Characterizing many-body dynamics with projected ensembles on a superconducting quantum processor.

Quantum simulators allow the experimental exploration of nonequilibrium quantum many-body dynamics, which have traditionally been characterized through expectation values or entanglement measures, based on density matrices of the system. Recently, a more general framework for studying quantum many-body systems based on projected ensembles has been introduced, revealing quantum phenomena, such as deep thermalization in chaotic systems. Here, we experimentally investigate a chaotic quantum many-body system using projected ensembles on a three-dimensional-integrated frequency-tunable superconducting processor, enabling both high-fidelity control and scalable architecture. Our results provide direct evidence of deep thermalization by observing a Haar-distributed projected ensemble for the steady states within a charge-conserved sector. Moreover, by introducing an ensemble-averaged entropy as a metric, we establish a benchmark for many-body information leakage from the system to its environment. Our work paves the way for studying quantum many-body dynamics using projected ensembles, and the scalability of our benchmark method represents a notable advance toward quantum computation and simulation.