Digital quantum simulation of thermal observables using a global quench

Thermal state preparation is essential for quantum simulation since it describes the natural equilibrium states of matter. We discuss the thermalization protocol based on a global quench that induces all-to-all random interaction within a few-qubit system. The interaction constants are drawn from complex Gaussian distribution. Running the protocol multiple times and averaging the results over realizations of the interaction constants leads to thermal observables. We implement our protocol on the IBM quantum computer for a four-qubit system. Using circuit recompilation, we restore the thermal observables predicted by the exact dynamics evaluated on a classical computer. We show thermal occupation probabilities for the sixteen states with temperature controlled by the variance of the interaction constants and duration of the quench protocol.