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Phase-space representations based on coherent states (P, Q, Wigner) have beensuccessful in the creation of stochastic differential equations (SDEs) for theefficient stochastic simulation of high dimensional quantum systems. Howevermany problems using these techniques remain intractable over long integrationstimes. We present a number-phase Wigner representation that can be unraveledinto SDEs. We demonstrate convergence to the correct solution for an anharmonicoscillator with small dampening for significantly longer than other phase spacerepresentations. This process requires an effective sampling of a non-classicalprobability distribution. We describe and demonstrate a method of achievingthis sampling using stochastic weights.

Number-Phase Wigner Representation for Efficient Stochastic Simulations