Linear-depth quantum circuits forn-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 that consists of elementary two-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 long-standing construction by A. Barenco et al. [Phys. Rev. A 52, 3457 (1995)], which uses a quadratic-size, quadratic-depth quantum circuit for an n-qubit Toffoli gate.