Random-Matrix Models of Monitored Quantum Circuits

authored by: Vir B. Bulchandani, S. L. Sondhi, J. T. Chalker
Abstract: We study the competition between Haar-random unitary dynamics and measurements for unstructured systems of qubits. For projective measurements, we derive various properties of the statistical ensemble of Kraus operators analytically, including the purification time and the distribution of Born probabilities. The latter generalizes the Porter–Thomas distribution for random unitary circuits to the monitored setting and is log-normal at long times. We also consider weak measurements that interpolate between identity quantum channels and projective measurements. In this setting, we derive an exactly solvable Fokker–Planck equation for the joint distribution of singular values of Kraus operators, analogous to the Dorokhov–Mello–Pereyra–Kumar (DMPK) equation modelling disordered quantum wires. We expect that the statistical properties of Kraus operators we have established for these simple systems will serve as a model for the entangling phase of monitored quantum systems more generally.
Organisation(s): Institute of Theoretical Physics
External Organisation(s): Princeton University
University of Oxford
Type: Article
Journal: Journal of statistical physics
Volume: 191
No. of pages: 31
ISSN: 0022-4715
Publication date: 03.05.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Statistical and Nonlinear Physics, Mathematical Physics
Electronic version(s): https://doi.org/10.48550/arXiv.2312.09216 (Access: Open)
https://doi.org/10.1007/s10955-024-03273-0 (Access: Open)

BibTeX

@article{b961f680e4f2433798e421be54aaaea6,
title = "Random-Matrix Models of Monitored Quantum Circuits",
abstract = "We study the competition between Haar-random unitary dynamics and measurements for unstructured systems of qubits. For projective measurements, we derive various properties of the statistical ensemble of Kraus operators analytically, including the purification time and the distribution of Born probabilities. The latter generalizes the Porter–Thomas distribution for random unitary circuits to the monitored setting and is log-normal at long times. We also consider weak measurements that interpolate between identity quantum channels and projective measurements. In this setting, we derive an exactly solvable Fokker–Planck equation for the joint distribution of singular values of Kraus operators, analogous to the Dorokhov–Mello–Pereyra–Kumar (DMPK) equation modelling disordered quantum wires. We expect that the statistical properties of Kraus operators we have established for these simple systems will serve as a model for the entangling phase of monitored quantum systems more generally.",
keywords = "DMPK equation, Measurement-induced phase transition, Monitored quantum circuits, Random-matrix theory",
author = "Bulchandani, {Vir B.} and Sondhi, {S. L.} and Chalker, {J. T.}",
note = "Funding Information: This research was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958 at KITP. V.B.B. was supported by a fellowship at the Princeton Center for Theoretical Science during part of the completion of this work. J.T.C. was supported in part by EPSRC Grant EP/S020527/1. S.L.S. was supported by a Leverhulme Trust International Professorship, Grant Number LIP-202-014. For the purpose of Open Access, the authors have applied a CC BY public copyright license to any Author Accepted Manuscript version arising from this submission. ",
year = "2024",
month = may,
day = "3",
doi = "10.48550/arXiv.2312.09216",
language = "English",
volume = "191",
journal = "Journal of statistical physics",
issn = "0022-4715",
publisher = "Springer New York",
number = "5",
}