Experimental quantum annealing: case study involving the graph isomorphism problem

TL;DR

This paper presents an experimental study of quantum annealing applied to the graph isomorphism problem, demonstrating how classical pre- and post-processing can enhance solver performance on a 504-qubit quantum device.

Contribution

It introduces a compact Hamiltonian for problem reduction and evaluates classical error correction, providing insights into hybrid quantum-classical approaches for real-world quantum annealing.

Findings

Median variables reduced from N^2 to fewer than N lg N

Solvable graph size increased from N=5 to N=13

Correct classification of all mapped problems with advantages over baseline

Abstract

Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical pre- and post-processing; at this early stage, little is known about how to partition and optimize the processing. This article presents an experimental case study of quantum annealing and some of the factors involved in real-world solvers, using a 504-qubit D-Wave Two machine and the graph isomorphism problem. To illustrate the role of classical pre-processing, a compact Hamiltonian is presented that enables a reduced Ising model for each problem instance. On random N-vertex graphs, the median number of variables is reduced from N^2 to fewer than N lg N and solvable graph sizes increase from N = 5 to N = 13. Additionally, a type of classical post-processing error correction is evaluated. While the solution times are not competitive with classical approaches to graph isomorphism, the enhanced solver ultimately classified correctly every problem that was mapped to the processor and demonstrated clear advantages over the baseline approach. The results shed some light on the nature of real-world quantum annealing and the associated hybrid classical-quantum solvers.