Fig. 1: Quantum processor and experimental scheme.

a, Optical micrograph of the 78-qubit superconducting processor, Chuang-tzu 2.0. The processor is designed as a 6 × 13 square lattice, comprising 78 qubits interconnected by 137 couplers that link all adjacent qubits. b, Schematic diagram of the RMD protocol, characterized by the temporal multipolar order n. The 0-RMD is constructed by randomly selecting elements from the two elementary operators \(\{{\hat{U}}_{+},{\hat{U}}_{-}\}\), and the n-RMD sequence consists of a random selection of two n-multipoles, which are obtained by anti-aligning two (n − 1)th-order operators. c, Elementary operators are generated as \({\hat{U}}_{\pm }=\exp \{-i{\hat{H}}_{\pm }T\}\), with a driving period T, where \({\hat{H}}_{\pm }\) differs in the staggered potential in the y direction. d, Experimental procedure. First, we initialize the system in a density-wave state, where even sites along the y axis are occupied (represented by red spheres), and odd sites are unoccupied (represented by grey spheres). The symbol X denotes X-gate pulses that excite qubits to their first excited states. Next, we implement the RMD protocol that destabilizes the density-wave order, and the system heats up. Finally, we use multiqubit QST to determine the entanglement entropy and perform particle number measurement to characterize the non-equilibrium time evolution.