  The law of statistical physics dictates that generic closed quantum many-body
systems initialized in nonequilibrium will thermalize under their own dynamics.
However, the emergence of many-body localization (MBL) owing to the interplay
between interaction and disorder, which is in stark contrast to Anderson
localization that only addresses noninteracting particles in the presence of
disorder, greatly challenges this concept because it prevents the systems from
evolving to the ergodic thermalized state. One critical evidence of MBL is the
long-time logarithmic growth of entanglement entropy, and a direct observation
of it is still elusive due to the experimental challenges in multiqubit
single-shot measurement and quantum state tomography. Here we present an
experiment of fully emulating the MBL dynamics with a 10-qubit superconducting
quantum processor, which represents a spin-1/2 XY model featuring programmable
disorder and long-range spin-spin interactions. We provide essential signatures
of MBL, such as the imbalance due to the initial nonequilibrium, the violation
of eigenstate thermalization hypothesis, and, more importantly, the direct
evidence of the long-time logarithmic growth of entanglement entropy. Our
results lay solid foundations for precisely simulating the intriguing physics
of quantum many-body systems on the platform of large-scale multiqubit
superconducting quantum processors.
