English

QIP = PSPACE

Quantum Physics 2009-08-03 v2

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.

Cite

@article{arxiv.0907.4737,
  title  = {QIP = PSPACE},
  author = {Rahul Jain and Zhengfeng Ji and Sarvagya Upadhyay and John Watrous},
  journal= {arXiv preprint arXiv:0907.4737},
  year   = {2009}
}

Comments

21 pages; v2 includes corrections and minor revisions

R2 v1 2026-06-21T13:29:37.533Z