Decomposition of orthogonal matrix and synthesis of two-qubit and three-qubit orthogonal gates
Hai‐Rui Wei, Yao-Min Di · Quantum Information and Computation · 2012
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 R_y gates. For the general three-qubit unimodular orthogonal gate, it can be synthesized by 16 CNOT gates and 36 one-qubit R_y and R_z gates in the worst case.