Towards arbitrary QUBO optimization: analysis of classical and quantum-activated feedforward neural networks

Abstract

Quadratic unconstrained binary optimization (QUBO) is at the heart of many industries and academic fields such as logistics, supply chain, finance, pharmaceutical science, chemistry, IT, and energy sectors, among others (Bangert 2012 Optimization for Industrial Problems (Springer Science & Business Media)). These problems typically involve optimizing a large number of binary variables, which makes finding exact solutions exponentially more difficult. Consequently, most QUBO problems are classified as NP-hard (Garey and Johnson 1979 Computers and Intractability vol 174 (Freeman); Lucas 2014 Front. Phys. 2 5). To address this challenge, we developed a powerful feedforward neural network (FNN) optimizer for arbitrary QUBO problems. In this work, we demonstrate that the FNN optimizer can provide high-quality approximate solutions for large problems, including dense 80-variable weighted MaxCut and random QUBOs, achieving an average accuracy of over 99% in less than 1.1 s on an 8-core CPU. Additionally, the FNN optimizer outperformed the Gurobi optimizer (Gurobi Optimization, LLC 2023 Gurobi Optimizer Reference Manual) by 72% on 200-variable random QUBO problems within a 100 s computation time limit, exhibiting strong potential for real-time optimization tasks. Building on this model, we explored the novel approach of integrating FNNs with a quantum annealer-based activation function to create a quantum–classical encoder–decoder optimizer, aiming to further enhance the performance of FNNs in QUBO optimization.