What is the number of qubits for the numerical simulations? Reads like it is one fixed number but certainly that cannot be the case?
Thank you for your kind and detailed reply!
...(continued)I think this is a fair question! We were guided to our construction by considering the XZZX cluster state, but that doesn't mean this is the only way to understand our construction.
Certainly, in the case of the 4-star construction, there *are* no qubits that correspond to the RHG/XZZX cluster stat
...(continued)Very interesting work! May I ask you a small question? I think the idea to confine erasure errors caused by failed fusions on 2D planes also can be applied to the normal Raussendorf's lattice. In other words, we can freely choose the fusion basis (two distinguishable Bell states) for each fusion so
Thanks for the reference! This seems to be exactly the same result, but obtained in a slightly different manner.
...(continued)Very interesting result! A quick question on the unitary permutation inversion problem. I think this unitary permutation oracle was studied under the name of the in-place permutation, and a similar result was shown in https://arxiv.org/abs/1510.06750, Section 3.2. Is there any difference between the
...(continued)I thank for the comments of Jan Eisert, whose survey on the area law btw. has been a very illuminating work for me. Let me address the points made:
1. Indeed, the two papers look at different NPO (NP-Optimization) problems. To understand the NPO landscape, here is somewhat of a background. The t
...(continued)Nice work. I am not well versed with the literature in the field so I am a bit confused; Is the result that a unital qubit channel can be expressed as the average of 4 unitary channels (Theorem 3.1) new here? I think one can derive it from Corollary 1.3 of [arXiv:1802.01337][1] and that the set of
...(continued)We are excited to see that Mario Szegedy as a leading expert on the PCP theorem has looked at the problem that we lay out in our work arXiv:2212.08678 and has suggested an alternative proof of a similar statement as we present it in our work based on the PCP theorem. With this note, we would kindly
...(continued)Apologies for a bit of shameless self-promotion, but I wrote a paper on the connection between the Loschmidt echo and quantum metrology back in 2013: https://doi.org/10.1103/PhysRevA.88.021801, which is a bit earlier than a lot of the papers cited here, e.g., Macri, Smerzi, Pezze, "Loschmidt echo fo
Minor but annoying errata: the future work section has the placeholder text "[reference to jupyter]" instead of an actual reference to the notebook.
...(continued)The [web of science journal indexing][1] database indexes each article in journals. HIGS has a complete list of [Web of Science Journal list][2] . Get connected with our team now and download the list. Our team also provides so many free add-ons. [For More Information][3]
[1]: http://higssof
...(continued)I leave some references on Time-varying quantum channels which I missed in the article (I know I am the author of those, but there is little literature on the topic):
https://www.nature.com/articles/s41534-021-00448-5
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.105.012432
https:/
...(continued)You write "the linearity of $H_{i,j}$" (penultimate paragraph). I think that should read "the existence of $H_{i,j}$"; the thing that is linear is the map. But a map from density matrices to probabilities is linear if and only if it can be written as the trace of $H \rho$ for some $H$. If your main
We have written a response which can be found here https://scirate.com/arxiv/2212.03629
Yesterday's Quanta magazine article on this: [link][1].
[1]: http://www.quantamagazine.org/after-a-classical-clobbering-a-quantum-advantage-remains-20221207/
...(continued)Note that Problem 1 of Appendix C is equivalent to the construction of a perfect [Golomb ruler][1] of length $m$. This problem admits no solution for $m \geq 5$.
We discuss some implications of this for the Fourier spectra of quantum models in ([2209:05523][2]).
[1]: https://en.wikipedia.
...(continued)In Fig. 4, it looks to me like the three logical qubits could be described by the following pairs of logical $Z$ and $X$:
* $Z_1 Z_2$ and $X_1 X_5 X_9$;
* $Z_3 Z_4$ and $X_1 X_3$;
* $Z_7 Z_8$ and $X_7 X_9$.From these it seems that the code is in fact distance 2, rather than distance 3.
Am I miss
Ah I see. Thanks for your reply!
...(continued)Thank you for your question. Because the error of our scheme is larger than what we need in the hardness conjecture of that paper, our result does not contradict the conjecture.
Please refer to AA's original boson sampling paper, where a similar thing happened for the permanent and Gurvits's algorit
...(continued)Hi, amazing work! I was wondering if your results would affect the structure of proof in [https://www.science.org/doi/epdf/10.1126/sciadv.abi7894][1], which is based on the conjecture that |Haf|^2 is #P-hard to approximate to within *additive* error (Conjecture 2 in the paper)? Thanks!
[1]: h
Amazing work! Look forward to reading it in more detail!
...(continued)Thanks for the nice question. In this framework, in the simplest case, we have two systems (the main system and the heat bath) coupled by an energy-conserving interaction. Therefore, any change in the energy of the system
is equivalent to the same (with a minus sign) change on the bath (therefore
I really like your axiomatic formalization!
One suggestion, though:
I would rename "efficiency" to "faithfulness".
...(continued)Thanks for the reply. I have a small question content-wise. Is there no distinction between work and heat in this framework? It seems like all the energy influx into a system is counted as 'heat', but I think somehow work can be exchanged too between systems with different temperatures through a ene
Thanks for the comment. You are right. The second statement about heat flows should be just as you wrote, i.e: "heat will flow from the environment". The right statement is captured by Eq. (5).
