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 long-standing construction by Barenco et al. (Phys. Rev. A, 52: 3457-3467, 1995, arXiv:quant-ph/9503016), which uses a quadratic-size, quadratic-depth quantum circuit for an $n$-qubit Toffoli gate.

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