Unraveling Open Quantum Dynamics with Time-Dependent Variational Monte Carlo

TL;DR

This paper presents a novel method combining time-dependent variational Monte Carlo with quantum trajectory techniques to efficiently simulate open quantum many-body dynamics, capturing complex non-equilibrium phenomena without exponential cost.

Contribution

The authors develop a scalable, neural-network-compatible approach to simulate open quantum systems by unraveling Lindblad equations into stochastic Schrödinger equations within a variational framework.

Findings

Successfully simulated dissipative quenches in long-range Ising models

Accurately captured non-equilibrium magnetization and spin squeezing

Method is compatible with neural-network wavefunctions and scalable

Abstract

We introduce a method to simulate open quantum many-body dynamics by combining time-dependent variational Monte Carlo (tVMC) with quantum trajectory techniques. Our approach unravels the Lindblad master equation into an ensemble of stochastic Schr\"{o}dinger equations for a variational ansatz, avoiding the exponential cost of density matrix evolution. The method is compatible with generic ans\"{a}tze, including expressive neural-network wavefunctions. We derive the nonlinear stochastic equations of motion for the variational parameters and employ suitable Stratonovich numerical solvers. To validate our approach, we simulate quenches in the locally dissipative long-range Ising model in a transverse field, accurately capturing non-equilibrium magnetization and spin squeezing dynamics relevant to trapped-ion and Rydberg atom experiments. The framework is computationally efficient, scalable on high-performance computing platforms, and can be readily integrated into existing tVMC implementations. This work enables large-scale simulations of complex, dissipative quantum systems in higher dimensions, with broad implications for quantum technology and fundamental science.