A Simple Proof of PreciseQMA = PSPACE

TL;DR

This paper provides a new, simplified proof that the complexity class PreciseQMA equals PSPACE, by adapting the Quantum Cook-Levin Theorem to show PSPACE is contained in PreciseQMA.

Contribution

It offers an alternative, more straightforward proof of PreciseQMA = PSPACE, building on prior work and adapting existing theorems.

Findings

PreciseQMA equals PSPACE.

The proof simplifies understanding of quantum complexity classes.

The approach adapts classical proof techniques to quantum settings.

Abstract

We give an alternative proof of PreciseQMA = PSPACE, first proved by Fefferman and Lin (Innov. Theor. Comp. Sci. 2018), where PreciseQMA is the class Quantum Merlin-Arthur with inverse exponential completeness-soundness gap. We adapt the proof of Quantum Cook-Levin Theorem to prove the inclusion PSPACE in PreciseQMA.