  We report the digital quantum simulation of a hamiltonian involved in the
generation of quantum entanglement by gravitational means. In particular, we
focus on a pair of quantum harmonic oscillators, whose interaction via a
quantum gravitational field generates single-mode squeezing in both modes at
the same time, a non-standard process in quantum optics. We perform a
boson-qubit mapping and a digital gate decomposition specific for IBM quantum
devices. We use error mitigation and post-selection to achieve high-fidelity,
accessing a parameter regime out of direct experimental reach.
