Two-bit gates are universal for quantum computation

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.

Abstract

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