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Quantum
Information and Computation
ISSN: 1533-7146
published since 2001
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Vol.3 No.2, March 2003 |
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Optimal
realizations of controlled unitary gates
(pp139-156)
G. Song and A. Klappenecker
doi:
https://doi.org/10.26421/QIC3.2-5
Abstracts:
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 trU\neq 0, tr(UX)\neq 0, and detU\neq 1. We also derive
optimal implementations in the remaining non-generic cases.
Key words:
Quantum circuits, quantum gates, controlled unitary gates, lower bounds
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