A case study in programming a quantum annealer for hard operational planning problems

TL;DR

This study explores programming a quantum annealer for complex operational planning problems, comparing different mappings and embeddings to understand their impact on performance and provide insights for future quantum annealer design.

Contribution

It is one of the first to analyze a quantum annealer's performance on parametrized, practical planning problems using various mappings and embeddings.

Findings

Mapping choice significantly affects performance

Embedding properties influence solution efficiency

Annealing profile impacts problem-solving effectiveness

Abstract

We report on a case study in programming an early quantum annealer to attack optimization problems related to operational planning. While a number of studies have looked at the performance of quantum annealers on problems native to their architecture, and others have examined performance of select problems stemming from an application area, ours is one of the first studies of a quantum annealer's performance on parametrized families of hard problems from a practical domain. We explore two different general mappings of planning problems to quadratic unconstrained binary optimization (QUBO) problems, and apply them to two parametrized families of planning problems, navigation-type and scheduling-type. We also examine two more compact, but problem-type specific, mappings to QUBO, one for the navigation-type planning problems and one for the scheduling-type planning problems. We study embedding properties and parameter setting, and examine their effect on the efficiency with which the quantum annealer solves these problems. From these results we derive insights useful for the programming and design of future quantum annealers: problem choice, the mapping used, the properties of the embedding, and the annealing profile all matter, each significantly affecting the performance.