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Phys. Rev. A 69, 010301(R) (2004) [4 pages]

Universal quantum circuit for two-qubit transformations with three controlled-NOT gates

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G. Vidal1 and C. M. Dawson2
1Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125, USA
2Center for Quantum Computer Technology and Department of Physics, The University of Queensland, Brisbane 4072, Australia

Received 12 August 2003; published 8 January 2004

We consider quantum circuits made of controlled-NOT (CNOT) gates and single-qubit unitary gates and look for constructions that minimize the use of CNOT gates. We show, by means of an explicit quantum circuit, that three CNOT gates are necessary and sufficient in order to implement an arbitrary unitary transformation of two qubits. We also identify the subset of two-qubit gates that can be performed with only two CNOT gates and provide a simple characterization for them.

© 2004 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevA.69.010301
DOI:
10.1103/PhysRevA.69.010301
PACS:
03.67.Lx, 03.67.Mn
 
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