Vibration Analysis of Cyclic Symmetrical Systems by Quantum Algorithms

Quantum computers have provided exponentially faster solutions to several physical and engineering problems over existing classical solutions. In this paper we present two quantum algorithms to analyze the forced vibration of a mechanical system with cyclic symmetry. Our main algorithm solves the equation of motion of an undamped and nonelastic rotating system with cyclic symmetry consisting of n sectors, by encoding the displacements of each sector at time t in a quantum state. The runtime of this algorithm is polylog in both n and t, thus exponentially faster than the analogous classical algorithm. Also we consider damped and elastic systems with cyclic symmetry and present another quantum algorithm to solve it in runtime polylog in n and polynomial in t.