Fluctuation-Informed Quantum Annealing Schedules

A quantum-inspired classical algorithm, the so-called mean-field approximate optimization algorithm [PRX Quantum 4, 030335 (2023)], is emerging as a novel tool to assess the hardness of a given combinatorial optimization problem. Furthermore, the study of quantum fluctuations around the mean-field trajectories allows to determine critical intervals during an annealing schedule, as caused closing mini-gaps. This knowledge can now be fed back to the quantum annealing routine, thus creating a mechanism for schedule adaptivity. The resulting steep sections in the schedules can be mitigated additionally by including approximate adiabatic gauge potentials [Physics Reports 697, 1 (2017)]. We apply our methods to a well-known set of hard MAX 2-SAT instances [arXiv:1401.7320, Phys. Rev. Res. 5, 023151 (2023)] to improve the ground-state fidelity systematically.