Quantum chaos and information processing with kicked <i>p</i>-spin models

We introduce a family of kicked collective spin models describing an ensemble of spin-1/2 particles with p-body interactions. These constitute a generalization of the quantum kicked top (p=2), a paradigmatic example of a chaotic quantum system. We fully characterize the classical nonlinear dynamics in the thermodynamic limit, including the nature of the transition to global chaos, along with the most relevant signatures of chaos in the quantum regime. Our analysis allows us to classify this family of models, with special emphasis on the differences between the p = 2 and p > 2 cases. These models are further studied in the context of two applications of quantum information processing. First, we explore how these models can be applied to the analysis of Trotter errors in the quantum simulation of dynamical critical phenomena in p-spin models. Second, we analyze how the quantum chaotic properties of these models provide a metrological advantage over the traditional protocol for sensing an external magnetic field.