Universal Dilation of Linear It o SDEs: Quantum Trajectories and Lindblad Simulation of Second Moments
This work creates a universal framework to simulate N-dimensional linear Itô stochastic differential equations (SDEs) on quantum computers. It maps classical SDEs to stochastic Schrödinger equations (SSEs) using a unitary moment-matching dilation. This allows for two simulation methods: trajectory-based weak simulation and ensemble-based Lindblad evolution for second moments, bridging classical dynamics with quantum primitives.