Fidelity Decay as an Efficient Indicator of Quantum Chaos

Recent work has connected the type and rate of fidelity decay in some quantum models to the presence of chaos in the associated classical models. We outline how the fidelity decay may be measured efficiently on a quantum information processor, and analyze how this indicator can be applied as a reliable probe of quantum chaos and related properties. We find that the type and rate of fidelity decay is not directly related to the spectral properties of the system, but depends sensitively on the system's eigenvector statistics in the eigenbasis of the perturbation operator. For models with random eigenvectors in this basis the decay is exponential with a rate given by the variance of the perturbation's energy spectrum. These results point to restrictions on the choice of perturbation for which regular and chaotic systems may be efficiently distinguished