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Quantum annealing is a proposed combinatorial optimization technique meant toexploit quantum mechanical effects such as tunneling and entanglement.Real-world quantum annealing-based solvers require a combination of annealingand classical pre- and post-processing; at this early stage, little is knownabout how to partition and optimize the processing. This article presents anexperimental case study of quantum annealing and some of the factors involvedin real-world solvers, using a 504-qubit D-Wave Two machine and the graphisomorphism problem. To illustrate the role of classical pre-processing, acompact Hamiltonian is presented that enables a reduced Ising model for eachproblem instance. On random N-vertex graphs, the median number of variables isreduced 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 errorcorrection is evaluated. While the solution times are not competitive withclassical approaches to graph isomorphism, the enhanced solver ultimatelyclassified correctly every problem that was mapped to the processor anddemonstrated clear advantages over the baseline approach. The results shed somelight on the nature of real-world quantum annealing and the associated hybridclassical-quantum solvers.

Experimental quantum annealing: case study involving the graph isomorphism problem