2002/07/12 by Michael J. Bremner, Christopher M. Dawson, Jennifer L. Dodd +5
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1103/physrevlett.89.247902
published as Phys. Rev. Lett. 89, 247902 (2002) · 3 pages, online implementation of procedure described can be found at http://www.physics.uq.edu.au/gqc/
arxiv created 2002/07/12 · arxiv updated 2009/12/01
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/].