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21 January 2021
  » arxiv » quant-ph/0308125

 Article overview

Quantum NP and a Quantum Hierarchy
Tomoyuki Yamakami ;
Date 23 Aug 2003
Subject Quantum Physics; Computational Complexity | quant-ph cs.CC
AbstractThe complexity class NP is quintessential and ubiquitous in theoretical computer science. Two different approaches have been made to define "Quantum NP," the quantum analogue of NP: NQP by Adleman, DeMarrais, and Huang, and QMA by Knill, Kitaev, and Watrous. From an operator point of view, NP can be viewed as the result of the exists-operator applied to P. Recently, Green, Homer, Moore, and Pollett proposed its quantum version, called the N-operator, which is an abstraction of NQP. This paper introduces the exists^{Q}-operator, which is an abstraction of QMA, and its complement, the forall^{Q}-operator. These operators not only define Quantum NP but also build a quantum hierarchy, similar to the Meyer-Stockmeyer polynomial hierarchy, based on two-sided bounded-error quantum computation.
Source arXiv, quant-ph/0308125
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