Two-Bit Gates are Universal for Quantum Computation

TL;DR

This paper proves that quantum gates acting on just two qubits are sufficient for universal quantum computation, simplifying the requirements for building quantum computers.

Contribution

It establishes the universality of two-bit quantum gates using Lie algebra, improving upon previous three-bit gate results.

Findings

Two-bit gates are sufficient for universal quantum computation.

A physical implementation using magnetic resonance is feasible.

Potential for experiments on entangled states with simplified systems.

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.