  We showcase the digital quantum simulation of the action of a Hamiltonian
that governs the interaction between a quantum mechanical oscillator and an
optical field, generating quantum entanglement between them via gravitational
effects. This is achieved by making use of a boson-qubit mapping protocol and a
digital gate decomposition that allow us to run the simulations in the quantum
computers available in the IBM Quantum platform. We present the obtained
results for the fidelity of the experiment in two different quantum computers,
after applying error mitigation and post-selection techniques. The achieved
results correspond to fidelities over 90%, which indicates that we were able to
perform a faithful digital quantum simulation of the interaction and therefore
of the generation of quantum entanglement by gravitational means in
optomechanical systems.
