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A practical scheme for quantum computation with any two-qubit entangling gate

Michael J. Bremner·Christopher M. Dawson·Jennifer L. Dodd·Alexei Gilchrist·Aram W. Harrow·Duncan Mortimer·Michael A. Nielsen·Tobias J. Osborne
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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 (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/].

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Michael J. Bremner, Christopher M. Dawson, Jennifer L. Dodd, Alexei Gilchrist, Aram W. Harrow, Duncan Mortimer, Michael A. Nielsen, Tobias J. Osborne. 2002-07-12. A practical scheme for quantum computation with any two-qubit entangling gate. https://doi.org/10.1103/physrevlett.89.247902

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