Quantum Mechanics Simulated as Branching Process

TL;DR

This paper introduces a novel simulation method for certain branching diffusion processes in quantum mechanics that removes the need for infinitesimal time steps by embedding the process into a solvable one, improving computational efficiency.

Contribution

It presents a new approach to simulate branching diffusion processes without infinitesimal time steps by embedding them into analytically or numerically solvable processes.

Findings

Elimination of infinitesimal time step in simulations.

Embedding process simplifies computational complexity.

Applicable to quantum groundstate computations.

Abstract

Diffusion processes with branching play an important role in statistical dynamics. They are a common approach to the computing of quantum mechanical groundstates, and serve as models for population dynamics and as physical pictures for biological evolution. On a computer the efficiency of this simulation method is limited by the approach to the infinitesimal time step, which is necessary to perform alternating diffusion and branching steps. In this paper, a method is described, which eliminates the infinitesimal time step for a certain class of branching processes, if the process of interest can be ``embedded'' into another process, which is solvable by other analytic and/or numerical methods. The simplest choice for the embbeding process is given by a process with a constant branching rate, which dominates the rate of the embedded process.