Linear-Depth Quantum Circuits for n-qubit Toffoli gates with no Ancilla

We design a circuit structure with linear depth to implement an n-qubit Toffoli gate. The proposed construction uses a quadratic-size circuit consists of elementary 2-qubit controlled-rotation gates around the x axis and uses no ancilla qubit. Circuit depth remains linear in quantum technologies with finite-distance interactions between qubits. The suggested construction is related to the longstanding construction by Barenco et al. (Phys. Rev. A, 52: 3457-3467, 1995) [1], which uses a quadratic-size, quadratic-depth quantum circuit for an n-qubit Toffoli gate.