Recent comments from SciRate

Link to github: [https://github.com/saforem2/l2hmc-qcd](https://github.com/saforem2/l2hmc-qcd)

Thanks for that reference. It relies on having a source of many copies of 3 different states. It is much closer to our model, but still seems not to answer the question.

Yes definitely different than the exchange interaction only work (though clearly the representation theory of the symmetric group is both our friend). But doesn’t this paper answer the question about the power of the model https://arxiv.org/abs/quant-ph/0503151 ?

This time no fisherman's story?

Thank you for the reference, btw. We used in our paper a particular encoding of a qubit as part of proving PostSTP=PostBQP, but perhaps the reference you mentioned gives another encoding that can be used as well. I need to look at it in more detail.

Hi Matt, yes, right, thanks for clarifying.

If I understand correctly, that paper considers unitary evolution under the exchange interaction with controllable time-dependent couplings. In particular, unitary gates exp(i J \vec S_1 \cdot \vec S_2), with J controllable. We consider only a much smaller set of operations: just measuring in s/t

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There are early papers which show that the SU(2)-invariant exchange interaction suffices for universal QC (and measuring in the singlet-triplet basis), see https://arxiv.org/pdf/quant-ph/0005116.pdf so would that work not answer the conjecture?

What a fantastically written review! Very much enjoyed reading this.

This has been an incredibly helpful guide! I very much recommend it.

Makes sense, thanks! In the future I expect we'll try to publish some more code for using and analyzing the THC qubitization approach via OpenFermion, in order to at least make that technique a bit more accessible.

I recently came across this interesting paper (and subsequent work by Aharonov et al. on quantum algorithmic measurements). I wonder if the idea (in this 1610.09619) is in any way similar to the theory in Higgins et al., Nature 450, 393 (2007) (https://www.nature.com/articles/nature06257), which als

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Hey Ryan, thanks for the questions!

(1) Here we considered _all_ of the electrons, including core electrons. It's true that core electrons are not the primary factor in determining the chemical bondings, and thus including them to calculate ground state energies is neither necessary nor the most

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Thanks for your thoughtful comment, Dave. You're right, my one-liner was not particularly considerate and constructive. I did have my doubts about posting it and I'm still not sure how to properly react to this paper. But I also didn't want it to go unnoticed.

What triggered me is the wide gap be

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Thanks for the message and setting the tone Dave. I completely agree with you and, speaking for the moderating team, we will aim to do a better job.

I've been thinking a lot about this comment (probably more than I should!) Certainly it's funny, "quant-hype" is a laugh out loud line. It reminds me of calling the US food retailer "Whole Foods" by the name "Whole Paycheck".

But I would also point out that if we want a community that is kind

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This looks like a very thorough study with multiple substantial contributions, especially on the error-correction side. I have two questions:

(1) Are you simulating active spaces here, like other prior fault-tolerant studies using molecular orbitals, or are you including all the electrons (includ

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I'm having trouble understanding the definitions of "reasonable" and "connected" given at the top of p.3 in this paper, maybe someone can help. The easiest, in order to clarify it, would be to say explicitly what is the graph $G_{supp(S)}$ for $S = Z_1$ and also for $S = Z_1 Z_2$ (in the example giv

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This should have been posted under [quant-hype].

Thanks to a careful reader (thanks to him!), we realized there were a typo in the affiliations: so no breaking news, Elham is not moving to Maryland ;-) I'm not sure how we missed that typo, but a v2 is waiting approval and should appear tomorrow to fix this.

Dear Ramis,

Thanks so much for your kind words. Thank you also for your insightful comments. Indeed, your beautiful work very nicely complements ours, in particular in the way you look at the asymptotic limits of large bond or physical dimensions. We have now discussed and cited your work in the

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Hello,

I wish I could understand it more...
so I have a question about Fig. 3 (Fig. 2 in New J. Phys.-version) and all the argumentation from p. 4 hinged upon:

What if the proces depicted is not about some particle decay, but about some fully (FAPP) deterministic clock-gun mechanism that is s

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Thank you for clarifying! The history of this subject is complicated by independent rediscoveries, different terminologies being used by different fields, etc. We wrote [a review article](https://scirate.com/arxiv/1703.07901) four years ago that is already in some respects outdated!

Dear Blake, thanks for pointing out that confusing statement in the appendix. In the statement, we were indeed referring to their choice of the tetrahedron. We will amend the sentence to reflect this, and also the fact that it was not introduced by them.

I'm a little confused by the statement in Appendix C that

> The second SIC-POVM used in this paper is the one introduced by Jiang et al.

From context, this doesn't appear to be referring to the specific method that [Jiang et al.](https://quantum-journal.org/papers/q-2020-06-04-276/) use (a Bel

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Probably a typo in the abstract: " In this paper, _we_ develop a method..."

