How to steer a quantum system over a Schroedinger bridge

A new approach to the steering problem for the Schroedinger equation relying on stochastic mechanics and on the theory of Schroedinger bridges is presented. Given the initial and final states psi_0 and psi_1, respectively, the desired quantum evolution is constructed with the aid of a reference quantum evolution. The Nelson process corresponding to the latter evolution is used as reference process in a Schroedinger bridge problem with marginal probability densities | psi_0 |^2 and | psi_1 |^2. This approach is illustrated by working out a simple Gaussian example.