  Topology played an important role in physics research during the last few
decades. In particular, the quantum geometric tensor that provides local
information about topological properties has attracted much attention. It will
reveal interesting topological properties in non-Abelian systems, which have
not been realized in practice. Here, we use a four-qubit quantum system in
superconducting circuits to construct a degenerate Hamiltonian with parametric
modulation. By manipulating the Hamiltonian with periodic drivings, we simulate
the Bernevig-Hughes-Zhang model and obtain the quantum geometric tensor from
interference oscillation. In addition, we reveal its topological feature by
extracting the topological invariant, demonstrating an effective protocol for
quantum simulation of a non-Abelian system.
