Quantum Merlin-Arthur with Clifford Arthur

TL;DR

This paper proves that restricting the verifier in quantum complexity classes QMA and QIP[3] to Clifford gates plus classical XOR does not reduce their computational power, leveraging the universality of magic states.

Contribution

It demonstrates that quantum verification complexity classes remain unchanged under Clifford-only verifier restrictions, using magic states for universality.

Findings

QMA equals Clifford-restricted QMA

QIP[3] equals Clifford-restricted QIP[3]

Magic states enable universal quantum computation with Clifford gates

Abstract

We show that the class QMA does not change even if we restrict Arthur's computing ability to only Clifford gate operations (plus classical XOR gate). The idea is to use the fact that the preparation of certain single-qubit states, so called magic states, plus any Clifford gate operations are universal for quantum computing. If Merlin is honest, he sends the witness plus magic states to Arthur. If Merlin is malicious, he might send other states to Arthur, but Arthur can verify the correctness of magic states by himself. We also generalize the result to QIP[3]: we show that the class QIP[3] does not change even if the computational power of the verifier is restricted to only Clifford gate operations (plus classical XOR gate).