Quantum information scrambling in the presence of weak and strong thermalization

Quantum information scrambling under many-body dynamics is of fundamental interest. The tripartite mutual information can quantify the scrambling via its negative value. Here, we first study the quench dynamics of tripartite mutual information in a non-integrable Ising model where the strong and weak thermalization are observed with different initial states. We numerically show that the fastest scrambling can occur when the energy density of the chosen initial state possesses the maximum density of states. We then present an experimental protocol for observing weak and strong thermalization in a superconducting qubit array. Based on the protocol, the relation between scrambling and thermalization revealed in this work can be directly verified by superconducting quantum simulations.