Graph Partitioning using Quantum Annealing on the D-Wave System

TL;DR

This paper demonstrates how quantum annealing on the D-Wave system can effectively perform graph partitioning, improving computational efficiency in quantum molecular dynamics simulations.

Contribution

It introduces a novel approach to graph partitioning using quantum annealing, including handling constraints via QUBO reformulation and employing the graph complement.

Findings

Quantum annealing achieves comparable or better results than classical methods.

The approach successfully partitions various types of graphs, including benchmark and material system graphs.

Hybrid classical-quantum methods show promising performance improvements.

Abstract

In this work, we explore graph partitioning (GP) using quantum annealing on the D-Wave 2X machine. Motivated by a recently proposed graph-based electronic structure theory applied to quantum molecular dynamics (QMD) simulations, graph partitioning is used for reducing the calculation of the density matrix into smaller subsystems rendering the calculation more computationally efficient. Unconstrained graph partitioning as community clustering based on the modularity metric can be naturally mapped into the Hamiltonian of the quantum annealer. On the other hand, when constraints are imposed for partitioning into equal parts and minimizing the number of cut edges between parts, a quadratic unconstrained binary optimization (QUBO) reformulation is required. This reformulation may employ the graph complement to fit the problem in the Chimera graph of the quantum annealer. Partitioning into 2 parts, 2^N parts recursively, and k parts concurrently are demonstrated with benchmark graphs, random graphs, and small material system density matrix based graphs. Results for graph partitioning using quantum and hybrid classical-quantum approaches are shown to equal or out-perform current "state of the art" methods.