Quantum simulations of dissipative dynamics: time-dependence instead of size

TL;DR

This paper presents a novel method for simulating open quantum system dynamics using a finite environment and a time-dependent Hamiltonian, enabling continuous-time simulation with practical advantages over existing methods.

Contribution

It introduces a minimal environment approach with a time-dependent Hamiltonian for continuous open quantum system simulation, improving upon methods requiring infinite environments.

Findings

Established conditions for well-behaved Hamiltonians

Developed approximate Hamiltonians when conditions are not met

Demonstrated applicability to realistic quantum systems

Abstract

The simulation of quantum systems has been a key aim of quantum technologies for decades, and the generalisation to open systems is necessary to include physically realistic systems. We introduce an approach for quantum simulations of open system dynamics in terms of an environment of minimal size and a time-dependent Hamiltonian. This enables the implementation of a continuous-time simulation with a finite environment, whereas state of the art methods require an infinite environment or only match the simulation at discrete times. We find necessary and sufficient conditions for this Hamiltonian to be well behaved and, when these are not met, we show that there exists an approximate Hamiltonian that is, and look into its applications.