Orateur
Description
The state of a Markovian open quantum system is completely determined by its density matrix which evolves according to a Lindblad master equation. When the system is composed by many interacting particles, the complexity arising from the many-body problem merges with the necessity to represent mixed states. In this work [1] we exploit a variational ans¨atz described by a neural network to represent a generic nonequilibrium density matrix [2]. By deriving a variational principle, we show that it is possible to define an iterative procedure where the network parameters are varied in order to minimize a cost function quantifying the distance from the asymptotic steady-state. Such a procedure, similar in spirit to supervised learning, can be performed efficiently by means of a Montecarlo sampling of the cost function [3]. As a first application and proof-of-principle, we apply the method to the dissipative quantum transverse Ising model [4].
[1] F. Vicentini, A. Biella, N. Regnault, and C. Ciuti, arXiv:1902.10104 [quant-ph] (2019)
[2] G. Torlai and R. G. Melko, Phys. Rev. Lett. 120, 240503 (2018)
[3] G. Carleo and M. Troyer, Science 355, 602 (2017)
[4] J. Jin, A. Biella, O. Viyuela, C. Ciuti, R. Fazio, and D. Rossini, Phys. Rev. B 98(R), 241108 (2018).
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