Towards a quantum-inspired proof for IP = PSPACE

TL;DR

This paper advances quantum-inspired interactive proof systems by demonstrating protocols with limited provers for complexity classes like NP^PP and connecting these to QMA verification, shedding light on the IP=PSPACE equivalence.

Contribution

It introduces strengthened quantum-inspired protocols for NP^PP and shows their application in verifying QMA computations, linking sum-check protocols with previous quantum proof systems.

Findings

Proves an IP protocol for NP^PP with a limited prover.

Shows how to verify QMA computations using the protocol.

Provides insights into the quantum-inspired proof of IP=PSPACE.

Abstract

We explore quantum-inspired interactive proof systems where the prover is limited. Namely, we improve on a result by [AG17] showing a quantum-inspired interactive protocol ($\sf IP$) for $\sf PreciseBQP$ where the prover is only assumed to be a $\sf PreciseBQP$ machine, and show that the result can be strengthened to show an $\sf IP$ for $\sf NP^{PP}$ with a prover which is only assumed to be an $\sf NP^{PP}$ machine - which was not known before. We also show how the protocol can be used to directly verify $\sf QMA$ computations, thus connecting the sum-check protocol by [AAV13] with the result of [AG17, LFKN90]. Our results shed light on a quantum-inspired proof for ${\sf IP} = {\sf PSPACE}$, as $\sf PreciseQMA$ captures the full $\sf PSPACE$ power.