...(continued)Thank you for an interesting work and citation of our paper!
I'm reading your paper and noticed that our work is described as "Qubit and gate resources required for Trotterized Hamiltonian simulation algorithms of fully local Hamiltonians (without intercell interactions) have recently been investiga
...(continued)For an article whose title starts with "the battle of clean and dirty", and about barren plateaus, I felt compelled to make a meme with this classic template! I hope you enjoy! (Please understand that I'm not trying to make any religious statement here :) )
![a meme of Jesus and Satan fighting ab
...(continued)This paper for studying the optimality for collective measurements seems very interesting. One of the nice points of this paper is to apply error mitigation for metrology; however, our paper has already proposed error mitigation to metrology .... but it is not referred in this paper. Our paper demon
This paper of Hilary Carteret
https://arxiv.org/abs/quant-ph/0309216
already put forward the method given, for estimating the moments of the partially transposed density matrix of a bipartite state. It does not appear to be cited in the manuscript.
...(continued)This is a cool result. The Glynn-Kan operator looks correct, which is really neat because it formulates solving the matrix permanent in terms of the expectation value (over the uniform superposition of **2N** qubits) of a diagonal 2-local Hamiltonian with **N^2** terms, which is straightforward to s
...(continued)In order for this result to actually efficiently solve a #P hard problem, this result just needs to be able to approximate the permanent for any real matrix within *any* relative error. This is due to Corollary 6 of https://www.scottaaronson.com/papers/sharp.pdf.
If I recall correctly, the JSV al
Your answer is very clear!! Thank you very much, and this result is very interesting, and I will read this paper!
...(continued)Hi Suguru, thanks for your question! We find exponential concentration of observables, as in a normal noise induced barren plateau. However, in our setting now the exponent is now rescaled by the ratio of the number of noisy qubits to the total number of qubits. So indeed this can be thought of as m
Thank you very much for a very interesting work! Does this work help the mitigation of noise induced barren plateau, i.e., the base of the exponential concentration of the observable is reduced?
...(continued)Hi Steve, thanks for your comments.
Regarding your second concern:
This is addressed by the "Ising-type" recovery dissipators we define,
which have the form $aP$ with $a$ being the annihilation operator on a
given site and $P$ being a projector on a particular configuration of
domain walls surroun
...(continued)I guess I have two concerns. First, it seems that to get a mathematical threshold requires taking $N\to\infty$. This fact does not say anything about finite-size scaling (as you point out), but it does mean that this proposal requires infinite energy density to have a true threshold. If infinite ene
...(continued)Actually, our experiment and analysis goes up to 16 qubits, not 8 qubits, and uses a million measurements. Your paper estimates the number of measurements for 16 qubits at about 1e8, two orders of magnitude more pessimistic than what we found.
The quote I selected from our appendix mentions a certa
...(continued)Hi Steve, Thanks for the comment. While $N\to\infty$ is the ideal limit, the logical phase-flip error rate is exponentially small in $N$ so that for practical purposes $N$ might not need to be too big to achieve the desired level of accuracy (such as for a single cat qubit experiment). Similarly, we
...(continued)Ryan, mostly in the main text you write "...we propose a **scalable**, noise-resilient..." and "...the flexibility and **scalability** of our proposed approach..." etc. The emphasis on scalability certainly pervades the whole article and it's one of the main selling points. The appendix does not rea
This construction achieves self-correction by requiring the mean photon number N → ∞, which costs infinite energy per subsystem.
...(continued)In Appendix F we write: “Therefore, as the system size increases towards the thermodynamic limit, we would expect that QC-AFQMC formally requires exponentially more measurements to maintain the relative precision”. I’m sorry if you found that statement unclear (the point of that appendix was to eluc
...(continued)Several points of clarification are in order here:
1. We believe that referring to general computational complexity arguments to explain the intrinsic lack of scalability of a given algorithm only obfuscates the discussion and introduces further elements of confusion in the field.
The issue
...(continued)The challenge referred to in this paper was first identified and discussed extensively in the original text by Huggins et al. - see, e.g., Appendix F. Although there are some differences, the problem is similar in spirit to the vanishing of initial state overlaps when preparing ground states via qua
Minor typo - de Beaudrap is spelled wrong in your abstract! Thanks for posting!
A previous construction of so-called "dual unitaries" from biunimodular functions appeared in
https://arxiv.org/abs/quant-ph/0306144. (See Theorem 7 and the discussion in section 4.)
...(continued)Hi Johannes,
Sorry for the delay in responding -- this has been a busy period for both Bálint and myself.
We appreciate your input, and will certainly address these points comprehensively in an updated version of the paper.
Additionally, we will reach out to you to ensure that our comment
The approach of Jerrum/Sinclair/Vigoda is restricted to matrices with non-nonnegative entries. My understanding is that this is viewed as an "essentially easy" case, no? Joonsuk Huh's algorithm would be more exciting to apply to matrices that include negative entries?
The claim made in the final sentence of this abstract is not substantiated by any available evidence. This sort of hype is detrimental to the quantum computing field and should be called out, especially when it is difficult to believe such claims are made in good faith.
...(continued)Thanks a lot for your quick answer!
Regarding the normal distribution, I think there is a difference in the meaning of $N=2^n$ in our papers; for you it appears to be the resolution over a fixed domain (if I'm not mistaken?), whereas in 2009.10709 it is an absolute coordinate. This means that in
...(continued)Dear Johannes,
Thank you for your comment. The black-box state preparation techniques you have referenced are quite interesting and will certainly be useful in practice!
