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Inferring Markovian quantum master equations of few-body observables in interacting spin chains

Carnazza, Francesco; Carollo, Federico; Zietlow, Dominik; Andergassen, Sabine; Martius, Georg; Lesanovsky, Igor

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Authors

Francesco Carnazza

Federico Carollo

Dominik Zietlow

Sabine Andergassen

Georg Martius



Abstract

Full information about a many-body quantum system is usually out-of-reach due to the exponential growth - with the size of the system - of the number of parameters needed to encode its state. Nonetheless, in order to understand the complex phenomenology that can be observed in these systems, it is often sufficient to consider dynamical or stationary properties of local observables or, at most, of few-body correlation functions. These quantities are typically studied by singling out a specific subsystem of interest and regarding the remainder of the many-body system as an effective bath. In the simplest scenario, the subsystem dynamics, which is in fact an open quantum dynamics, can be approximated through Markovian quantum master equations. Here, we formulate the problem of finding the generator of the subsystem dynamics as a variational problem, which we solve using the standard toolbox of machine learning for optimization. This dynamical or 'Lindblad' generator provides the relevant dynamical parameters for the subsystem of interest. Importantly, the algorithm we develop is constructed such that the learned generator implements a physically consistent open quantum time-evolution. We exploit this to learn the generator of the dynamics of a subsystem of a many-body system subject to a unitary quantum dynamics. We explore the capability of our method to recover the time-evolution of a two-body subsystem and exploit the physical consistency of the generator to make predictions on the stationary state of the subsystem dynamics.

Journal Article Type Article
Acceptance Date Jul 4, 2022
Online Publication Date Jul 21, 2022
Publication Date Jul 21, 2022
Deposit Date Jul 15, 2022
Publicly Available Date Jul 18, 2022
Journal New Journal of Physics
Electronic ISSN 1367-2630
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 24
Issue 7
Article Number 073033
DOI https://doi.org/10.1088/1367-2630/ac7df6
Keywords General Physics and Astronomy
Public URL https://nottingham-repository.worktribe.com/output/8857279
Publisher URL https://iopscience.iop.org/article/10.1088/1367-2630/ac7df6

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