Entanglement-Optimal Trajectories of Many-Body Quantum Markov Processes

TL;DR

This paper introduces a new method combining wave function trajectories and matrix product states to efficiently simulate open quantum many-body systems by minimizing entanglement, demonstrated on a 1D Brownian circuit.

Contribution

It presents an adaptive quantum stochastic propagator that reduces entanglement growth, enabling efficient simulation of open quantum systems with phase transition detection.

Findings

Identifies an entanglement phase transition in the model.

Demonstrates the method's ability to find area law unravellings.

Shows reduced computational cost for simulations.

Abstract

We develop a novel approach aimed at solving the equations of motion of open quantum many-body systems. It is based on a combination of generalized wave function trajectories and matrix product states. We introduce an adaptive quantum stochastic propagator, which minimizes the expected entanglement in the many-body quantum state, thus minimizing the computational cost of the matrix product state representation of each trajectory. We illustrate this approach on the example of a one-dimensional open Brownian circuit. We show that this model displays an entanglement phase transition between area and volume law when changing between different propagators and that our method autonomously finds an efficiently representable area law unravelling.