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Decomposition of orthogonal matrix and synthesis of two-qubit and three-qubit orthogonal gates

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arxiv 1203.0722 v1 pith:4AYSEF6H submitted 2012-03-04 quant-ph

classification quant-ph
keywords gatesorthogonaltwo-qubitdecompositiongatesynthesisthree-qubitcnot
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The decomposition of matrices associated to two-qubit and three-qubit orthogonal gates is studied, and based on the decomposition the synthesis of these gates is investigated. The optimal synthesis of general two-qubit orthogonal gate is obtained. For two-qubit unimodular orthogonal gate, it requires at most 2 CNOT gates and 6 one-qubit Ry gates. For the general three-qubit unimodular orthogonal gate, it can be synthesized by 16 CNOT gates and 36 one-qubit Ry and Rz gates in the worst case.

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