Recent comments from SciRate

Anthony Polloreno Jul 27 2023 17:19 UTC

Haha, the mis-parsing of scirate doesn't help the fishiness. "Firs".

Jonas Helsen Jul 26 2023 19:00 UTC

So.. do we have any experts on high Tc superconductors around to comment on this? It smells pretty fishy to me, but this is not my neck of the woods.

Mark M. Wilde Jul 21 2023 07:55 UTC

A wonderful tribute to Göran Lindblad!

Seok Hyung Lie Jul 17 2023 10:55 UTC

Thanks for your answers. After reading a bit more, I also have a few comments:
When you defined the decomposition of $\Pi_\nu=\sum_n |\mathcal{E}^\nu_n\rangle\langle\mathcal{E}^\nu_n|$ on Page 3, I think you meant the order of non-decreasing local energies of $A$, not non-increasing. Moreover, since

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Patryk Lipka-Bartosik Jul 17 2023 06:23 UTC

Thanks, Seok! Indeed, Fig. 2(a) is missing in the arXiv preprint. We will add it in the next version. The missing figure shows a diagram of interactions between subsystems in the illustrative example, which hopefully should be clear from the form of the Hamiltonian in Eq. (8).

You are also right

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Seok Hyung Lie Jul 13 2023 09:10 UTC

Great work! But I think Fig.2 (a) is missing... (It refers to the "main text" in the main text so I guess something's gone wrong in editing?)

+) Also, I think the notation for the eigenstates of the local Hamiltonian $H_A$ is inconsistent; it is $|{i}\rangle_A$ in the beginning and it is $|\epsilon

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Josu Etxezarreta Martinez Jul 11 2023 07:33 UTC

I leave some references on considering the instability of the noise experienced by superconducting qubits which I missed in the article:

https://www.nature.com/articles/s41534-021-00448-5

https://www.nature.com/articles/s41534-019-0168-5

https://arxiv.org/abs/2207.06838

Definitely an int

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MariusK Jun 29 2023 15:48 UTC

Dear Joseph,

I see, the memory cost of the weights themselves is included too.
Thanks for the answer!

Joseph Bowles Jun 28 2023 14:43 UTC

Hi Marius, thanks for your question.

The memory cost of backprop generally does scale super-logarithmically with the parameters, but so does the forward evaluation.

To do the forward pass, you need to store all the weights of the neural network in memory. For the gradient computation via backpro

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MariusK Jun 28 2023 13:16 UTC

Great work!

I have a question about your Equation (5), the backpropagation memory efficiency: Is it true that the memory cost is essentially the same as for inference? If I remember right, for the forward pass in backpropagation, one has to store all the intermediate results after each layer in m

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Paul Skrzypczyk Jun 27 2023 07:32 UTC

Hi Dantong,

Thanks for the kind words about the book.

Just to clarify, the aim of the book is to demonstrate how semidefinite programming *may* be used broadly in the context of quantum information. As such, we picked a range of topics in order to try and teach the basics of semidefinite prog

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Once Upon Jun 26 2023 19:42 UTC

!["joker meme: to me a twisted quantum eraser is just a normal quantum eraser"][1]

Coming in with the meme, probably not the joke you expected for this abstract! ([Context][2], if unfamiliar with the meme format)

[1]: https://i.ibb.co/gzS8kM5/arxiv-2306-13620.jpg
[2]: https://knowyourme

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Dantong Li Jun 26 2023 02:28 UTC

very nice textbook! just a minor comment on measurement incompatibility, we proposed [an alternative][1] to quantify how incompatible two measurements are, which can be evaluated without solving a SDP. it makes perfect sense to introduce Joint measurability in the SDP textbook, but it does remain an

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Shu Kanno Jun 25 2023 06:13 UTC

Thank you for your valuable research. Your novel decomposition strategy for SWAP networks and the extension for using overcomplete sets of native gates represent significant contributions in this field. By the way, it is known that a fermionic SWAP can be implemented using two CNOT gates (please see

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Yu-Jie Liu Jun 23 2023 12:26 UTC

Thanks for sharing your results! The presented algorithm seems to be a special case of [Grover and Rudolph (2002)][1]? Or am I missing anything?

Best,
Leo

[1]: https://arxiv.org/abs/quant-ph/0208112

Rajiv Krishnkaumar Jun 15 2023 08:30 UTC

During the peer-review process, one of the referees from Quantum suggested a modification that was also a valid method and used fewer quantum resources. The main idea is to measure the remainder bits, flip biased coin based on the result, store the result in a bit and control the rounding on that bi

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Gokul Subramanian Ravi Jun 12 2023 13:04 UTC

Thank you! That's an excellent point - we will try to explore that further.

