  Which gates are universal for quantum computation? Although it is well known
that certain gates on two-level quantum systems (qubits), such as the
controlled-not (CNOT), are universal when assisted by arbitrary one-qubit
gates, it has only recently become clear precisely what class of two-qubit
gates is universal in this sense. Here we present an elementary proof that any
entangling two-qubit gate is universal for quantum computation, when assisted
by one-qubit gates. A proof of this important result for systems of arbitrary
finite dimension has been provided by J. L. and R. Brylinski
[arXiv:quant-ph/0108062, 2001]; however, their proof relies upon a long
argument using advanced mathematics. In contrast, our proof provides a simple
constructive procedure which is close to optimal and experimentally practical
[C. M. Dawson and A. Gilchrist, online implementation of the procedure
described herein (2002), http://www.physics.uq.edu.au/gqc/].
