Association Rules in QUBO Samples and Where to Find Them

Tian Huang, Siong Thye Goh, Rick Siow Mong Goh, Tao Luo

Keywords: Association rule, Annealing, QUBO

TL;DR: Find valuable association rules from QUBO samples to simplify QUBO problem and improve optimisation results

Abstract: There are sometimes strong associations between variables in the samples to a Quadratic Unconstrained Binary Optimization (QUBO) problem. A natural question arises to us: Are there any value in these association? We study max-cut problem and observe that association can be represented as rules to simplify QUBO problem. Classical and quantum annealers work better when the problem size is smaller. To effectively and efficiently find associations between variables, we adapt traditional association rule mining in the case of QUBO samples and propose a Fast Association Rule Mining algorithm (FARM) specifically for mining QUBO samples. We also propose strategies and a workflow to select and apply promising rules and simplify QUBO problems. We evaluate our method on D-Wave Quantum Annealer as well as Fujitsu Digital Annealer. The experiments demonstrate the utility of FARM as a visualisation tool for understanding associations in QUBO samples. The results also demonstrate the potential of our method in closing the gap between samples and ground truth. The source code will be disclosed to the public if the manuscript is accepted.

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