Beating the House: Fast Simulation of Dissipative Quantum Systems with Ensemble Rank Truncation

TL;DR

The paper presents Ensemble Rank Truncation (ERT), a novel method for efficiently simulating dissipative quantum systems by approximating the Lindblad equation and truncating ensembles, outperforming existing methods in accuracy and speed.

Contribution

Introduces ERT, a new technique combining Kraus map decomposition and principal component analysis for efficient dissipative quantum system simulation.

Findings

ERT outperforms wavefunction Monte-Carlo methods in accuracy and speed.

ERT combined with MPS techniques is more efficient for large systems.

ERT is practical for quantum information, metrology, and thermodynamics applications.

Abstract

We introduce a new technique for the simulation of dissipative quantum systems. This method is composed of an approximate decomposition of the Lindblad equation into a Kraus map, from which one can define an ensemble of wavefunctions. Using principal component analysis, this ensemble can be truncated to a manageable size without sacrificing numerical accuracy. We term this method \emph{Ensemble Rank Truncation} (ERT), and find that in the regime of weak coupling, this method is able to outperform existing wavefunction Monte-Carlo methods by an order of magnitude in both accuracy and speed. We also explore the possibility of combining ERT with approximate techniques for simulating large systems (such as Matrix Product States (MPS)), and show that in many cases this approach will be more efficient than directly expressing the density matrix in its MPS form. We expect the ERT technique to be of practical interest when simulating dissipative systems for quantum information, metrology and thermodynamics.