Quantum Trajectories with Dynamic Loop Scheduling and Reinforcement Learning

Abstract

The study of many problems in quantum mechanics is based on finding the solution to the time-dependent Schrodinger equation which describes the dynamics of quantum-mechanical systems composed of a particle of mass m moving in a potential V. Based on the hydrodynamic interpretation of quantum mechanics by Bohm (1952), an unstructured grid approach, the quantum trajectory method (QTM) was developed by Lopreore and Wyatt (1999). Derivatives needed for updating the equations of motion are obtained using curve-fitting by a moving weighted least squares algorithm, and analytically differentiating the least squares curves. The calculations involve computationally-intensive parallel loops with nonuniform iterate execution times