title: Practical scheme for quantum computation with any two-qubit entangling gate.
abstract: 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, 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. 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 result for systems of arbitrary finite dimension has been provided by Brylinski and Brylinski; however, their proof relies on a long argument using advanced mathematics. In contrast, our proof provides a simple constructive procedure which is close to optimal and experimentally practical.
authors.affiliation: Centre for Quantum Computer Technology and Department of Physics, The University of Queensland, QLD 4072, Australia.
authors.forename: Michael J
authors.initials: MJ
authors.lastname: Bremner
authors.forename: Christopher M
authors.initials: CM
authors.lastname: Dawson
authors.forename: Jennifer L
authors.initials: JL
authors.lastname: Dodd
authors.forename: Alexei
authors.initials: A
authors.lastname: Gilchrist
authors.forename: Aram W
authors.initials: AW
authors.lastname: Harrow
authors.forename: Duncan
authors.initials: D
authors.lastname: Mortimer
authors.forename: Michael A
authors.initials: MA
authors.lastname: Nielsen
authors.forename: Tobias J
authors.initials: TJ
authors.lastname: Osborne