  We present an approach to the simulation of quantum systems driven by
classical stochastic processes that is based on the polynomial chaos expansion,
a well-known technique in the field of uncertainty quantification. The
polynomial chaos expansion represents the system density matrix as a series of
orthogonal polynomials in the principle components of the stochastic process
and yields a sparsely coupled hierarchy of linear differential equations. We
provide practical heuristics for truncating this expansion based on results
from time-dependent perturbation theory and demonstrate, via an experimentally
relevant one-qubit numerical example, that our technique can be significantly
more computationally efficient than Monte Carlo simulation.
