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

TL;DR

This paper optimizes the quantum annealing schedule in the LHZ scheme using a variational approach, leading to improved performance in solving Ising models without increasing the energy gap.

Contribution

It introduces a variational method to optimize the annealing schedule for the LHZ quantum annealing scheme, enhancing solution quality.

Findings

Nonmonotonic schedules improve residual energy and fidelity.

Optimization does not significantly increase the energy gap.

Dynamical effects are crucial in practical quantum annealing.

Abstract

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.