• Milestone

Elementary gates for quantum computation

Adriano Barenco, Charles H. Bennett, Richard Cleve, David P. DiVincenzo, Norman Margolus, Peter Shor, Tycho Sleator, John A. Smolin, and Harald Weinfurter
Phys. Rev. A 52, 3457 – Published 1 November 1995
An article within the collection: Physical Review A 50th Anniversary Milestones
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Abstract

We show that a set of gates that consists of all one-bit quantum gates [U(2)] and the two-bit exclusive-OR gate [that maps Boolean values (x,y) to (x,xy)] is universal in the sense that all unitary operations on arbitrarily many bits n [U(2n)] can be expressed as compositions of these gates. We investigate the number of the above gates required to implement other gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2) transformation to one input bit if and only if the logical and of all remaining input bits is satisfied. These gates play a central role in many proposed constructions of quantum computational networks. We derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two- and three-bit quantum gates, the asymptotic number required for n-bit Deutsch-Toffoli gates, and make some observations about the number required for arbitrary n-bit unitary operations.

  • Received 22 March 1995

DOI:https://doi.org/10.1103/PhysRevA.52.3457

©1995 American Physical Society

Collections

This article appears in the following collection:

Physical Review A 50th Anniversary Milestones

The collection contains papers that have made important contributions to atomic, molecular, and optical physics and quantum information by announcing significant discoveries or by initiating new areas of research.

Authors & Affiliations

Adriano Barenco, Charles H. Bennett, Richard Cleve, David P. DiVincenzo, Norman Margolus, Peter Shor, Tycho Sleator, John A. Smolin, and Harald Weinfurter

  • Clarendon Laboratory, Oxford University, Oxford OX1 3PU, United Kingdom
  • IBM Research, Yorktown Heights, New York 10598 Department of Computer Science, University of Calgary, Calgary, Alberta, Canada T2N 1N4
  • Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • AT&T Bell Laboratories, Murray Hill, New Jersey 07974
  • Physics Department, New York University, New York, New York 10003
  • Physics Department, University of California at Los Angeles, Los Angeles, California 90024
  • Institute for Experimental Physics, University of Innsbruck, A-6020 Innsbruck, Austria

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Vol. 52, Iss. 5 — November 1995

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