Graph Partitioning using Quantum Annealing on the DWave System
Abstract
In this work, we explore graph partitioning (GP) using quantum annealing on the DWave 2X machine. Motivated by a recently proposed graphbased 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 classicalquantum approaches are shown to equal or outperform current "state of the art" methods.
 Publication:

arXiv eprints
 Pub Date:
 May 2017
 arXiv:
 arXiv:1705.03082
 Bibcode:
 2017arXiv170503082U
 Keywords:

 Quantum Physics;
 Computer Science  Other Computer Science