An open source MATLAB program for fast numerical Feynman integral calculations for open quantum system dynamics on GPUs

TL;DR

This paper introduces an open-source MATLAB program that efficiently computes open quantum system dynamics using Feynman integrals, leveraging GPU acceleration to significantly speed up calculations compared to CPU-based methods.

Contribution

The paper presents a MATLAB implementation that utilizes GPU computing to accelerate Feynman integral calculations for open quantum systems, with minimal overhead from data transfer.

Findings

GPU acceleration greatly speeds up the Feynman integral propagation

Data transfer overhead between CPU and GPU is negligible

The program can run entirely on CPU if GPU memory is insufficient

Abstract

This MATLAB program calculates the dynamics of the reduced density matrix of an open quantum system modeled by the Feynman-Vernon model. The user gives the program a vector describing the coordinate of an open quantum system, a hamiltonian matrix describing its energy, and a spectral distribution function and temperature describing the environment's influence on it, in addition to the open quantum system's intial density matrix and a grid of times. With this, the program returns the reduced density matrix of the open quantum system at all (or some) moments specified by that grid of times. This overall calculation can be divided into two stages: the setup of the Feynman integral, and the actual calculation of the Feynman integral for time-propagation of the density matrix. When this program calculates this propagation on a multi-core CPU, it is this propagation that is usually the rate limiting step of the calculation, but when it is calculated on a GPU, the propagation is calculated so quickly that the setup of the Feynman integal actually becomes the rate limiting step for most cases tested so far. The overhead of transfrring information from the CPU to the GPU and back seems to have negligible effect on the overall runtime of the program. When the required information cannot fit on the GPU, the user can choose to run the entire program on a CPU.