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We present the results of the quantum calculation of the ground stateenergies and magnetic g-factors of two rare earth (RE) ions: Yb3+ in Y2Ti2O7crystal and Er3+ in YPO4 crystal. The Variational Quantum Eigensolver (VQE)algorithm has been performed on 5-qubit IBM superconducting quantum computervia IBM Quantum Experience cloud access. The Hamiltonian of the lowestspectroscopic multiplet of each RE ion, containing crystal field and Zeemaninteraction, has been projected to the collective states of three (Yb3+) andfour (Er3+) coupled transmon qubits. The lowest-energy states of RE ions havebeen found minimizing the mean energy in ~ 250 iterations of the algorithm: thefirst part performed on a quantum simulator, and the last 25 iterations - onthe real quantum computing hardware. All the calculated ground-state energiesand magnetic g-factors agree well with their exact values, while the estimatederror of 2{\div}15% is mostly attributed to the decoherence associated with thetwo-qubit operations.

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