Quantum simulation of gravitational-like waves in minisuperspace with an artificial qubit

On the background of the Born-Oppenheimer (adiabatic) approximation, we investigate the geometrical and topological structure in the theory of quantum gravity by using the path integral method and halfclassical approximation. As we know, Berry curvature can be extracted from the linear response of a driven two-level system to nonadiabatic manipulations of its Hamiltonian. In parameter space of the Hamiltonian, magnetic monopoles can be artificially simulated. Ripples occur in Hilbert space when the monopole travels from inside to outside the surface of energy manifold spanned by system parameters. From this point of view, we set up the connection between the ripples characterized by the fidelity of quantum states in Hilbert space and gravitational-like waves in minisuperspace. This might open a window for the study of geometrical and topological properties of quantum gravity with the help of quantum physical systems.