Number-Phase Wigner Representation for Efficient Stochastic Simulations

TL;DR

This paper introduces a number-phase Wigner representation that enables more efficient and longer stochastic simulations of high-dimensional quantum systems by using stochastic weights for sampling non-classical distributions.

Contribution

The paper presents a novel number-phase Wigner representation that can be unraveled into SDEs, improving long-term simulation accuracy for quantum systems.

Findings

Demonstrates convergence for an anharmonic oscillator over longer times

Uses stochastic weights to sample non-classical probability distributions

Outperforms existing phase space representations in long-term simulations

Abstract

Phase-space representations based on coherent states (P, Q, Wigner) have been successful in the creation of stochastic differential equations (SDEs) for the efficient stochastic simulation of high dimensional quantum systems. However many problems using these techniques remain intractable over long integrations times. We present a number-phase Wigner representation that can be unraveled into SDEs. We demonstrate convergence to the correct solution for an anharmonic oscillator with small dampening for significantly longer than other phase space representations. This process requires an effective sampling of a non-classical probability distribution. We describe and demonstrate a method of achieving this sampling using stochastic weights.