  We obtain sufficient conditions for the efficient simulation of a continuous
variable quantum algorithm or process on a classical computer. The resulting
theorem is an extension of the Gottesman-Knill theorem to continuous variable
quantum information. For a collection of harmonic oscillators, any quantum
process that begins with unentangled Gaussian states, performs only
transformations generated by Hamiltonians that are quadratic in the canonical
operators, and involves only measurements of canonical operators (including
finite losses) and suitable operations conditioned on these measurements can be
simulated efficiently on a classical computer.
