plateaus, it has recently been argued that in all those standard cases (that can be proven to avoid them) the resulting

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Thanks a lot for the comment, Ruslan. We will update Table I. (As for the citation, I will have a look at this paper, and get back to you by email.)

I believe there is a typo in Table I. As of June 2024, Quantinuum H2 has 56 qubits (https://www.quantinuum.com/press-releases/quantinuum-launches-industry-first-trapped-ion-56-qubit-quantum-computer-that-challenges-the-worlds-best-supercomputers), not 30 as stated in the table.

Additionally, it m

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Thanks for spotting this, @Joe Gibbs. We will fix this typo in the updated version of the manuscript.

I believe there is a typo in the line under Myth 2: 'circuits of size $\mathcal{O}(\epsilon)$ can be executed without prohibitive overhead', this should be $\mathcal{O}(1/\epsilon)$ ?

Steve Flammia gave [a talk at QIP2024](https://www.youtube.com/watch?v=cUSV0unYHw4) that may be a gentler introduction than the paper, which is a big slab of very mathy math.

Dear Dominik and Gergely,

thank you very much for your highly interesting arXiv:2412.15912 on the relationship of stabilizer Rényi entropy (SRE) and T-doped Clifford circuits.

Here, I would like to point out our recent https://arxiv.org/abs/2406.04190:

- We show analytically that each T-gat

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This is basically using unary, right? I think the abstract should advertise a little more clearly that the energy cost is O(N).

Hi,

Yes, as you say, all these factors (circuit noise model, shuttling noise, etc) will further reduce the performance of the protocol over what is shown in the numerics. For these reasons we do not intend for the numerical performance values presented here to be taken as actual estimates of rea

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Hi Tom,

Thanks for the answer! I know it is difficult to estimate without the data, it was just to see if you had some intuition behind. For the conclusions I meant the bit where you discuss the overhead for $P_{ccz}=10^{−7}$, since the extra overhead required for the CLN case may inply that the co

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Hi,

Thanks for your interest. To answer points 1 and 2, it is difficult to estimate exactly how much of an effect a circuit noise model would have on the logical error rates for the JIT decoder due to the lack of data on this, and I wouldn't feel confident making any kind of guess. The decoder do

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Dear Authors,

This is a very interesting approach. However, I have a couple of questions regrding it:

- As far I see, the analysis for the new approach is done considering a phenomenological noise model. While you acknowledge that considering a circuit-level noise model will lead to requiring

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I have updated this paper to v2. The decoder is now much more accurate (25% more than Union–Find over the tested regime) and faster than before, due to a small modification I call the '2:1 schedule'.

Weyl fermions by definition cannot exist in 2 dimensions. Dirac fermions can, and those have long been observed (graphene).

I believe that such a Pauli correction always exists. This is reflected in Remark 3 of [arXiv:1910.09333][1]. My intuition is that one can find a basis for the $Z$-type stabilizers as $O_1, O_2, \ldots, O_r$ such that there exist (using a linear algebra argument on symplectic spaces) Pauli operators

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Thanks for the clarification! I agree that the result is unaffected by Pauli corrections.

However, my concern also has a more general aspect to it, namely, is it always possible to find a character vector (or equivalently, Pauli corrections) that satisfies the sign condition and make the quantum C

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Hi Shubham,

Thank you for your comment. Your observation is indeed relevant, and an X-type Pauli correction must be applied to map to the correct code space. However, in this case, the Pauli correction does not affect our final result. Specifically, in the example you mentioned above, the corresp

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Dear Markus,

Thank you for your answer, it really helps a lot!

As for the self-refuting mode of reasoning: yes, it is a much more general problem, and the accusal is perhaps a century old. "Nine to five" it is wise to make science as usual and leave such troubles for the evening, with hopes fo

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This is impressive work.

However, for a fair comparison against pytket you should have implemented the block encoding with the ripple carry adders aswell.

Also, your block encoding in pytket using the controlled QFT adder is sub-optimal because you do not exploit the conjugation structure in the Q

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Dear authors,

Great results!
Maybe I am missing something but I think equation (7) does not hold for all even CSS-T codes. For example: the $[[6,2,2]]$ CSS-T code mentioned in [arxiv:1910.09333][1] is an even CSS-T code by your definition but there doesn't exist any logical OP corresponding to $ T

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