Thanks Hsin-Yuan Huang!
...(continued)Thank you so much for pointing out the typo in Eqs. (83)-(87)! Also, the rank condition in Eq. (78) should be replaced by "All eigenvalues of $O_i$ are $+1$ or $-1$". This is satisfied by all the explicit constructions we consider later in the section.
Now, the relation between Eq. (81) and the hyp
Thanks for pointing point.
...(continued)Interesting work! The separation between separable and entangled measurements is an old and underappreciated topic in quantum estimation theory (Gill and Massar https://arxiv.org/abs/quant-ph/9902063; see also Belliardo and Giovannetti https://doi.org/10.1088/1367-2630/ac04ca). People in that area h
Dear Changhao Yi, for the purpose of solving linear systems with the quantum walk, we need to show that there is no phase error either, see our appendix G. This is because we need to keep track of two states in a superposition, and there should not be a phase factor introduced between them.
...(continued)Dear authors：Thanks for mentioning our work in [27]. I think we are looking at a similar question. But our contribution is, sometimes even when ||U_T - U_T^A|| is large, in terms of fidelity, the discrete adiabatic process still works as the error can accumulate in the phase. The detail is in Sec II
How can the authors deduce hope for a lack of barren plateaus from demonstrating non-vanishing gradients for 4-qubit examples? Am I missing something?
...(continued)Dear Alexander, thank you for your interest in our work! This is indeed a typo, there should be no restriction on the parameter a here—I will update the arXiv version shortly, thanks for spotting this. In particular, there is no restriction on the functions that may be represented by the factorizati
...(continued)Dear authors,
today we talked about your work in a group meeting and stumbled across the HW factorization theorem (equation 6). We thought that there are holomorphic functions satisfying equation 5 which can not be represented in the way you proposed. Specifically, consider the function f(z) = z-
...(continued)Would it make sense to just make entanglement a free resource in quantum information theory? From a quantum field theory standpoint (entanglement harvesting), one could argue this is physically motivated. This would make a lot of things more natural, such as reversibility in entanglement manipulatio
...(continued)Ah -- that motivation is interesting! I've spent a lot of hours trying to do those integrals too. To me, that framing -- i.e., around understanding and demonstrating obstacles to doing the Bayesian integrals for pure-state or low-rank priors -- is more compelling than the current framing. That's
...(continued)Very true! And this is something that a couple others have also suggested, that I perhaps should make more clear in a revision. This paper was born from me initially trying to find an efficient closed-form calculation for Bayesian computations, and then determining that this was (modulo complexity a
...(continued)It is worth noting that finding the MLE or Bayesian mean/MAP estimate of a d-dimensional quantum state is only hard when the candidate states are restricted to a nonconvex prior. Finding the most likely *pure* state is indeed hard for arbitrary measurement records, but the hardness goes away if you
...(continued)Yes, we deal with entanglement in the usual way, by assuming that the underlying Hilbert space is bipartite -- separable but possibly infinite dimensional. I'm not sure how to define the theory of entanglement manipulation, and in particular the problem we are tackling here, without these basic ingr
...(continued)Just wondering, it seems like this work deals with infinite Hilbert spaces by assuming that they have a tensor product structure. Have you thought about what would happen if instead the Hilbert spaces were communitive? I'm not too familiar with how entanglement in these systems work, but this seem
Indeed, thanks for catching that!
Great work! I think there is a typo; before Eq.(17), "||X_3||_1=2" should be "||X_3||_∞=2", I guess.
Unfortunately there is a problem with making boundaries this way. There are space-time constant-size logical errors. An updated version will appear soon.
...(continued)Craig raises a good question. Measurement & feedback are really important. Although so far I am only familiar with a few examples (e.g. the 4T CCZ and friends) that were found by hand.
Currently, I think there is no general theory (not 1 paper that I know of) on how to formalize or solve the
...(continued)For the Pusey-Masanes experiment, one could consider the simple special case in which all measurement directions were the same (i.e., a1 = b1 = a2 = b2) . This special case does not lead to violation of the CHSH inequality, but is enough to reveal the conflict between results of Pusey-Masanes an
The algorithm assumes the input is a n-qubit unitary and the output is a circuit with gates from a universal gate set consisting of Clifford+non-Clifford gates. It does not consider measurement or classical feedback in the generating set.
Does this algorithm consider circuits that use measurement and classical feedback? All the state of the art constructions make heavy use of that now. Eg. does the algorithm find the 4T CCZ, the 6T CCCZ, and the 4n+-O(1) 2s complement adder?
...(continued)Regarding the conjecture from the old [samizdat](https://arxiv.org/abs/1405.2390): It wasn't directly about the number of free parameters needed to write a fiducial vector, but rather about the number of simultaneous equations that need to be solved. [Our 2017 review](https://arxiv.org/abs/1703.0790
This idea has been popping up in the literature quite a bit, mostly as a first step in some iteratively grown ansatz. See e.g. 2008.08615, 2009.10095 or 2102.05566
Disclaimer: I'm a co-author of the last paper
...(continued)Previous work 2101.07267 has already introduced the single-qubit rotation ansatz for MaxCut and presented its connection to continuous MaxCut, which delivers the hardness of VQA optimization. Moreover, 2105.01114 has done an extended study on this ansatz for MaxCut.
