Quantum Annealing with chaotic driver Hamiltonians

TL;DR

This paper explores the use of chaotic driver Hamiltonians, inspired by the SYK model, in quantum annealing, showing potential for speedups in solving complex optimization problems like MaxCut and LABS.

Contribution

It introduces a novel chaotic driver Hamiltonian based on the SYK model and demonstrates its effectiveness in enhancing quantum annealing performance on challenging problems.

Findings

SYK-based driver Hamiltonians achieve significant speedups on MaxCut instances.

SYK fluctuations outperform traditional transverse field schedules in large-scale optimization.

Chaotic drivers show promise for scalable quantum advantage in complex problems.

Abstract

Quantum annealing is a computational approach designed to leverage quantum fluctuations for solving large-scale classical optimization problems. Although incorporating standard transverse field (TF) terms in the annealing process can help navigate sharp minima, the potential for achieving a scalable quantum advantage for general optimization problems remains uncertain. Here, we examine the effectiveness of including chaotic quantum driver Hamiltonians in the annealing dynamics. Specifically, we investigate driver Hamiltonians based on a bosonic spin version of the Sachdev-Ye-Kitaev (SYK) model, which features a high degree of non-locality and non-commutativity. Focusing on MaxCut instances on regular graphs, we find that a considerable proportion of SYK model instances demonstrate significant speedups, especially for challenging graph configurations. Additionally, our analysis of time-to-solution scalings for the low autocorrelation binary sequence (LABS) problem suggests that SYK-type fluctuations can outperform traditional transverse field annealing schedules in large-scale optimization tasks.