QIP = PSPACE

  • Authors:

  • Rahul Jain;Zhengfeng Ji;Sarvagya Upadhyay;John Watrous

  • Affiliations:

  • National University of Singapore, Singapore, Singapore;Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada;University of Waterloo, Waterloo, ON, Canada;University of Waterloo, Waterloo, ON, Canada

  • Venue:
  • Proceedings of the forty-second ACM symposium on Theory of computing
  • Year:
  • 2010

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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.