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Nonlocal correlations in noisy multiqubit systems simulated using matrix product operators

by H. Landa, G. Misguich

This is not the latest submitted version.

Submission summary

As Contributors: Haggai Landa
Arxiv Link: https://arxiv.org/abs/2203.05871v1 (pdf)
Date submitted: 2022-03-16 11:08
Submitted by: Landa, Haggai
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Computational
  • Quantum Physics
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:
Has been resubmitted


Submission & Refereeing History

Resubmission 2203.05871v2 on 12 August 2022

Reports on this Submission

Anonymous Report 2 on 2022-5-31 (Invited Report)

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.

  • validity: high
  • significance: low
  • originality: ok
  • clarity: high
  • formatting: good
  • grammar: excellent

Anonymous Report 1 on 2022-4-8 (Invited Report)

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).

  • validity: high
  • significance: good
  • originality: good
  • clarity: top
  • formatting: excellent
  • grammar: excellent

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