Primitive quantum gate realizations of multiple-controlled Toffoli gates

Multiple-controlled Toffoli gates are extensively used in quantum and reversible circuits. However, very limited attempt has been made for primitive quantum gate realizations of these gates. In this paper, we present realization of three-qubit Toffoli gate requiring five primitive quantum gates. We then propose realization of four-qubit Toffoli gate requiring 13 primitive quantum gates and one ancilla input. Finally, we propose realizations of (n + 1)-qubit (n > 3 control lines) Toffoli gates using (⌈n/2⌉ + 1)-qubit and (⌊n/2⌋ + 1)-qubit Toffoli gates and ancilla inputs, which make a trade off between quantum cost and number of ancilla inputs. Our proposed method outperforms the best result so far presented in the literature in terms of quantum cost and number of ancilla inputs.