Two-bit Gates Are Universal for Quantum Computation Typeset Using Revt E X 1

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 suucient 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 Tof-foli 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.