Optimal Realizations of Controlled Unitary Gates

Details Optimal Realizations of Controlled Unitary Gates Optimal Realizations of Controlled Unitary Gates

2002-07-27

arxiv.org/abs/quant-ph/0207157v1

Journal of Quantum Information and Computation, 3(2), pages 139-155, 2003

Physics

Quantum Physics

32 figures, 22 pages

Scientific paper

The controlled-not gate and the single qubit gates are considered elementary gates in quantum computing. It is natural to ask how many such elementary gates are needed to implement more elaborate gates or circuits. Recall that a controlled-U gate can be realized with two controlled-not gates and four single qubit gates. We prove that this implementation is optimal if and only if the matrix U satisfies the conditions tr U != 0, tr UX != 0, and det U != 1. We also derive optimal implementations in the non-generic cases.

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