Two-bit gates are universal for quantum computation

Phys. Rev. A 51, 1015 – Published 1 February 1995
David P. DiVincenzo

Abstract

A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit. The best previous result had shown the universality of three-bit gates, by analogy to the universality of the Toffoli three-bit gate of classical reversible computing. Two-bit quantum gates may be implemented by magnetic resonance operations applied to a pair of electronic or nuclear spins. A ‘‘gearbox quantum computer’’ proposed here, based on the principles of atomic-force microscopy, would permit the operation of such two-bit gates in a physical system with very long phase-breaking (i.e., quantum-phase-coherence) times. Simpler versions of the gearbox computer could be used to do experiments on Einstein-Podolsky-Rosen states and related entangled quantum states.

DOI: http://dx.doi.org/10.1103/PhysRevA.51.1015

  • Received 24 June 1994
  • Published in the issue dated February 1995

© 1995 The American Physical Society

Authors & Affiliations

David P. DiVincenzo

  • IBM Research Division, Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598

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