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Quantum Computational Complexity

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Book cover Computational Complexity

Article Outline

Glossary

Definition of the Subject

Introduction

The Quantum Circuit Model

Polynomial‐Time Quantum Computations

Quantum Proofs

Quantum Interactive Proof Systems

Other Selected Notions in Quantum Complexity

Future Directions

Bibliography

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Abbreviations

Quantum circuit:

A quantum circuit is an acyclic network of quantum gates connected by wires: the gates represent quantum operations and the wires represent the qubits on which these operations are performed. The quantum circuit model is the most commonly studied model of quantum computation.

Quantum complexity class:

A quantum complexity class is a collection of computational problems that are solvable by a chosen quantum computational model that obeys certain resource constraints. For example, BQP is the quantum complexity class of all decision problems that can be solved in polynomial time by a quantum computer.

Quantum proof:

A quantum proof is a quantum state that plays the role of a witness or certificate to a quantum computer that runs a verification procedure. The quantum complexity class QMA is defined by this notion: it includes all decision problems whose yes‐instances are efficiently verifiable by means of quantum proofs.

Quantum interactive proof system:

A quantum interactive proof system is an interaction between a verifier and one or more provers, involving the processing and exchange of quantum information, whereby the provers attempt to convince the verifier of the answer to some computational problem.

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Authors and Affiliations

  1. Institute for Quantum Computing and School of Computer Science, University of Waterloo, Waterloo, Canada

    John Watrous

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Editor information

Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Watrous, J. (2012). Quantum Computational Complexity. In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_147

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