Variational optimization of the quantum annealing schedule for the Lechner-Hauke-Zoller scheme

The annealing schedule is optimized for a parameter in the Lechner-Hauke-Zoller (LHZ) scheme for quantum annealing designed for the all-to-all-interacting Ising model representing generic combinatorial optimization problems. We adapt the variational approach proposed by Matsuura et al. (arXiv:2003.09913) to the annealing schedule of a term representing a constraint for variables intrinsic to the LHZ scheme with the annealing schedule of other terms kept intact. Numerical results for a simple ferromagnetic model and the spin-glass problem show that nonmonotonic annealing schedules optimize the performance measured by the residual energy and the final ground-state fidelity. This improvement does not accompany a notable increase in the instantaneous energy gap, which suggests the importance of a dynamical viewpoint in addition to static analyses in the study of practically relevant diabatic processes in quantum annealing.

Automated summary

The nonmonotonic annealing schedules optimize the performance of quantum annealing for the all-to-all-interacting Ising model, improving the final ground-state fidelity without a notable increase in the instantaneous energy gap, highlighting the importance of a dynamical viewpoint alongside static analyses in the study of diabatic processes.