Conditions for optimal construction of two-qubit nonlocal gates
Yong-Sheng Zhang, Ming-Yong Ye, Guang‐Can Guo · Physical Review A · 2005
Optimal implementation of quantum gates is crucial for designing a quantum computer. The necessary condition for optimal construction of a two-qubit unitary operation is obtained. It can be proved that the $B$ gate is the unique gate that can construct a two-qubit universal circuit with only two applications, i.e., this condition is also sufficient in the case of two applications of the elementary two-qubit gate. It is also shown that many perfect entanglers cannot simulate an arbitrary two-qubit gate with only three applications. We show how a two-qubit gate's construction power is related to the construction power of its mirror gate, and introduce a specific kind of two-qubit entangling gate, i.e., a super controlled gate, which can construct an arbitrary two-qubit gate by three applications.