Programmable higher-order nonequilibrium topological phases on a superconducting quantum processor

Topological phases of matter are of both fundamental and practical interest. In this study, we implemented both equilibrium and nonequilibrium higher-order topological phases using a two-dimensional programmable superconducting quantum processor. Quantum programming of nonequilibrium higher-order topological phases was achieved by constructing quantum circuits comprising >50 cycles of Floquet operators on a six-by-six qubit array. Additionally, we introduce a universal approach based on measuring the dynamics of chiral density to identify distinct nonequilibrium higher-order topological features, including Floquet corner topological invariants and π-energy topological corner modes. Our work may enable the use of programmable quantum processors to explore exotic higher-order nonequilibrium topological phases of matter.