Abstract
Joint unitary operations play a central role in quantum communication and computation. We give a quantum circuit for implementing a type of unconstructed useful joint unitary evolutions in terms of controlled-NOT (CNOT) gates and single-qubit rotations. Our synthesis is optimal and possible in experiment. Two CNOT gates and seven R (x) , R (y) or R (z) rotations are required for our synthesis, and the arbitrary parameter contained in the evolutions can be controlled by local Hamiltonian or external fields.