Computation of relativistic and many-body effects in atomic systems using quantum annealing

We report 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 is achieved using the Quantum Annealer Eigensolver (QAE) algorithm on the D-Wave Advantage 5000-qubit hardware, which is substantially higher than that attained on a gate-based quantum device to date. We obtain these results in the framework of the many-electron Dirac theory. We implement QAE using a hybrid quantum annealing method that includes an alternative qubit encoding scheme and decomposing the problem into smaller ones based on perturbation theory.