Quantum Algorithm for Searching Resonant Frequency Based on Frequency Response Encoding

Frequency response and resonant frequency are crucial aspects of system analysis and design. Quantum computers offer efficient algorithms for solving linear differential equations and performing discrete Fourier transforms. This paper introduces a quantum algorithm that encodes the quantum frequency response state to represent a system's frequency response. We also propose a condition to probabilistically determine resonant frequency of the system with higher-order derivatives. This condition has been validated through computer simulations.