  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.
