QIP = PSPACE

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Jain, Rahul
Ji, Zhengfeng
Upadhyay, Sarvagya
Watrous, John
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Abstract
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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.
Comment: 21 pages; v2 includes corrections and minor revisions
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Quantum Physics
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