In the following, we assume that $n$ is the number of qubits, and $N = 2^n$ is the resolution.
First, our query complexi
...(continued)Dear Arthur, dear Balint,
Really interesting paper, thanks! As Craig I have a question regarding your technique's efficient, namely in comparison to known black box state preparation tasks, for instance 1807.03206, 2009.10709, and more recently 2105.06230. (1) and (2) are of the same nature; (3)
...(continued)In https://dl.acm.org/doi/10.1145/1008731.1008738 it is shown how to classically approximate within polynomial time the permanent up to some given error epsilon. The trick there is that the time dependence is on poly(1/epsilon). If the time dependence is poly(log(1/epislon)) then the problem becomes
...(continued)We refer to the algorithm as *quasi-deterministic* because (for analytical convenience) we only proved our error-bound using a single outcome of the measurement of the ancillary register (which happens asymptotically with probability 1), and assumed that we rejected all other outcomes. However, in p
...(continued)Ah, the deterministic aspect is important in some chemistry algorithms based on PREP+SELECT oracles. PREP is a bit poorly named because it has to run in contexts where its input is not all reset qubits, in order to maintain coherence during amplitude amplification. You would want to have very good c
...(continued)Hello Craig,
Thank you for your question.
While rejection sampling adds an ancillary qubit to an initial state and applies conditional single-qubit rotations to it (such that after measuring out the ancilla qubit the desired state is obtained with some probability), we go all the way and devi
What are the advantages of this method over rejection sampling, which also scales inversely in the filling ratio and requires one call to the oracle per attempt?
Ah, that makes sense. Thank you for the detailed answer. I will try Qermit out!
...(continued)Hi Victory, many thanks for your message! Mitiq is great, and you're quite right that it breaks down the implementations of each protocol. In the case of Mitiq this could be seen as a result of the attentive development of the software. In the case of Qermit this breakdown of protocols into submodul
Thanks, Lorenzo, for your reply. That makes sense, and I fully agree with everything you say :).
Maybe it's worth to stress that point then: your result applies to *families of states* that are defined by their amount of magic rather than individual states, correct?
...(continued)Thanks for this package! The paper says
> Qermit is complementary to Mitiq [23], which is an opensource Python toolkit that implements an overlapping set of error mitigation schemes. Qermit takes a different approach that
breaks-down the implementation of each protocol into standalone modular un
...(continued)Dear Dominik, happy to hear from you. We are sorry for the late response.
The answer is yes and no. From the one hand, what you say is true. You can perform direct fidelity estimation on the state $(U_{1}\otimes\ldots U_{n})|\psi\rangle $ by expanding the fidelity between the theoretical state an
...(continued)What is referred to as "dual unitaries" was previously called "maximally entangled unitaries" in https://arxiv.org/abs/quant-ph/0306144, and more such operators were constructed there from biunimodular functions. They are maximally entangled in the sense of Mike Nielsen's operator schmidt decomposi
...(continued)Hi Lorenzo, Salvatore and Alioscia,
consider an $n$-qubit stabilizer state $| \psi \rangle$ with stabilizers $S_1,\ldots, S_n$. Then the state $U | \psi \rangle$ with $U = U_1 \otimes \cdots \otimes U_n$ for *arbitrary* single qubit unitaries $U_1, \ldots, U_n$ is stabilized by $U S_1 U^\dagger
...(continued)*I've removed the text of this comment, because it addressed a prior comment that has since been deleted. Absent the prior comment, there is no need for my words to appear here. However, I've chosen not to delete the comment entirely in order to leave a record that there was once a discussion here
Comments are welcome!
...(continued)This is an interesting development!
Up until this point, it has seemed to me that while the RQM literature endorsed up front a strong form of relationalism, when one dug into the details, the writing backed away from it. For example, measurement outcomes were treated as relative to an observer, b
Hey Hong-Ye, yes thank you for the reply!
Hi Jerome,
Thank you so much for the additional references! We will include these works in the next update.
Best regards,
Robert (Hsin-Yuan Huang)
...(continued)Very interesting! Regarding Section III.G about variational quantum-classical algorithms, it could be worth mentioning grouping methods that are not directly related to randomized measurements. Indeed, these methods seem to outperform classical shadow methods in several examples. See Fig. 3 in http
I enjoyed this paper! One question, on equation (3) and the immediately preceding definition of P_n(U), is the a_n supposed to be a_{n+1}?
...(continued)Hi Tom, thanks for your interest. In the second case you mentioned, it is still a $[[N=nk,k]]$ error correction code.
If one uses global Clifford group for shadow tomography, the sample complexity for predicting O scales as the rank of operator, here it would be P*O, where P is the projection op
...(continued)Really nice! One thing I'm not sure about after reading is whether the $k$ in the $4^k$ in the bound for sample complexity refers to either:
1. the $k$ in the stabiliser code definition i.e. $[n,k]$ indicates you can encode $k$ logical qubits in $n$ physical qubits.
2. The total number of logi
Hi,
I found your work quite interesting and original in the way you change the storage of an operator. Maybe you would be interested in this somewhat similar work, that also works for weakly dissipative bosonic systems https://arxiv.org/abs/2102.04265 (see appendix I.5 and figure 6)
Best
This was an important conversation to start, thank you for doing it.
Braneshop, and
the US National Science Foundation.
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