Quantum circuits have been shown to be a fertile ground for realizing long-range entangled phases of matter. While various quantum double models with nonchiral topological order have been theoretically investigated and experimentally implemented, the realization and characterization of chiral topological phases have remained less explored. Here we show that chiral topological phases in spin systems, i.e., chiral spin liquids, can be prepared in quantum circuits using the variational quantum eigensolver (VQE) framework. On top of the VQE ground state, signatures of the chiral topological order are revealed using the recently proposed tangent-space excitation ansatz for quantum circuits. We show that both topological ground-state degeneracy and the chiral edge mode can be faithfully captured by this approach. We demonstrate our approach using the Kitaev honeycomb model, finding excellent agreement between the low-energy excitation spectrum on quantum circuits and the exact solution in all topological sectors. Further applying this approach to a non-exactly solvable chiral spin liquid model on a square lattice, the results suggest that this approach works well even when the topological sectors are not exactly known.

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• Quantum circuits
• Spin liquid
• Topological phases of matter