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 gapless many-body systems is challenging due to the inherent complex quantum entanglement. Here, we demonstrate an experimental study of the topological properties in the critical cluster Ising model on a superconducting processor with up to 100 qubits. By applying entanglement Hamiltonian tomography to the experimentally prepared low-lying states, we successfully reconstruct the reduced density matrices of the underlying ground states for subsystems with up to 12 qubits, based on which we extract the scaling dimension and central charge of the critical cluster Ising model. Furthermore, we recognize a robust two-fold topological degeneracy as well as the conformal-tower structure in the entanglement spectrum, experimentally revealing the bulk-boundary correspondence in topological critical systems. Our results demonstrate the low-lying states at critical points as useful quantum resources for investigating the interplay between topology and quantum criticality. Nontrivial topologies are long believed to survive only in gapped systems, yet recent progress suggests their existence even at quantum critical points. By preparing low-lying states on a superconducting processor up to 100 qubits and applying entanglement Hamiltonian tomography, the authors experimentally observe these nontrivial topological properties and suggest low-lying states as useful quantum resources.