Recent comments from SciRate

Should probably have a reference to the original NMR experimental implementation: [Benchmarking Quantum Computers: The Five-Qubit Error Correcting Code
](http://dx.doi.org/10.1103/PhysRevLett.86.5811)

Thanks for your detailed comments. I'm now convinced that the questions addressed in your two papers are interesting, and I currently have nothing to add to the discussion of these questions.

The statement in your first paragraph is partially correct, but also misleading. Part of the problem is that the word "measurement" has too many meanings. For the present purposes, let us say that a measurement consists of what Peres has called a "premeasurement" (i.e., a unitary interaction that

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Okay, now I understand that equations 10 and 13 are mathematically different, where before I had not. Is it correct to say that one of your key points here is something like "one must always set aside a subsystem of nontrivial dimension to be considered as inaccessible / unmeasured?"

A view that I

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The equivalence relation you describe is the standard one given in equation (10). It is not quite the same as the one I am proposing to use, which is the one given in equations (12) and (13). You are correct that the crucial question is which observables are allowed. Your circuit-size criterion i

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In your title you suggest that we should quotient the state of density matrices by an appropriate equivalence relation. Is your equivalence relation exactly

$\sigma \sim \rho \iff \operatorname{Tr}(P_i\sigma) = \operatorname{Tr}(P_i\rho)$ for all
"projections" $P_i$ which are part of the spectr

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I'm happy to see that the bibliography I compiled for [arXiv:1703.07901][1] is becoming more and more out of date!

[1]: https://scirate.com/arxiv/1703.07901

https://qbnets.wordpress.com/2019/06/27/comments-on-quant-ph-arxiv1906-10726-quantum-causal-models-by-jonathan-barrett-robin-lorenz-ognyan-oreshkov/

Interesting work! Are the authors aware that there is other recent work which has formulated and examined the question of curing the sign problem from complexity and algorithmic perspectives: https://arxiv.org/abs/1802.03408 and https://arxiv.org/abs/1806.05405

Reference 2, which is used to define QBism, is to Caves, Fuchs and Schack (2002). This is an incorrect attribution; Caves does not call himself a QBist and disagrees with some turns that the other two authors made in the following years. (One migh

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Regarding your first point, the blocking strategy *can* be applied. See our reply to Earl Campbell's comment.

See the first sentence of the main text..

=> A similar block decomposition as in the stabilizer case can be applied. Namely, for a total of n copies of |H>, one can expand the first set of k copies with respect to the robustness of our paper, and the other n/k -1 sets of k copies w.r.t. the (stabilizer) robustness of magic. For such very r

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=> There is nothing else to consider for classical simulation of QC with magic states. There may a priori be Clifford unitaries, but they can all be propagated past the last measurement, conjugating the measurements in this process. The measurement statistics are the same, for instance, see [20]. F

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All of these results are for Shor's algorithms. More specifically, the results are for various derivatives of Shor's original algorithms. These derivatives are specialized for problems that are relevant in cryptography. They provide various constant factor improvements with respect to the number of

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How about using shor's algorithm?

Regarding your first point, I have had exactly the same thoughts. It seems that the "blocking strategy" cannot be applied to the Raussendorf et. al robustness measure and I would be interested if there is a different way of extending low-dimensional solutions. Simulating a quantum circuit with $n$ m

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Opp.... I wrote a reply yesterday but as a separate comment (see below). My main question is essentially the same as Patrick's above: these LPs are typically only tractable up to 5 qubits so you need some suboptimal method to perform larger simulations.

The last point confuses me somewhat: if I understand correctly your algorithm only supports potentially non-classical input states followed by Pauli measurements. How can this be used to simulate an arbitrary quantum circuit? With an MBQC approach, the initial state would have to scale with the size

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Thanks Robert for confirming those technical points.

I hope it is OK if I ask a few more questions here.

Regarding the classical simulation algorithm and the consequences of the non-multiplicativity of your robustness monotone. I am wondering what you are able to say about the negativity of *k

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Campbell writes: ``For odd dimension, we have that if ρ and σ both have positive Wigner functions, then ρ⊗σ will also have a positive Wigner function. I would expect any qubit counterpart of the Veitch el al result to also have this property."

=> We confirm that our phase point operators and Wign

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I agree that the construction lacks this 'nice' property under composition, but I would argue that this was expected... and is a feature rather than a bug. One of the main lessons I take from Angela Karanjai's paper https://scirate.com/arxiv/1802.07744 is that the phase space on which you define an

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I thought it worth flagging up that there remain significant differences between the qubit Wigner functions introduced here and those encountered in odd dimension. My impression from reading the abstract was that all these differences had been removed, but this is not the case. There are lots of

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Podolsky is like banana: One knows how to spell it, but one does not know how to stop.

Thanks! We'll add a citation. :)

FYI, there is a minor (but amusing) typo in the first paragraph: "Einstein-Pododolsky-Rosen" should be just "Einstein-Podolsky-Rosen."

