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{\div}15% is mostly attributed to the decoherence associated with the
two-qubit operations.
K. M. Makushin E. I. Baibekov