Hi Oscar! Thanks for letting us know about your work. It looks very nice and relevant, and I'm sorry we missed it. We will be sure to cite it in the next version.
...(continued)In the [[10,3,3]] code (Fig. 8), let us write two sets of paths for πΜ β one with weight two and one with weight three. The operators of weight two commuting with the stabilizers are {π1 π3, π2 π4, π7 π9, π8 π10}. The operators of weight three are {π1 π5 π7, π3 π5 π7, π1 π5 π9, π3 π5 π9, π2 π6 π8, π
...(continued)Congratulations on this very nice result! On page 6 you say "To the best of our knowledge, this provides the first example of high-rate LDPC codes achieving the pseudo-threshold close to 1% under the circuit-based noise model." In https://arxiv.org/abs/2010.09626 and https://arxiv.org/abs/2308.03750
...(continued)Thanks for bringing this interesting article to our attention! There does seem to be a comparison between the thermodynamic algorithms we presented and these Monte-Carlo algorithms, because 1) both are nondeterministic, and can be seen as Markov processes, and 2) both can achieve O(d^2) operations a
...(continued)Hi Alex,
Thank you for your very important question! Though we do think a lot about this, we do not have a good theoretical handle on the QAOA behavior. Let me say two things.
First, the speedup we observe is not unique; Boulebnane and Montanaro ([arXiv:2208.06909][1]) observed a similar speed
...(continued)I am curious about how your results relate to the various Monte Carlo algorithms for matrix inversion and linear algebra. From a superficial skim, your algorithms seem to be a continuous time formulation of an MC algorithm for Matrix inversion.
See for instance
https://link.springer.com/conten
...(continued)Reaching+beating state of the art performance is great and certainly the most important metric, but is there a deep theory here *why* QAOA would be expected to do well here? Something about the geometry of the Hilbert space to naturally reflect the problem? I'd be curious to know, in the authors' es
The circuit qftentangled in Table 3 has 279 2Q gates, (typo in paper says 0). This will be fixed in next version.
:)
Hi Kishor, many thanks for highlighting this, we're looking forward to seeing your upcoming work.
Nice work. Awesome. Congratulations. I just wanted to point out that we also have one paper under preparation on hyperbolic Floquet codes :)
Here is the APS March meeting version.
https://meetings.aps.org/Meeting/MAR23/Session/N64.9
...(continued)Hi LC,
Firstly I would like to thank you for your interests in our work. Itβs great to see that you have applied some results of the QPP model in your work, and I would be certainly interested in reading the paper when itβs available!
Thank you for your valuable comments that help to clarify the d
...(continued)Hi Danial,
Thank you for your reply. We appreciate it that you take a look at our paper and discuss the differences of these two models.
For the bound condition, as LC pointed out (with thanks), we could simply replace the bound on coefficients 1-norm with the bound on the polynomial in our th
...(continued)Hi all, first of all, thanks to you both for amazing papers. These are really neat results, and look to be pretty game-changing contributions to the theory of QSP!
I just wanted to quickly make a pointβI've been using some of the results in the QPP paper in my own work over the past couple months
...(continued)Dear Zhan Yu,
Thanks for your message (I also received your email). I agree that your QPP model closely resembles our work, although at a first glance there seem to be a few differences such as the use of both $U$ and $U^{\dagger}$ in your method (leading to negative degrees in the trigonometric po
...(continued)Dear Danial and Nathan,
I would like to kindly point out that the generalized QSP model in this work looks pretty similar to the quantum phase processing (QPP) model proposed in our previous paper https://scirate.com/arxiv/2209.14278. The motivation mentioned in the introduction of this work also
Hi Patryk,
Thanks for clarifying! Glad that my comments were helpful.
...(continued)Hi Seok,
Many thanks for your comments and for spotting some unclear statements about our work! Also, sorry for quite a late reply.
In short, we agree with you that the current proof of Theorem 1 omits several important details. In the upcoming version we will add all the missing details.
Hahaha. Thanks Kunal - I should have then said that the original arXiv title doesn't help with the fishiness!
I think SciRate stores the original arXiv title, which had a typo. I updated it manually.
Haha, the mis-parsing of scirate doesn't help the fishiness. "Firs".
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.
A wonderful tribute to GΓΆran Lindblad!
...(continued)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
...(continued)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
...(continued)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
...(continued)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
Dear Joseph,
I see, the memory cost of the weights themselves is included too.
Thanks for the answer!
...(continued)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
...(continued)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
...(continued)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
...(continued)!["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
...(continued)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
...(continued)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
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
...(continued)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
Thank you! That's an excellent point - we will try to explore that further.
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.
...(continued)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
...(continued)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.121.090502wh
...(continued)Usually when constructing no-go criteria one starts from optimistic assumptions so that a pessimistic (βno-goβ) 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
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.
...(continued)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
...(continued)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%
...(continued)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)
...(continued)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
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.
...(continued)> 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
Braneshop, and
the US National Science Foundation.
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