Unconditional verification of quantum computation with classical light

Abstract

Verification of quantum computation is a task to efficiently check whether an output given from a quantum computer is correct. Existing verification protocols conducted between a quantum computer to be verified and a verifier necessitate quantum communication to unconditionally detect any malicious behavior of the quantum computer solving any promise problem in $\mathsf{BQP}$. In this paper, we remove the necessity of the communication of qubits by proposing a "physically classical" verification protocol in which the verifier just sends coherent light to the quantum computer.

13 pages, 2 figures, v2: Improved the presentation throughout and fixed an error in the proof of the soundness in Sec. III (The results are unchanged except for that the value of $m$ is slightly increased.)