  We report the first results for the computation of relativistic effects in
quantum many-body systems using quantum annealers. An average accuracy of 98.9%
in the fine structure splitting of boron-like ions with respect to experiments
has been achieved using the Quantum Annealer Eigensolver (QAE) algorithm on the
D-Wave Advantage hardware. We obtain these results in the framework of the
many-electron Dirac theory. We implement QAE through our quantum annealing
workflow that includes a novel qubit encoding scheme and a perturbation
theory-based decomposition strategy.
