  Complex quantum many-body dynamics spread initially localized quantum
information across the entire system. Information scrambling refers to such a
process, whose simulation is one of the promising applications of quantum
computing. We demonstrate the Hayden-Preskill recovery protocol and the
interferometric protocol for calculating out-of-time-ordered correlators to
study the scrambling property of a one-dimensional kicked-Ising model on
20-qubit trapped-ion quantum processors. The simulated quantum circuits have a
geometrically local structure that exhibits the ballistic growth of
entanglement, resulting in the circuit depth being linear in the number of
qubits for the entire state to be scrambled. We experimentally confirm the
growth of signals in the Hayden-Preskill recovery protocol and the decay of
out-of-time-ordered correlators at late times. As an application of the created
scrambling circuits, we also experimentally demonstrate the calculation of the
microcanonical expectation values of local operators adopting the idea of
thermal pure quantum states.
