Guang Hao Low Apr 23 2019 02:18 UTC

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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Blake Stacey Apr 21 2019 20:11 UTC

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.

Barbara Terhal Apr 18 2019 08:22 UTC

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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Isaac Kim Apr 18 2019 03:14 UTC

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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Dyakonov Apr 17 2019 15:13 UTC

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

Dyakonov Apr 17 2019 14:01 UTC

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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Wojciech Kryszak Apr 17 2019 08:59 UTC

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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Barbara Terhal Apr 16 2019 16:53 UTC

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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Terry Apr 16 2019 12:19 UTC

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

Wojciech Kryszak Apr 16 2019 08:42 UTC

> 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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Blake Stacey Apr 15 2019 23:00 UTC

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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sudipta roy Apr 15 2019 20:05 UTC

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?

Dyakonov Apr 15 2019 14:53 UTC

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?

Barbara Terhal Apr 11 2019 14:48 UTC

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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Isaac Kim Apr 11 2019 07:24 UTC

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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Dyakonov Apr 10 2019 10:12 UTC

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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Dyakonov Apr 10 2019 09:43 UTC

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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C. Jess Riedel Apr 05 2019 19:05 UTC

> 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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Dyakonov Apr 02 2019 18:41 UTC

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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Barbara Terhal Apr 02 2019 11:37 UTC

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.

Aram Harrow Apr 02 2019 11:06 UTC

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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Barbara Terhal Apr 02 2019 06:20 UTC

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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Elizabeth Crosson Apr 01 2019 21:56 UTC

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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Victory Omole Apr 01 2019 14:27 UTC

>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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Dyakonov Apr 01 2019 08:45 UTC

Dear Steve,

Thank you very much for your invitation and your friendly attitude! However it seems to me that we live in parallel worlds: the world of quantum information theory, which has a rather poor experimental support, and the world of physics, where the relationship between theory and experi

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Steve Flammia Apr 01 2019 00:58 UTC

Michel, you should come to a quantum information conference!

You may feel like your critiques have fallen on deaf ears, but that is not true. If we don't pay explicit attention it is because, as Aram and others have pointed out above, we feel that we have already addressed your concerns. I know

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Michel Dyakonov Mar 31 2019 19:01 UTC

OK, I have not studied these papers yet.
Let us return to this subject in 10 years when hopefully someone will manage to factor 15 by Shor (full Shor's algorithm, please, no cheating with the "compiled version".

Noon van der Silk Mar 30 2019 21:58 UTC

This is awesome!

Aram Harrow Mar 29 2019 15:39 UTC

One more thing. The fidelity between the actual and ideal states will be exponentially small but this is not a barrier to FTQC. The same occurs with classical memory.

The classical analogue of the fidelity expression you quote is: "What are the odds that all the spins in your hard drive are poi

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Victory Omole Mar 29 2019 15:36 UTC

That is some evidence it can be efficiently scaled up. You would have said the same thing if those experiments were not done at all; but the number and quality of qubits experimentalists encode fault tolerantly seem to be increasing with time and effort and there is no evidence it's going to stop.

Aram Harrow Mar 29 2019 15:30 UTC

This objection is a bit of a moving target. First there is the proposal that there is some reason that quantum computers cannot work _in principle_. Then when people respond by saying that this reason is (a) vague and unspecified and (b) contrary to accepted principles of locality in physics, the

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Aram Harrow Mar 29 2019 15:23 UTC

Of course there will be some undesired extra terms in the Hamiltonian, which we can call V. However, V is not a completely arbitrary $2^n$-dimensional matrix. We can expand it as
$$V = V_0 + V_1 + V_2 + \cdots + V_n .$$
where $V_j$ contains only tensor products of $j$ non-identity Pauli matrice

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Dyakonov Mar 29 2019 15:06 UTC

So far there is no evidence that this can be efficiently scaled up

Ashley Mar 29 2019 11:38 UTC

The good news is that some basic principles of quantum error-correction have already been demonstrated on existing quantum computing hardware, e.g. see https://arxiv.org/pdf/1806.02359.pdf and references therein.

Dyakonov Mar 29 2019 09:58 UTC

I would like to see an experimental realization of these ideas with a large enough number of qubits, say 10 -20

Isaac Kim Mar 29 2019 02:37 UTC

In quantum error correction we deal with this problem by actively performing error-detecting measurement and correcting the error. The measurement will be faulty in reality, but this can be dealt with by repeating the measurement; see Section IV of https://arxiv.org/abs/quant-ph/0110143 for example.

