Optimization by Quantum Annealing: Lessons from hard 3-SAT cases

TL;DR

This paper compares quantum and classical annealing methods on a large, hard 3-SAT problem, revealing qualitative differences and introducing a quantum protocol that outperforms classical annealing in short runs.

Contribution

It provides the first detailed comparison of quantum and classical annealing on large 3-SAT instances and introduces a novel quantum cooling protocol with improved short-term performance.

Findings

Quantum annealing explores the energy landscape differently than classical methods.

Linear-schedule quantum annealing performs worse than classical annealing on this problem.

A field-cycling quantum protocol outperforms classical annealing over short times.

Abstract

The Path Integral Monte Carlo simulated Quantum Annealing algorithm is applied to the optimization of a large hard instance of the Random 3-SAT Problem (N=10000). The dynamical behavior of the quantum and the classical annealing are compared, showing important qualitative differences in the way of exploring the complex energy landscape of the combinatorial optimization problem. At variance with the results obtained for the Ising spin glass and for the Traveling Salesman Problem, in the present case the linear-schedule Quantum Annealing performance is definitely worse than Classical Annealing. Nevertheless, a quantum cooling protocol based on field-cycling and able to outperform standard classical simulated annealing over short time scales is introduced.