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

TL;DR

This paper explores how quantum systems can simulate gravitational-like waves in minisuperspace by analyzing topological features and ripples in Hilbert space, linking quantum geometry with gravity.

Contribution

It introduces a novel approach to simulate gravitational-like waves using quantum systems and topological properties in the context of quantum gravity.

Findings

Artificial magnetic monopoles can be simulated in parameter space.

Ripples in Hilbert space relate to gravitational-like waves.

Fidelity of quantum states connects to gravitational phenomena.

Abstract

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.