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QIP = PSPACE

Published:01 December 2011Publication History
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Abstract

This work considers the quantum interactive proof system model of computation, which is the (classical) interactive proof system model’s natural quantum computational analogue. An exact characterization of the expressive power of quantum interactive proof systems is obtained: the collection of computational problems having quantum interactive proof systems consists precisely of those problems solvable by deterministic Turing machines that use at most a polynomial amount of space (or, more succinctly, QIP = PSPACE). This characterization is proved through the use of a parallelized form of the matrix multiplicative weights update method, applied to a class of semidefinite programs that captures the computational power of quantum interactive proof systems. One striking implication of this characterization is that quantum computing provides no increase in computational power whatsoever over classical computing in the context of interactive proof systems, for it is well known that the collection of computational problems having classical interactive proof systems coincides with those problems solvable by polynomial-space computations.

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  1. QIP = PSPACE

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        cover image Journal of the ACM
        Journal of the ACM  Volume 58, Issue 6
        December 2011
        209 pages
        ISSN:0004-5411
        EISSN:1557-735X
        DOI:10.1145/2049697
        Issue’s Table of Contents

        Copyright © 2011 ACM

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        Publication History

        • Published: 1 December 2011
        • Accepted: 1 September 2011
        • Revised: 1 August 2011
        • Received: 1 March 2011
        Published in jacm Volume 58, Issue 6

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