Simulating atomic nuclei with quantum annealing algorithms: role of the time

Abstract

The nuclear shell model describes atomic nuclei as interacting nucleons occupying different energy orbitals. In this framework, quantum computing raises an important interest due to its more favorable scaling with the number of nucleons compared to the exponential one of classical methods. Our work consists in performing time evolutions from an easily solvable driver Hamiltonian to the complex, target shell model Hamiltonian, known as quantum annealing. Within this approach, we simulate the ground state of light and medium-mass nuclei from 8Be to 44Ti. We perform time evolutions using linear, quadratic and cos2 time schedules and check whether the non-linear schedules improve the linear results in the same number of steps. For instance, for the 20Ne nucleus and 800 steps, we get a final relative difference in energy of 0.23% in the linear schedule and 0.01% and 0.09% for the quadratic and cos2 schedules, respectively. These results open new interesting ways of implementing quantum annealing algorithms.