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Dyakonov Mar 28 2019 15:36 UTC

No doubt that the Schroedinger equation describes the evolution of the wavefunction, hence of its 2^N amplitudes. The problem is that in reality the Hamiltonian, and hence the evolution of the quantum amplitudes, can never be exactly what you would like it to be: H=H_0 +V. Also, the initial conditio

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Aram Harrow Mar 27 2019 14:29 UTC

The wavevector is determined exactly as the solution to the equation
$$\frac{d}{dt}|\psi(t)\rangle = -iH(t) |\psi(t)\rangle.$$
While the state has $2^n$ dimensions, those do not show up as experimentalist-tunable parameters in this equation. How many tunable parameters are there? Well, those s

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Dyakonov Mar 27 2019 14:22 UTC

"The only place where 2^N parameters appear is in the wavefunction, not in the Hamiltonian or Lagrangian".

- Certainly. As explicitly stated, I am talking about the wavefunction, which describes the **state** of the quantum system at a given time. You seem to agree that this state is generally d

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Aram Harrow Mar 27 2019 09:33 UTC

This argument lacks detail so it is hard to clearly refute, however one point is clearly wrong. A quantum computer, or quantum mechanics experiment, with $N$ qubits can be described by $O(N)$ or at most $O(N^2)$ parameters. This is because physical Hamiltonians are usually described by 2-body inter

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Wojciech Kryszak Mar 15 2019 13:22 UTC

Dear Blake,

The packing (i.e. the title) is catchy and eye-candy indeed and you are right to accuse the autors of over-selling the content.
At the same time, to be fair, we need to acknowledge their reservation: ,,accepting the photons’ status as observers'' is condicio sine qua non for the resu

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Blake Stacey Mar 14 2019 21:58 UTC

I don't think one can call an experiment an implementation of the Wigner's friend scenario if it's an experiment on photons. The essence of the thought-experiment is that quantum weirdness should apply to a sufficiently careful preparation of *an entire living, thinking observer.* If the "friends" a

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Blake Stacey Mar 13 2019 22:39 UTC

This paper draws a connection between "antidistinguishability" and Symmetric Informationally Complete measurements. One example of such a connection was already known, and it's a bit of a funny story. If you go back to Caves, Fuchs and Schack's "Conditions for compatibility of quantum state assignme

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Jacques Pienaar Mar 13 2019 18:46 UTC

Yes, I was aware of Rovelli's paper and my aim was to be loosely consistent with it, although the papers differ in that he is concerned with the entropic arrow of time, whereas I am mainly concerned with the causal arrow. It is a deep question what the connection is between the two, though the sugge

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Jacques Pienaar Mar 13 2019 18:40 UTC

Yes, well spotted! I made an error of omission in the definition of `layered'. It should include the proviso that "every path from an ancestor of X to a descendant of X is intercepted by a node in the layer containing X". That is what I meant, and it is assumed in order to carry out the proofs in th

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Mark M. Wilde Mar 12 2019 23:46 UTC

We welcome any and all citation requests, even those having to do with pop culture. Thanks for sharing :)

"Thauma" is Greek for "wonder or marvel":

https://en.wiktionary.org/wiki/%CE%B8%CE%B1%CF%8D%CE%BC%CE%B1

which preceded Pratchett by several millennia :)

We indicated this Greek origi

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Nicole Yunger Halpern Mar 12 2019 22:34 UTC

Love the idea! I'm surprised to see no citation of Terry Pratchett, though. https://wiki.lspace.org/mediawiki/Thaum

Marcel Fröhlich Mar 04 2019 10:52 UTC

Makes sense. Thank you Wojciech.

Wojciech Kryszak Mar 04 2019 10:38 UTC

Dear Marcel,

This condition is just for the ,,All'' face of their Janus-like theorem, and would $\Omega$ be indeed inaccessible, we would experience just the ,,Nothing''-face.

That is how I understand that.

BR,
Wojciech

Marcel Fröhlich Mar 04 2019 10:01 UTC

I struggle a bit with section 3.4:
"... if the experimenters are given access to an incompressible number (such as Ω) ...".

Isn't the point that exactly this is not possible, because numbers like Ω are not computable?