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

TL;DR

This paper presents a novel linear-depth, ancilla-free quantum circuit for implementing n-qubit Toffoli gates, improving efficiency by reducing depth while maintaining quadratic size, suitable for finite-distance qubit interactions.

Contribution

It introduces a linear-depth, quadratic-size quantum circuit for n-qubit Toffoli gates that requires no ancilla qubits, advancing quantum circuit design.

Findings

Linear-depth circuit for n-qubit Toffoli gates

No ancilla qubits needed in the construction

Compatible with finite-distance qubit interactions

Abstract

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.