Variational preparation and characterization of chiral spin liquids in quantum circuits

TL;DR

This paper demonstrates how chiral spin liquids, a type of topological phase, can be prepared and characterized in quantum circuits using a variational quantum eigensolver approach, capturing key topological features.

Contribution

It introduces a method to realize and analyze chiral topological phases in quantum circuits with VQE and tangent space excitation ansatz, including models without exact solutions.

Findings

Successfully captures topological ground state degeneracy

Faithfully reproduces chiral edge modes

Accurately matches excitation spectra with exact solutions

Abstract

Quantum circuits have been shown to be a fertile ground for realizing long-range entangled phases of matter. While various quantum double models with non-chiral 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 of low-energy excitation spectrum on quantum circuits with exact solution in all topological sectors. Further applying this approach to a non-exactly solvable chiral spin liquid model on square lattice, the results suggest this approach works well even when the topological sectors are not exactly known.