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Nonlocal correlations in noisy multiqubit systems simulated using matrix product operators
by H. Landa, G. Misguich
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Submission summary
| Authors (as registered SciPost users): | Haggai Landa |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2203.05871v1 (pdf) |
| Date submitted: | 2022-03-16 11:08 |
| Submitted by: | Landa, Haggai |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Computational |
Abstract
We introduce an open source solver for the Lindblad master equation, based on matrix product states and matrix product operators. Using this solver we study the dynamics of tens of interacting qubits with different connectivities when an edge qubit is being continuously driven on resonance - a fundamental operation in quantum devices. Because of the driving, induced quasiparticles propagate through the qubits until the system reaches a steady state due to the incoherent terms. We find that with alternating-frequency qubits whose interactions with their off-resonant neighbors appear weak, the tunneling quasiparticles lead to large correlations between distant qubits in the system. Some two-qubit correlation functions are found to increase as a function of distance in the system (in contrast to the typical decay with distance), peaking on the two edge qubits farthest apart from each other.
Current status:
Reports on this Submission
Strengths
1- open source MPO code for open driven systems
2- well written paper
3- solid results
Weaknesses
1- physical motivation for the presented study is weak
2- main result (nonlocal correlations) is presented at the very end
Report
The paper presents and (in the appendix) documents an MPO code for open systems. The code is applied and benchmarked for a system of qubits (either along a line or on a ring, either being identical or alternating in frequency, either with or without dissipation, either with or without drive on one qubit). The results (expectations values of sigma_z, correlations, different entropies) for the different scenarios are compared. Some results are well understood (e.g. light cones in the absence of dissipation), others are more curious, like the advertised nonlocal correlations. Unfortunately, these different cases seem a bit random, the physical motivation of the study remains unclear. The main goal seems to benchmark the code. I think the manuscript is lacking a "groundbreaking" result to qualify for SciPost Phsyics, but I would recommend it for SciPost Physics Codebases.
Report #1 by Anonymous (Referee 1) on 2022-4-8 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2203.05871v1, delivered 2022-04-08, doi: 10.21468/SciPost.Report.4894
Strengths
1- I found the paper well written.
2- The open source library is properly documented on the git hub repository.
3- Solving the dynamics of a driven-dissipative quantum many-body system is a central problem in condensed matter and AMO physics.
4- I consider the idea of making open source, well documented, user-friendly codes for this class of systems a very important step in the study of many-body open system dynamics.
Weaknesses
1- I am not completely satisfied about the simulation part of the manuscript, Sec.3. See Report for the details.
Report
In this paper the authors propose an open source solver for the Lindblad master equation which exploit MPS and MPO representations of quantum states and Lindbladian. Then, they test it on some relevant physical setups: an XY chain with different local parameters and dissipation processes.
I found the paper well written and the open source library properly documented on the git hub repository. Solving the dynamics of a driven-dissipative quantum many-body system is a central problem in condensed matter and AMO physics. Many methods have been proposed in the last years and tensor-network methods have been proved to be very effective on a wide variety of physical problem. I thus consider the idea of making open source, well documented, user friendly codes for this class of systems a very important step in the study of many-body open system dynamics.
I do not have any particular remark about the structure true of the paper that I found very coherent and pedagogical. However I am not completely satisfied about the simulation part of the manuscript (Sec.3). In particular, I see that all the problem they choose to solve have an XY model as unitary part of the nearest-neighbour dynamics. After Jordan-Wigner transformations this dynamics maps onte free-fermion Hamiltonian in 1D.
In conclusion the paper could meet the publication Criteria of SciPost Physics after some revision on the simulation part I detailed below.
Requested changes
1- I propose to the authors to study also the effect of adding the interaction given by an ZZ coupling. This would make the problem “Interacting” and interesting effects may be seen in the deformation of the light come as well as in the entanglement properties (Rényi entropy and OSEE).
