NP has log-space verifiers with fixed-size public quantum registers

TL;DR

This paper demonstrates that NP membership proofs can be verified with fixed-size quantum registers in a log-space setting, expanding classical verification models with quantum resources.

Contribution

It introduces a model where NP verification is achieved using fixed-size quantum registers, showing quantum advantage in space-bounded verification.

Findings

NP verification with fixed-size quantum registers is possible

Quantum verification matches classical log-space verification in NP

Error bounds can be arbitrarily small in this quantum model

Abstract

In classical Arthur-Merlin games, the class of languages whose membership proofs can be verified by Arthur using logarithmic space (AM(log-space)) coincides with the class P \cite{Co89}. In this note, we show that if Arthur has a fixed-size quantum register (the size of the register does not depend on the length of the input) instead of another source of random bits, membership in any language in NP can be verified with any desired error bound.