Two-bit gates are universal for quantum computation

TLDR

Previous work established universality for three‑bit gates, analogous to the classical Toffoli gate, while two‑bit quantum gates can be realized via magnetic‑resonance operations on pairs of spins. The authors propose a gearbox quantum computer based on atomic‑force‑microscopy principles to enable two‑bit gates in systems with long phase‑breaking times. The gearbox computer employs atomic‑force‑microscopy techniques to implement two‑bit gates, and simpler variants can be used to study EPR and other entangled states. They prove that two‑bit quantum gates are universal for constructing arbitrary quantum circuits, using commutator algebra of unitary Lie groups.

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.