Efficient Variational Dynamics of Open Quantum Bosonic Systems via Automatic Differentiation

TL;DR

This paper presents a scalable variational approach using a multi-Gaussian ansatz and automatic differentiation to simulate complex open quantum bosonic systems, capturing critical phenomena in large-scale dynamics.

Contribution

The authors develop a novel variational method based on a multi-dimensional Wigner representation and Gaussian ansatz, enabling efficient simulation of large open quantum systems.

Findings

Finite-size scaling of Liouvillian spectral gap shows critical slowing down.

Method captures dynamical exponents consistent with 2D quantum Ising universality.

Demonstrates effectiveness in simulating driven-dissipative Bose-Hubbard lattices.

Abstract

We introduce a scalable variational method for simulating the dynamics of interacting open quantum bosonic systems deep in the quantum regime. The method is based on a multi-dimensional Wigner phase-space representation and employs a Variational Multi-Gaussian (VMG) ansatz, whose accuracy is systematically controlled by the number of Gaussian components. The variational equations of motion are derived from the Dirac-Frenkel principle and evaluated efficiently by combining the analytical structure of Gaussian functions with automatic differentiation. As a key application, we study a driven-dissipative two-dimensional Bose-Hubbard lattice with two-boson coherent driving and two-body losses. Using our dynamical approach, we compute the finite-size scaling of the Liouvillian spectral gap - extracted from the relaxation dynamics - which vanishes in the thermodynamic limit. Our results reveal critical slowing down with dynamical exponents of the 2D quantum Ising universality class, demonstrating the power of our method to capture complex quantum dynamics in large open systems.