2-Furthermore, since the authors propose a “new” solver, I suggest to compare the results of their simulation with some numerically exactly-solvable case. The most simplest case that I do have in mind is the 1D Ising model with decoherent spin flip. See Fig.2 of Vicentini et al., Phys. Rev. Lett. 122, 250503 (2019).
Author: Haggai Landa on 2022-08-12 [id 2725]
(in reply to Report 1 on 2022-04-08)
We would like to thank the referee for reading the manuscript and for her/his positive feedback and suggestions.
Regarding the referee's first suggestion - to add ZZ coupling to our numerical studies (mostly focused on XY coupling), we have followed the suggestion and added simulations of this type to the manuscript. We also note that the referee's comment on the free-fermion dynamics is exact at the bulk of the system, but does not strictly hold for the first qubit (being driven), and in the plaquette case the integrability supposedly breaks also at the two lattice points where a qubit interacts with three neighbors. The overall system dynamics with the drive and noise are complex and interesting.
Following the referee's suggestion we have considered the effect of small ZZ coupling terms on the dynamics of nonlocal correlations that form an important result of the paper. Perturbative ZZ interactions are a significant source of uncontrolled dynamics in superconduting devices and the coupling strengths we chose for the simulation are realistic in magnitude. The results are discussed in Sec. 3.4 (towards the end) and in Sec. 4, and presented in detail in App. G (Figs. 22-23). Indeed the extra interactions make the dynamics more complex as is evident in the entanglement properties, and when the ZZ interaction is large enough the nonlocal correlations are interestingly washed away.
Regarding the referee's second suggestion, we indeed implemented it and added in Appendix C a study of the quantum Ising model on a ring with strong dissipation. The results coincide with those of the reference pointed out by the referee. We note also that, as detailed in the manuscript, we have systematically compared the solver results with independent numerical simulations for all setups studied in the paper (for up to 10 qubits), which realizes a comprehensive numerical test of the solver.
Author: Haggai Landa on 2022-08-12 [id 2724]
(in reply to Report 2 on 2022-05-31)We would like to thank the referee for pointing out the fact that the results are solid and that the paper is well written, and for his/her suggestions.
Regarding the first weakness pointed out by the referee (physical motivation for the work), we agree that this point was not properly addressed in the manuscript previously, and following the referee's comment we have now clarified the motivation and the relevance of the results to current state-of-the-art quantum hardware. As now emphasized in the introduction and conclusion sections, the models studied in the work consist a first step towards simulating many body dynamics of quantum devices. In essence, resonant driving of single qubits is the fundamental workhorse of quantum information processing in many qubit devices, being employed to realize single-qubit rotations and generate entanglement. The driven dynamics are often studied by focusing on small qubit systems, however, the focus of the current work is on the many body and nonlocal effects. Since uncontrolled nonlocal correlations of qubits in large devices could be detrimental to their usage for computational tasks, the ability to simulate and explore such aspects is important.
Regarding the second weakness (main result presented at the end), we have further emphasized this result in the introduction. Since the manuscript progresses towards this result by gradually increasing the complexity of the analysis and adding elements into the studied problem, it seems natural to us that the main result be at the end of the paper, which is an accepted choice in many publications.
Regarding the referee's comment that the main goal of the study seems to be benchmarking the code and that the paper should be published in SciPost Physics Codebases, we have a different opinion. The paper does not seem suitable for SciPost Physics Codebases since according to its website, a submission to Codebases consists of "a detailed userguide and a source code". Being neither of those, our paper is a proper research paper focused on two physical setups and new results presented together with a thorough analysis. With the numerical tool used for the study being new and state-of-the-art, the paper is meant to link numerical practices with the physical properties of the system and contribute to the readers' understanding of both aspects. Some important effort has been made to make the presentation pedagogical and it should be stressed that both referees indicated that the paper is indeed well written.
To conclude our reply, as supported by Report 1, we believe that the novelty of the results that we find and the relevance of the techniques to a multidisciplinary audience of researchers interested in open quantum system dynamics merit publication in SciPost Physics.