Quantum Circuits for General Multiqubit Gates

We consider a generic elementary gate sequence which is needed to implement a general quantum gate acting on n qubits—a unitary transformation with 4ⁿ degrees of freedom. For synthesizing the gate sequence, a method based on the so-called cosine-sine matrix decomposition is presented. The result is optimal in the number of elementary one-qubit gates, 4ⁿ, and scales more favorably than the previously reported decompositions requiring 4ⁿ-2ⁿ⁺¹ controlled NOT gates.