Numerical representation of quantum states in the positive-P and Wigner representations

TL;DR

This paper discusses numerical methods for simulating quantum states in quantum optics and Bose-Einstein condensates using stochastic integration with Gaussian and uniform random numbers.

Contribution

It introduces practical numerical techniques for representing quantum states in the positive-P and Wigner frameworks using common random number generators.

Findings

Demonstrates simulation of quantum states with Gaussian and uniform random numbers.

Shows applicability to quantum optics and Bose-Einstein condensates.

Provides examples of numerical simulations for these systems.

Abstract

Numerical stochastic integration is a powerful tool for the investigation of quantum dynamics in interacting many body systems. As with all numerical integration of differential equations, the initial conditions of the system being investigated must be specified. With application to quantum optics in mind, we show how various commonly considered quantum states can be numerically simulated by the use of widely available Gaussian and uniform random number generators. We note that the same methods can also be applied to computational studies of Bose-Einstein condensates, and give some examples of how this can be done.