Implementing multi-controlled X gates using the quantum Fourier transform

TL;DR

This paper introduces a quantum Fourier transform-based method for implementing multi-controlled X gates that reduces circuit depth and resource requirements, improving feasibility on noisy intermediate-scale quantum computers.

Contribution

It presents a novel approach to implement multi-controlled gates using quantum Fourier transform, lowering circuit depth and ancilla qubits needed.

Findings

Significantly reduced circuit depth for multi-controlled X gates.

Efficient implementation with few ancilla qubits.

Applicable to noisy intermediate-scale quantum computers.

Abstract

Quantum computing has the potential to solve many complex algorithms in the domains of optimization, arithmetics, structural search, financial risk analysis, machine learning, image processing, and others. Quantum circuits built to implement these algorithms usually require multi-controlled gates as fundamental building blocks, where the multi-controlled Toffoli stands out as the primary example. For implementation in quantum hardware, these gates should be decomposed into many elementary gates, which results in a large depth of the final quantum circuit. However, even moderately deep quantum circuits have low fidelity due to decoherence effects and, thus, may return an almost perfectly uniform distribution of the output results. This paper proposes a different approach for efficient cost multi-controlled gates implementation using the quantum Fourier transform. We show how the depth of the circuit can be significantly reduced using only a few ancilla qubits, making our approach viable for application to noisy intermediate-scale quantum computers. This quantum arithmetic-based approach can be efficiently used to implement many complex quantum gates.