Quantum computing is an exciting field that uses quantum principles, such as quantum superposition and entanglement, to tackle complex computational problems. Superconducting quantum circuits, based on Josephson junctions, is one of the most promising physical realizations to achieve the long-term goal of building fault-tolerant quantum computers. The past decade has witnessed the rapid development of this field, where many intermediate-scale multi-qubit experiments emerged to simulate nonequilibrium quantum many-body dynamics that are challenging for classical computers. Here, we review the basic concepts of superconducting quantum simulation and their recent experimental progress in exploring exotic nonequilibrium quantum phenomena emerging in strongly interacting many-body systems, e.g., many-body localization, quantum many-body scars, and discrete time crystals. We further discuss the prospects of quantum simulation experiments to truly solve open problems in nonequilibrium many-body systems.
