Exploring nontrivial topology at quantum criticality on a superconducting processor

The discovery of nontrivial topology in quantum critical states has revised the classification of quantum phase transitions and opened a new direction for exploiting topological phases. However, the experimental investigation of nontrivial topology in gapless many-body systems is challenging due to the inherent complex quantum entanglement. Here, we experimentally explore the topological properties in the critical cluster Ising model by preparing its low-lying critical states on a superconducting processor with up to 100 qubits. We develop an efficient method to probe the boundary g-function, which allows us to uniquely identify the nontrivial topology of the critical systems under study. Furthermore, we probe and recognize two-fold topological degeneracy in the entanglement spectrum under periodic boundary conditions and experimentally reveal the novel bulk-boundary correspondence in topological critical systems. Our results demonstrate the low-lying critical states as useful quantum resources for investigating the interplay between topology and quantum criticality.