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

Accurate Computation of Relativistic Excitation Energies Using Quantum Annealing