MariusK Jun 12 2023 07:53 UTC

Nice work!

Your strategy to only measure some output qubits at once and consider all such subsets reminds of the famous insight that global loss functions lead to barren plateaus, but can be replaced with sums of local loss functions.

Joseph Harris Jun 08 2023 07:39 UTC

Thanks very much for your comment; this is very useful feedback. We do discuss the potential to apply the work to the circuit model in the paper and to some extent this was our motivation.
However, you're certainly right that the protocol 'best' fits to photonics so we should try to draw more conc

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Josu Etxezarreta Martinez Jun 08 2023 06:59 UTC

Which is your motivation for considering fluctuating noise?

For example, it is known that relaxation and dephasing times do fluctuate for superconducting qubits:

- https://www.nature.com/articles/s41534-019-0168-5
- https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.090502

wh

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Ryan Babbush Jun 06 2023 17:06 UTC

Usually when constructing no-go criteria one starts from optimistic assumptions so that a pessimistic (“no-go”) conclusion can be reached whenever the criteria is met. However, this work starts from pessimistic assumptions. For example, when analyzing how VQE errors affect energy, a global depolariz

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Matty Hoban Jun 06 2023 07:34 UTC

You might want to look at https://arxiv.org/pdf/1301.1995.pdf - for one thing it shows you can get larger depth for other noise models.

Seok Hyung Lie May 30 2023 06:23 UTC

Thank you for your profound work.
I have a few questions reading through the first few pages.

(1) The notation for CP maps is a bit confusing; The dot product is defined to be the adjoint map on page 3, i.e., $A\cdot \rho := A \rho A^\dagger$. Does $E\cdot \rho$ mean $E(\rho)$ for $E\in CP(\math

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Craig Gidney May 26 2023 19:21 UTC

Based on TableS2 and Fig S5, the physical noise strength "p" that characterizes your device is approximately p=1%. Based on Fig1c, your simulations suggest that a noise strength of p=1% results in a postselected logical error rate of L~=10%. This value of L~=10% is 300 times worse than the L~=0.03%

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Zhian Jia May 26 2023 15:26 UTC

Hi Tianfeng. The doubled density operator (DDO) is different from PDM in several ways: (i) The PDM assigns one Hibert space for each event, the DDO assigns two local spaces for each event; (ii) The PDM is Hermitian but not positive semidefinite in general, the DDO is in general not Hermitian; (iii)

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Tianfeng Feng May 26 2023 14:22 UTC

Hi Zhian,
I'm a bit confused that your work seems to be the same idea as pseudo-density operator (PDM). Of course your math tricks are a little different but they have the same form. Maybe I miss someting... Could you tell me what is the iessentially difference between double density matrix and PD

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Varun Narasimhachar May 26 2023 04:09 UTC

Thank you for your thought-provoking work. May I take this opportunity to bring to your attention my preprint arxiv:2010.01167? There I make similar arguments in section V.D, although in my preprint I do not work out the technical details as thoroughly as you do.

Victory Omole May 24 2023 16:52 UTC

> Originally, quantum computers emerged as a promising platform to
solve certain computational problems that would otherwise be unfeasible to solve on classical computers.

This is true, but let's not forget that quantum computers were also originally studied for the potential energy consumption

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MariusK May 23 2023 19:41 UTC

The following papers also consider fast-forwarding and reversal of Hamiltonian evolution in quantum systems, and may be of interest:

https://arxiv.org/abs/2205.01131

https://arxiv.org/abs/2205.01122

https://arxiv.org/abs/1903.10568

MariusK May 23 2023 17:44 UTC

Dear Craig and Arthur, thanks for your answers, they are very helpful!

Matteo Lostaglio May 23 2023 17:05 UTC

Dear Ryan, thanks for the interest in our work!

Our comparison is between our query complexity upper bound and the best upper bound given in arXiv:2111.08152. For kappa=10^3 we have an effective constant upper bound of ~800 versus ~6023 given in arXiv:2111.08152 (Dominic told us the smaller numbe

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William J. Huggins May 23 2023 05:23 UTC

I only regret that I have but one Scite to give.

Arthur G. Rattew May 23 2023 05:17 UTC

Hi Marius,

I agree with Craig -- hopefully the following different perspective also helps.

Sorry for the confusion, when I said logarithmic difference, I meant logarithmic in the dimension of the Hilbert space, i.e. linear in the number of qubits being used in the computation.