Thanks for mentioning the typos. We plan to update the arXiv version soon; We'll get rid of them :)
Classic work establishing, among other things, equivalence between establishing high entanglement fidelity and low diamond-norm error. However, the arxiv version has an incorrect proof of this fact (Thm 1 in section V.A); see the IEEE IT version for the correct proof.
...(continued)Nice work. I am still reading the paper but I think "Heat will always flow towards the environment " and "the environment will always absorb
heat" on the first page mean the same thing. It seems like the second sentence should say that the heat will flow from the environment as it is hotter than $\r
...(continued)The proof that the stoquastic local Hamiltonian problem is in AM also applies to stoquastic Hamiltonians that are sparse, but non-local. On [page 5][1]:
"Moreover, we will prove that evaluation of the largest eigenvalue of any n-qubit non-negative matrix whose matrix elements are efficiently co
...(continued)I see. We are no experts in the technicalities here so we will correct the section here accordingly. I believe MA is correct since the Hamiltonian corresponding to a graph is frustration-free. But we will need to clarify this.
All we were trying to say (and the gist this holds) that the algorithm
...(continued)Thanks for this interesting result, but I am confused about the discussion regarding stochastic Hamiltonians (on Page 7):
> The problem of calculating the ground energy of stoquastic local Hamiltonians was shown to be contained in MA by Bravyi, Divincenzo, Oliveira, and Terhal [BDOT08].As far as
We updated our paper. In the new version (ver. 2), we removed an unnecessary assumption, which rarely holds in general as pointed out, and further improved Theorem 1. We mentioned the comparison of the performance of our decoder with previous ones as an interesting future problem.
...(continued)Nice work on superchannels. However, I have a simple question about the motivation of studying QSCs. Superchannels are naturally characterized by the requirement that they should map bipartite quantum channels to bipartite quantum channels even if they act on one party of the channel. On the other
...(continued)It might be worth saying more about the implementability of your encoding $R_f$.
Your Figure 1 (b) seems to suggest that one needs over 50 orders of magnitude of precision.
You mention that this leads to numerical instabilities.
However, I am more worried about experimental implementations in act
...(continued)It seems to be a nice clash between you and Nicolas - a lot to think about, thank you (both)!
> Wouldn’t we be more free if we can determine our next decisions
> based on how we are now, rather than letting them at the mercy of
> randomness?My nearest next decision is just almost now so I
Thanks for the clarifications, and for the nice paper!
...(continued)Hi, thanks a lot for the reply! Our paper’s results mainly differ from them as follows:
- In the two papers you mentioned, the authors consider the *exact* tensor contraction of the *approximate* QFT (AQFT) on product inputs and outputs. Specifically, they are simulating $\langle x| C |y\rangle$,
How do your results relate to, [arXiv:quant-ph/0611156] and [Phys. Rev. A 76,
042321 (2007)]? On the surface, the conclusions look quite similar.
...(continued)Interesting paper! One point: I wouldn't say that current quantum NNs don't have inductive biases; my paper on QRNNs (https://arxiv.org/abs/2006.14619) has a circuit designed to mimick latent state read and write operations; as well as many circuits used in the context of many-body Hamiltonians feat
Thanks for letting us know a relevant paper. We have not compared our bound with yours. We will have a closer look and write you back.
Have you compared your new bound to those of equation (153) of https://arxiv.org/abs/0907.3386? Note that this is NOT the Petz map, and furthermore the gamma quantities do not involve anything at all similar to a petz map.
...(continued)Thank you for pointing it out. You are right, the basis $F_{\diamond}$ satisfying our condition rarely exists unless $E$ and $F$ are already MUBs.
We will update the paper soon, but we would like to mention here that our main message is still valid: $\Delta_q$ is bounded by $\Delta_{cl, E}$, $\De
...(continued)To put this another way, choosing the computational basis to be the $F$-basis , equation 12 and the one directly above it say that the vectors in $F_\Diamond$ are formed by rescaling each coordinate of each $E$ -vector (by a positive real number multiple) to have magnitude $d^{1/2}$.
However the
...(continued)Unfortunately, there a bug in equation (12), which overdetermines the phases of the coordinates of the mutually unbiased basis F_diamond in the F-basis.
Since generally there is no MUB satisfying all these phase conditions, the decoder of Theorem 1 does not exist for most bases E and F in dimension
...(continued)Contrary to the author, I certainly don't know that I or anyone else has free will. I just know that I exist as I keep experiencing things. I can't even imagine how free will would work. One would first have to define free will in a coherent manner to have a meaningful discussion about it. What exac
...(continued)The basic suggestion of "maybe we can combine economics with gauge theory" is at least as old as a 1994 essay by Lane Hughston, better known to physicists for his work on [density-matrix decompositions](https://en.wikipedia.org/wiki/Schr%C3%B6dinger%E2%80%93HJW_theorem):
L. P. Hughston (1994), "S
...(continued)Hi Robert
I fully agree :). Indeed high weigh Paulis are an "expensive" observable for classical shadows in general as they have exponential sample complexity in all three depth regimes. Nevertheless, the sample complexity can be orders of magnitude different depending on the choice of depth used
Hi there is an error on Figure 1. Your logical Z doesn't commute with one of the stabilizers.
...(continued)Hi Hakop,
Thank you for the prompt reply! That makes the advancement much clearer!
To summarize, for the computational task (1), the efficiency in your work refers to the fact that one can compute the estimated value of any linear combination of $\mathrm{poly}(n)$ general Paulis from classical sha
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the US National Science Foundation.
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