Number-phase wigner representation for efficient stochastic simulations

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 integration 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 nonclassical probability distribution. We describe and demonstrate a method of achieving this sampling using stochastic weights.