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Quantum computation of lowest-energy Kramers states and magnetic g-factors of rare earth ions in crystals

We present the results of the quantum calculation of the ground state energies and magnetic g-factors of two rare earth (RE) ions: Yb3+ in Y2Ti2O7 crystal and Er3+ in YPO4 crystal. The Variational Quantum Eigensolver (VQE) algorithm has been performed on 5-qubit IBM superconducting quantum computer via IBM Quantum Experience cloud access. The Hamiltonian of the lowest spectroscopic multiplet of each RE ion, containing crystal field and Zeeman interaction, has been projected to the collective states of three (Yb3+) and four (Er3+) coupled transmon qubits. The lowest-energy states of RE ions have been found minimizing the mean energy in ~ 250 iterations of the algorithm: the first part performed on a quantum simulator, and the last 25 iterations - on the real quantum computing hardware. All the calculated ground-state energies and magnetic g-factors agree well with their exact values, while the estimated error of 2÷15% is mostly attributed to the decoherence associated with the two-qubit operations.