QIP = PSPACE

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.

• Type: Conference
• Year: 2010
• Where: STOC
• Authors: Rahul Jain, Zhengfeng Ji, Sarvagya Upadhyay and John Watrous
• Keywords: Algorithms, Complexity Class Qip, Equality Qip, STOC 2010, Well-known Equality Ip