Exploring nontrivial topology at quantum criticality on a superconducting processor
摘要
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.