Let $n$ be the numb

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Ryan Babbush May 23 2023 00:01 UTC

Interesting work! I want to note, however, that the bound you are comparing to from arXiv:2111.08152 (Costa et al.) was not meant to accurately give the constant factor except as an upper bound. When we've tested it numerically, we find that the actual constant factor is about five orders of magnitu

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Craig Gidney May 22 2023 15:12 UTC

Marius, you're thinking of the overhead in terms of gates instead of in terms of the area*time. Yes, error correction adds gate count overhead that grows linearly (or worse) with the number of qubits times the duration. But in terms of area*time, which is what actually determines the cost of buildin

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MariusK May 22 2023 13:51 UTC

Dear Arthur, thanks for answering my question!
Yes, you understood it right. :)

However, the statement about the logarithmic overhead is far from obvious to me.

I imagine an argument that goes like this: Let us say we have access to K parallel classical processes, independently of the input

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Arthur G. Rattew May 22 2023 03:43 UTC

Hi, thank you for your comment.

Yes, the opportunity cost arguments are more general than just for QRAM, they also apply to any error corrected quantum computer (and more generally, any quantum computer with active gates). So, it many cases it would make more sense to compare an $n$ qubit quantum

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MariusK May 21 2023 18:29 UTC

It seems to me that your arguments concerning error correction of circuit-based QRAM generalize to all quantum circuits. In particular, your Figure 1 seems to be a generic quantum circuit, not necessarily a QRAM.

I don't know much about quantum error correction, so I am wondering what does this

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Joe Fitzsimons May 20 2023 11:46 UTC

Craig, yes, I've been thinking about it concretely since seeing the paper and posting my initial comment. However, in relation to your comment on the consequences, I should say that none of that depends on QRAM (or QROM): the polynomial code allows for a finite number of transversal Toffoli gates at

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Craig Gidney May 19 2023 19:28 UTC

Joe, you should really do a numerical estimate of how well this address encoding idea would work, with a specific chosen code. I'd be interested to see the result. My guess is you'll find the constant factors just don't work out. But if it does work out, it's a big deal.

Suppose your technique wo

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Miles Stoudenmire May 19 2023 15:55 UTC

Hi Bibek,
Thanks for your helpful comments & sorry for the very slow reply. Let me reply to your two questions or points in reverse order.

(1) first of all, we think very highly of your experimental demonstration of Grover's and it's an important milestone in demonstrating how it can be done and

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Connor Hann May 19 2023 15:34 UTC

Joe: Yes, thanks for clarifying—you're right that the specific mechanism I described isn't actually an issue. On second thought, my statement was really just equivalent to saying that QRAM can easily propagate an error into (a superposition of) high-weight errors. I agree that with a proper code tha

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Joe Fitzsimons May 19 2023 00:01 UTC

Sam: Quantum polynomial codes allow for only a bounded number of transversal Toffolis which depend on the distance. If you choose the code distance large enough you can make it enough to support enough Toffolis to be able to implement the routing circuit. Each time you apply a Toffoli, it reduces th

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Sam Jaques May 18 2023 17:52 UTC

Hi Connor, that's a really interesting observation -- I would love to incorporate it (with attribution of course) into a revision of our paper, if you would allow it. The output register need not be explicitly encoded (for QRACM you can use an arrangement of X gates, e.g.) but your argument would st

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Connor Hann May 18 2023 16:39 UTC

Hi Joe, Sam,
I wanted to comment that this idea of encoding the address and only performing corrections between queries may have some additional subtleties—it’s not obvious to me that it’s quite so straightforward.

In particular, it seems to me that with this approach you should also encode th

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Joe Fitzsimons May 18 2023 16:19 UTC

I should add that I have not seen this approach in the literature, but it strikes me as a rather obvious one. As I think you realised in your second comment, you can make a Fredkin gate out of a Toffoli and two cnots (which are also transversal in polynomial codes), so you can implement the switchin

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Korbinian Kottmann May 18 2023 16:02 UTC

Making the code public would help putting these impressive numbers into context :-)

Joe Fitzsimons May 18 2023 15:01 UTC

Yes, that’s what I mean. It gives you the best of both worlds. Similar to gate level efficiency but for any finite QRAM you have an error correction threshold.

Sam Jaques May 18 2023 14:28 UTC

On further thought, I see what you're saying: transversal gates are closed under composition, and QRAM circuits can be built from Toffoli + X + ancilla, therefore the two cases I distinguished above are the same case.

Sam Jaques May 18 2023 07:05 UTC

Thank you for your comment. In our analysis of "circuit" QRAM, we assume error correction on the bucket-brigade, but we also consider "gate" QRAM, and different approaches to implement the bucket-brigade without fault tolerance on each node (specifically in Section VII).

We'll look into quantum p

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