Simulating Chern insulators on a superconducting quantum processor

Abstract The quantum Hall effect, fundamental in modern condensed matter physics, continuously inspires new theories and predicts emergent phases of matter. Analysing Chern insulators, a lattice version of the quantum Hall effect without external magnetic field, by testing the bulk-edge correspondence remains challenging on quantum simulation platforms. Here we experimentally demonstrate three types of Chern insulators with synthetic dimensions on a programable 30-qubit-ladder superconducting processor. Using a dynamic spectroscopic technique, we directly measure the band structures of the 2D Chern insulator along synthetic dimensions with various configurations of Aubry-André-Harper chains. By monitoring the quantum walks of an excitation initialised at the edge qubit, we observe dynamical localisation of the topologically protected chiral edge states. With these two signatures of topology, our experiments implement the bulk-edge correspondence in the synthetic 2D Chern insulator. Moreover, we simulate two different bilayer Chern insulators on the ladder-type superconducting processor. With the same periodically modulated on-site potentials for two coupled chains, we observe topologically nontrivial edge states with zero Hall conductivity. When the on-site potentials of two coupled chains have opposite signs, we probe a Chern insulator with higher Chern numbers. Our work shows the potential of using superconducting qubits for investigating different intriguing topological phases of quantum matter.