GPU Implementation of the Feynman Path-Integral Method in Quantum Mechanics

The Path-Integral Formulation of Quantum Mechanics is introduced along with a detailed mathematical description of how it is used in quantum computations. The important concept of the kernel is explained, along with the free particle and harmonic oscillator as examples. Furthermore, the method for calculating expectation values of quantum operators is explained. The expectation values are naturally calculated by importance sampled Monte Carlo integration and by use of the Metropolis algorithm. This is due to the discretization of the path integral results in an integral with a high number of integration variables. The mathematical concepts of this calculation are explained. Also, a method for obtaining the probability density of the treated system is presented. The calculations are performed by a GPU, due to its high capabilities for numerical operations. This requires the mathematical computations to be parallelized and is done by use of the free software PyOpenCL. A thorough introduction to these concepts are given. The resulting ground state energies and probability densities for many particle systems interacting with harmonic as well as attractive and repulsive gaussian potentials are presented. The calculations worked exceedingly well for many particle systems. Source code is available at https://sourceforge.net/projects/ feynmangpu/files/