Note for those working in quantum algorithms: the `random access quantum memory` (RAQM) implemented in this manuscript deals with addressing data in qubits, where the qubit index is selected by classical control. This should not be confused the `quantum random access memory` (QRAM), where a superpos

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There is a more recent article by Appleby, following up on the one that is Ref. 1 in your paper, which may be pertinent: arXiv:1602.09002.

Hi,

I have looked at the paper that you refer to: leakage, that is, the qubits are not in |0> or |1> but in some other state (say, the excited state |2>) are indeed very concrete issues that one has to deal with, as it makes getting error information unreliable ('silent stabilizer'). It then part

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Hi Mikhail,

In the paper you linked, the author addresses the possibility that the qubits may "leak." Qubit is often encoded in two lowest energy eigenstates of some physical system(e.g., transmon, ion, photon, quantum dot, etc.) but of course, the actual system can have higher energy states. If

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See the recent article https://arxiv.org/pdf/1702.07688.pdf. The author makes a professional analysis of errors and error correction (of which I am not capable) and his conclusions are worth considering

Thanks for explanation. The rotating frame will not help if all the energy differences are not exactly equal (equidistant energy spectrum). This very specific requirement will never be satisfied in any real system, where the time evolution will be chaotic. This is the general case.

See the recent

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If someone is interested, the earlier version is still available [here][1]

The pith stays the same but the new version strongly emphasises that we are faced with two alternatives for

> the relation between a physical theory T and the system of logic supporting inferences on T-propositions

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Sorry for not being clear: x would be an N-bit string and \sum_x \Psi(x) |x> is the state of the quantum computer after having applied some sequence of gates. In making my comment I thought about a physics analogy with x being the position of a particle, of course one can discrete this space and rep

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Wow, thanks! Those are some impressive typo-spotting skills! :)

> This might imply that multi-agent paradoxes are linked to the notion of contextuality

That is exactly the point of [Sebastian Fortin and Olimpia Lombardi][1] (but with the scope limited to the original F-R argument):

> the contradiction resulting from the F-R argument is inferred by making c

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I loved the remark that "Heisenberg in his later years expresses his appreciation of the mathematical side by claiming that it was his own work in the first place."

Subtle typo on page 3: "but new very little about matrices". And another on page 16: "change slowly in phases space". Also, "propert

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At section 5.1, second paragraph, it is mentioned that Optimal fitting flat must contain the mean of the point set. Is there a simple proof for this fact?

Barbara, I don't quite understand: what Is \Psi(x) and what is x, as applied to a quantum system with N qubits? Also, since you have mentioned **energy**, are oscillations of the quantum amplitudes in time with frequencies delta E/h taken into account?

Dear Mikhail,

the reason that quantum computing theorists have a different perspective has two aspects. First, one has to be careful in stating what we need to control. If we move from quantum computing to classical stochastic computing (from a Schrödinger equation to a diffusion equation), we re

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Hi Mikhail,

You are basically saying that the exact overlap between the ideal and non-ideal state decays exponentially in N. I agree with you on this but you are merely attacking a straw man here. Exponentially small overlap does not imply that you cannot do fault-tolerant quantum computation. No

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Dear Barbara,
I agree, and this is also my point: " **it cannot be said that the theory of quantum error correction and fault-tolerance guarantees that robust quantum computers will ever be built**.
As well as that **this is given by "the physics"**.

In particular the **quantum physics** which

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Dear Elizabeth, I fully agree with what you are saying.

Except that faulty gates are not the only source of errors. There are also unwanted interactions within the system of qubits, as well as between this system and the environment, and also because the initial state cannot be exactly |000...>,

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> It's not a complete analogy to the authentication game that Sandu has
> the parties play

Here's a closer classical analogy: Alice prepares an ensemble of classical bits. Each bit is random (determined by a coin toss) and, for some fixed partitioning of the bits into pairs, Alice writes down i

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Victory Omole, The Nobel prize was given "for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems."

Here "Individual quantum systems*" means individual atoms and individual photons, definitely NOT many-body quantum systems, as you apparently

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My comment was not so much in reply to Dyakonov's paper (i.e. a corroboration or refutation of his points) but rather a general contribution to the discussion.

I think we sometimes tend to respond to critics by rewriting their criticism into something more reasonable. Are correlations in the power spectrum of noise something that may be influenced by our gates and may await more experimental data and more theoretical insight? Yes, probably. Is this what

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Naturally, it cannot be said that the theory of quantum error correction and fault-tolerance guarantees that robust quantum computers will ever be built. One particular challenge is the ability to turn gates off and on: in almost all implementations this works by meeting resonance conditions which a

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Even without studying quantum information theory, there is an immediate way to see that quantum computation is more robust than classical analog computation. This argument is based on linearity. Consider a sequence of unitary operators $U_1 ,...,U_T$. For concreteness, each $U_i$ acts on two qub

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>My previous experience tells me that it is never possible to control a many-body quantum (or even classical) system on a microscopic level.

If your previous experience tells you this, then i encourage you to gain new experience because experimentalists have been controlling many-body quantum sys

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