Post hoc verification with a single prover

TL;DR

This paper introduces a simple post hoc quantum verification protocol using a single prover restricted to X/Z basis measurements, requiring only one-way communication, and discusses the classical verifier limitations related to complexity classes.

Contribution

It presents a novel single-prover quantum verification protocol with minimal measurement restrictions and one-way communication, improving upon previous multi-prover methods.

Findings

Single-prover protocol with measurement restrictions

One-way communication from prover to verifier

Classical verifier protocols are unlikely unless BQP is in the third level of the polynomial hierarchy

Abstract

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.