**Just to clarify:** I am not
I believe that is correct.
Hi Xin! Just to check you don't need a quantum computer for this algorithm, right?
...(continued)Thank Sergio for your comments.
1. Google's output bit-strings have more 0 bits than 1, so do not pass the NIST random number tests (failure in frequency test, run test, template matching test, approximate entropy test, and cumulative sum test). In that sense, the word "Non-randomness" is used. If
...(continued)For anyone interested in playing around with tensor network decoding I recently released the TN contracting algorithm used as a stand-alone Julia package: [`SweepContractor.jl`][1]. Also [here][2] is a link my TQC talk on this work.
[1]: https://github.com/chubbc/SweepContractor.jl
[2]: h
...(continued)It is wrong to write that the Google experiment has “Non-Randomness”. What this paper says is that the experiment is not perfect, but that is not a requirement for the claim of beyond classical computation. Similar differences from the perfect distribution are documented in our paper, for instance F
...(continued)Perhaps it is worth elaborating upon this topic a little more. Here is what Di Biagio and Rovelli call a "proper reformulation" of Pienaar's fifth premise:
> **An interaction between two systems results in a correlation within the interactions
between these two systems and a third one.** With r
...(continued)I had hoped this would clarify things, but after reading it, I'm more confused about what RQM is supposed to be than ever before. Part of the trouble is passages that I just can't parse, like their replacement for Pienaar's fifth premise (it's important enough to be in bold):
> An interaction betwe
The URL in citation [47] should be https://github.com/sflammia/ACES.
It's been [a good couple weeks](https://scirate.com/arxiv/2109.13018) for the Hoggar SIC!
...(continued)Roberts' claims are in conflict with:
Shankland et al. (1955): https://doi.org/10.1103/RevModPhys.27.167
In their statistical analysis, they find a signal.Consoli et al. (2013): https://arxiv.org/abs/1302.3508
They point out an error in a method Roberts used.Pliet (2021): https://doi.or
Thanks for the comment Thomas! I must apologize, a few important words "X-type" and "Z-type" were missing. I have updated the draft, hopefully it is more clear now.
I've gotten much more feedback than I expected, so a v2 of this is in preparation.
Here's a short summary of the main points: https://arxiv.wiki/abs/2109.10833
Dear authors,
how does this paper relate to the results of Ouyang et al.:
https://arxiv.org/abs/1910.06255 ?
An implementation of this algorithm is now available here:
https://github.com/QAOAKit/QAOAKitExample use: https://github.com/QAOAKit/QAOAKit/blob/master/examples/classical_algorithms_vs_qaoa.py
This dataset is now available as a pandas DataFrame here: https://github.com/QAOAKit/QAOAKit
Example use: https://github.com/QAOAKit/QAOAKit/blob/master/examples/Tackling%20open%20problems.ipynb
This dataset is now available as a pandas DataFrame here:
https://github.com/QAOAKit/QAOAKitExample use:
https://github.com/QAOAKit/QAOAKit/blob/master/examples/Transferability%20to%20unseen%20instances.ipynb
I wrote a short summary on the arXiv wiki: https://arxiv.wiki/abs/2108.12477
Thank you very much for posting the code that goes along with this paper. In your "Code and Data" section, you link to https://github.com/LBNL-HEP-QIS/activereadouterrors when it should be https://github.com/LBNL-HEP-QIS/ReadoutErrors.
...(continued)Indeed, thanks for clarifying this. Going a bit off-topic, let me briefly summarise the important points: Being a group is very restrictive for a unitary design, as e.g. there is a only one finite group $t$-design for $t\geq 4$ which is in dimension $d=2$ for $t=5$. For quantum info purposes, even $
...(continued)Thanks, Markus, for spreading the word about the Bannai et al. paper (I was very surprised by it when it was brought to my attention by Jonas Helsen). Just in case somebody reads this without having a look at one of the papers afterwards: Bannai et al. enumerate all t-designs **that are also finite
...(continued)Dear Markus,
Thank you for alerting us to Banai's work and your translation of the key implications for quantum information. We will modify the "folklore" statement in the introduction and add a statement that we provide an explicit, self-contained, and intuitive proof, which is useful because th
...(continued)As the authors point out, there is indeed some confusion in the community about why the distinction between prime and non-prime dimension is important when dealing with the Clifford group (and, in fact, the stabiliser formalism overall). In fact, one has to be very careful when dealing with the non-
Intriguing result! I'm curious as to the hint in the outline of the paper at the existence of a conclusion with "open research problems," but I can't seem to find it. Did it perhaps get left out? Or maybe the open questions got resolved by the final draft? :)
Braneshop, and
the US National Science Foundation.
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