QIP = PSPACE

TL;DR

This paper proves that the class of problems with quantum interactive proof systems (QIP) is exactly the same as PSPACE, using advanced matrix methods and semidefinite programming techniques.

Contribution

It establishes the equality QIP = PSPACE by showing QIP is contained in PSPACE through novel application of matrix multiplicative weights and semidefinite programming.

Findings

QIP is contained in PSPACE.

QIP equals PSPACE, confirming the computational power of quantum interactive proofs.

Uses parallelized matrix multiplicative weights update method.

Abstract

We prove that the complexity class QIP, which consists of all problems having quantum interactive proof systems, is contained in PSPACE. This containment is proved by applying a parallelized form of the matrix multiplicative weights update method to a class of semidefinite programs that captures the computational power of quantum interactive proofs. As the containment of PSPACE in QIP follows immediately from the well-known equality IP = PSPACE, the equality QIP = PSPACE follows.