Experimental quantum annealing: case study involving the graph isomorphism problem

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 N2 to fewer than N log2 N and solvable graph sizes increase from N = 5 to N = 13. Additionally, error correction via classical post-processing majority voting 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.

Graph Partitioning using Quantum Annealing on the D-Wave System

“…Graph theory algorithms are used to determine the embedding of a problem graph on the D-Wave system using graph minors [20]. Other graph theory algorithms that have been implemented on the D-Wave system include graph coloring [21,22], a graph isomorphism solver [23], and spanning tree calculations [24]. This work is motivated by a recently proposed graph-based electronic structure theory applied to quantum molecular dynamics (QMD) simulations [25].…”

Performance Models for Split-Execution Computing Systems

“…The difficulty of these off-line calculations would not impact the performance of the application model, but use of the lookup table would require some variant of graph isomorphism to identify which embedding to apply. The graph isomorphism problem has recently been shown to be solvable using adiabatic quantum computing [11], [39], raising the prospects the D-Wave processor could be used to program the D-Wave processor!…”

Readiness of Quantum Optimization Machines for Industrial Applications

“…From the many applications implemented in quantum annealers (see, for example, Refs. [17,[23][24][25][26][27][28]), fault diagnosis has been one of the leading candidates to benchmark the performance of D-Wave devices as optimizers [26,29]. From the range of circuit model-based fault-diagnosis problems [30] we restrict our attention here to combinational circuit fault diagnosis (CCFD), which in contrast to sequential arXiv:1708.09780v2 [quant-ph] 2 Jul 2019 circuits, does not have any memory components and the output is entirely determined by the present inputs.…”