Post hoc verification with a single prover
  We propose a simple protocol for the verification of quantum computation after the computation has been performed. Our construction can be seen as an improvement on previous results in that it requires only a single prover, who is restricted to measuring qubits in the $X$ or $Z$ basis, while requiring only one way communication, from the prover to the verifier. We also show similar constant round protocols with purely classical verifiers are not possible, unless BQP is contained in the third level of the polynomial hierarchy. 
Tomoyuki Morimae, Joseph F. Fitzsimons
quant-ph