Quantum vs Classical Proofs and Subset Verification

TL;DR

This paper investigates the power of quantum verifiers in subset verification, establishing new oracle separations between QCMA, QMA, and AM, and introducing a general framework for such proofs.

Contribution

It develops a framework to prove limitations of QCMA verifiers and demonstrates new oracle separations between quantum complexity classes.

Findings

Proves an oracle separation between QCMA and QMA using an in-place permutation oracle.

Establishes a standard oracle separation between QCMA and AM.

Introduces a general framework for analyzing quantum verifier capabilities.

Abstract

We study the ability of efficient quantum verifiers to decide properties of exponentially large subsets given either a classical or quantum witness. We develop a general framework that can be used to prove that QCMA machines, with only classical witnesses, cannot verify certain properties of subsets given implicitly via an oracle. We use this framework to prove an oracle separation between QCMA and QMA using an "in-place" permutation oracle, making the first progress on this question since Aaronson and Kuperberg in 2007. We also use the framework to prove a particularly simple standard oracle separation between QCMA and AM.