Thanks for posting this! I was thinking along similar lines, though not nearly in organized enough a way to get anything written.

If I announced, "Instead of writing $a + bi$, now I will write ordered pairs $(a,b)$ that add entrywise and multiply like $(ac - bd, ad + bc)$," nobody would say that I

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I expanded on this comment in [arXiv:2103.09910](https://scirate.com/arxiv/2103.09910).

Does https://arxiv.org/abs/0912.4495 imply a very similar result?

For those interested, a related paper also hit the arXiv today on this topic: [_Experimental Characterization of Crosstalk Errors with Simultaneous Gate Set Tomography_](https://scirate.com/arxiv/2103.09890).

Our colleague Yasunari had a talk about this topic in March meeting session F32 from 2:23:23, so if you are curious, please watch the presentation! It is still available.

We discussed a similar concept in the paper uploaded to arXiv last October. We used quantum error mitigation for mitigating decoding errors due to failures of error correction and Solovay Kitaev approximation errors. Please check.

https://arxiv.org/abs/2010.03887

We discussed a similar concept in the paper uploaded to arXiv last October. We used quantum error mitigation for mitigating decoding errors due to failures of error correction and Solovay Kitaev approximation errors. Please check.

https://arxiv.org/abs/2010.03887

Sorry for the inconvenience, it's now updated.

Consider chiral tokens and twist odd number traversals (e.g., Berry phase)

Multiple slit matterwave interfere a homochiral molecular beam. Assay the (if any!) interference pattern enantiomer ratio. Hund's paradox: 100% |Left⟩ shoes entering Schrödinger's box exit 1:1 |Left⟩ plus |Right⟩ racemize

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The code repository that this paper references is [empty][1].
[1]: https://github.com/ElieGouzien/factoring_with_memory

Dear all,

We are excited to see this paper! We would like to point out that complementary results were obtained previously ([arXiv:1909.11769][1] and [arXiv:2004.14397][2]). In particular, an application of these two works is to the non-translationally invariant Ergodic MPS, which vastly general

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"we have generated one million ***correlated bitstrings with some entries fixed***." So one 'independent sample' from a single (nicely opened!) tensor network contraction?

To your last point: It is not known whether the actual performance of future quantum computers would scale adequately to maintain quantum supremacy over this classical algorithm.

Towards the bottom of this paper, it says:
> At the same time, our experiments also reflect that Google’s hardware has several advantages over our algorithm. The most significant one is that Google’s hardware is much faster in sampling the quantum circuits with sufficient depth, while our algorithm

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I think this paper would be improved by mention of the Horodecki's p-bits, which are really the right way to define secrecy from in environment in the quantum setting

I think indeed the main issue is the dependence on the confidence level. In Corollary 3 of our paper, as you mentioned, in order to achieve $1-\delta$ confidence level we only need a $\log(\delta^{-1})$ overhead, so the dependence is very weak. In the textbook version of QPE there is a linear $\delt

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Actually, indeed textbook PE https://arxiv.org/pdf/quant-ph/9708016.pdf does not reach Heisenberg scaling as the total simulation times T scales as T \sim 2^m where m is the number of bits in phase and I think m has to partially scale as like log(1/\delta)=log(1/\epsilon^2) where 1-\delta is confide

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I agree that MSE is the right quantity (only equal to variance if estimator is unbiased) and I agree with your choice of delta. So in Corollary 3, M has a dependence like \log(\epsilon^{-2}||H||) and you are saying that this only leads to a polylog(\epsilon^-1) factor in the total evolution time so

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The reason we can do this in our paper, but not in the setting of 0709.2996, is that they did not assume the error to be bounded. However in most Hamiltonians we care about it is straightforward to obtain a bound on $\|H\|$ that is polynomial in the number of qubits, so we think this is a reasonable

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Hello Professor Terhal, thank you for this very nice question! First as you correctly pointed out, we assume we start with a quantum state that only has a non-trivial overlap with the ground state, instead of the exact ground state. With this assumption a lot of phase estimation methods, such as the

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Hi authors, interesting results! How does your work relate to Heisenberg-limited scaling in Theorem V.1 in https://arxiv.org/pdf/1502.02677.pdf in which one bounds the variance of the estimator. You write that your error is epsilon (which you get with high probability in Corollary 3), but this is no

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Thanks for the question! Yes, we assume perfect free-fermion states. Also, we only require measurements in the standard basis, and we assume that they are performed without errors.

Thank you for sharing your paper on Fermion Sampling! Yes, based on your results, it appears that we wouldn't be abl

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Very nice paper!

Does the result assume perfect free fermion states or some imperfection is allowed (say in trace distance)?

I also wanted to remark on two of the open problems stated in the end of the paper.

1) Learning pdfs corresponding to superpositions of free states.
I think that it is u

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Is this a monotonic (aka non-increasing with respect to quantum channels) distance measure?