  Intermediate-scale quantum technologies provide new opportunities for
scientific discovery, yet they also pose the challenge of identifying suitable
problems that can take advantage of such devices in spite of their present-day
limitations. In solid-state materials, fractional quantum Hall (FQH) phases
continue to attract attention as hosts of emergent geometrical excitations
analogous to gravitons, resulting from the non-perturbative interactions
between the electrons. However, the direct observation of such excitations
remains a challenge. Here, we identify a quasi-one-dimensional model that
captures the geometric properties and graviton dynamics of FQH states. We then
simulate geometric quench and the subsequent graviton dynamics on the IBM
quantum computer using an optimally-compiled Trotter circuit with bespoke error
mitigation. Moreover, we develop an efficient, optimal-control-based
variational quantum algorithm that can efficiently simulate graviton dynamics
in larger systems. Our results open a new avenue for studying the emergence of
gravitons in a new class of tractable models on the existing quantum hardware.
