Quantum jump Monte Carlo simplified: Abelian symmetries

TL;DR

This paper introduces a simplified quantum jump Monte Carlo method for open quantum systems with Abelian symmetries, enabling more efficient simulations by exploiting symmetry properties to restrict dynamics within symmetry eigenspaces.

Contribution

It develops a weakly symmetric representation of the master operator that simplifies the construction and simulation of quantum trajectories in systems with Abelian symmetries.

Findings

Quantum jump Monte Carlo simulations are simplified using symmetry considerations.

Stochastic trajectories remain within a single symmetry eigenspace for symmetric initial states.

Method generalizes to multiple Abelian weak symmetries.

Abstract

We consider Markovian dynamics of a finitely dimensional open quantum system featuring a weak unitary symmetry, i.e., when the action of a unitary symmetry on the space of density matrices commutes with the master operator governing the dynamics. We show how to encode the weak symmetry in quantum stochastic dynamics of the system by constructing a weakly symmetric representation of the master operator: a symmetric Hamiltonian, and jump operators connecting only the symmetry eigenspaces with a fixed eigenvalue ratio. In turn, this representation simplifies both the construction of the master operator as well as quantum jump Monte Carlo simulations, where, for a symmetric initial state, stochastic trajectories of the system state are supported within a single symmetry eigenspace at a time, which is changed only by the action of an asymmetric jump operator. Our results generalize directly to the case of multiple Abelian weak symmetries.