Foundations of Information Technology in the Era of Network and Mobile Computing pp 323-336 | Cite as

# Quantum NP and a Quantum Hierarchy

## Abstract

The 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 ∃-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 ∃^{Q}-operator, which is an abstraction of QMA, and its complement, the ∀^{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.

## Keywords

quantum quantifier quantum operator quantum polynomial hierarchy## References

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