With recent progress on experimental quantum information processing, an important question has arisen as to whether it is possible to verify arbitrary computation performed on a quantum processor. A number of protocols have been proposed to achieve this goal, however all are interactive in nature, requiring that the computation be performed in an interactive manner with back and forth communication between the verifier and one or more provers. Here we propose two methods for verifying quantum computation in a non-interactive manner based on recent progress in the understanding of the local Hamiltonian problem. Provided that the provers compute certain witnesses for the computation, this allows the result of a quantum computation to be verified after the fact, a property not seen in current verification protocols.