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Topological photonics provides a novel platform to explore topologicalphysics beyond traditional electronic materials and stimulates promisingapplications in topologically protected light transport and lasers. Classicaldegrees of freedom such as polarizations and wavevectors are routinely used tosynthesize topological light modes. Beyond the classical regime, inherentquantum nature of light gives birth to a wealth of fundamentally distincttopological states, which offer topological protection in quantum informationprocessing. Here we implement such experiments on topological states ofquantized light in a superconducting circuit, on which three resonators aretunably coupled to a gmon qubit. We construct one and two-dimensionalFock-state lattices where topological transport of zero-energy states, straininduced pseudo-Landau levels, valley Hall effect and Haldane chiral edgecurrents are demonstrated. Our study extends the topological states of light tothe quantum regime, bridges topological phases of condensed matter physics withcircuit quantum electrodynamics, and offers a new freedom in controlling thequantum states of multiple resonators.

Coherent control of quantum topological states of light in Fock-state lattices