Reverse quantum annealing assisted by forward annealing

TL;DR

This paper introduces a method to enhance reverse quantum annealing by initializing it with solutions from forward annealing, improving solution quality and applicability for graph coloring problems on quantum annealers.

Contribution

The authors propose a general approach that feeds reverse annealing with low-quality solutions from forward annealing, significantly improving solution success rates and expanding reverse annealing's usefulness.

Findings

Successfully converted invalid solutions to valid ones in 57% of cases

Outperformed random initial states in solution quality and diversity

Extended the computational reach of reverse annealing for larger problems

Abstract

Quantum annealers conventionally use forward annealing to generate heuristic solutions. Reverse annealing can potentially generate better solutions but necessitates an appropriate initial state. Ways to find such states are generally unknown or highly problem dependent, offer limited success, and severely restrict the scope of reverse annealing. We use a general method that improves the overall solution quality and quantity by feeding reverse annealing with low-quality solutions obtained from forward annealing. An experimental demonstration of solving the graph coloring problem using the D-Wave quantum annealers shows that our method is able to convert invalid solutions obtained from forward annealing to at least one valid solution obtained after assisted reverse annealing for $57\%$ of $459$ random Erd\H{o}s-R\'enyi graphs. Our method significantly outperforms random initial states, obtains more unique solutions on average, and widens the applicability of reverse annealing. Although the average number of valid solutions obtained drops exponentially with the problem size, a scaling analysis for the graph coloring problem shows that our method effectively extends the computational reach of conventional forward annealing using reverse annealing.