Efficient Combinatorial Optimization Using Quantum Annealing

TL;DR

This paper evaluates the performance of the D-Wave 2X quantum annealer on NP-hard graph problems, comparing it to classical algorithms, and finds quantum advantage only for specially designed problem instances.

Contribution

It provides formulations for quantum annealing of graph problems and benchmarks quantum versus classical solvers, highlighting current limitations and specific cases of quantum speed-up.

Findings

Classical algorithms outperform quantum annealer on small, general instances.

Quantum annealer shows speed-up on problem instances tailored to its architecture.

Solution quality is comparable between quantum and classical methods for small problems.

Abstract

The recent availability of the first commercial quantum computers has provided a promising tool to tackle NP hard problems which can only be solved heuristically with present techniques. However, it is unclear if the current state of quantum computing already provides a quantum advantage over the current state of the art in classical computing. This article assesses the performance of the D-Wave 2X quantum annealer on two NP hard graph problems, in particular clique finding and graph partitioning. For this, we provide formulations as Qubo and Ising Hamiltonians suitable for the quantum annealer and compare a variety of quantum solvers (Sapi, QBSolv, QSage provided by D-Wave Sys, Inc.) to current classical algorithms (METIS, Simulated Annealing, third-party clique finding and graph splitting heuristics) on certain test sets of graphs. We demonstrate that for small graph instances, classical methods still outperform the quantum annealer in terms of computing time, even though the quality of the best solutions obtained is comparable. Nevertheless, due to the limited problem size which can be embedded on the D-Wave 2X chip, the aforementioned finding applies to most of problems of general nature solvable on the quantum annealer. For instances specifically designed to fit the D-Wave 2X architecture, we observe substantial speed-ups in computing time over classical approaches.