Performance-Driven QUBO for Recommender Systems on Quantum Annealers

Quantum annealers offer a promising hardware platform for solving combinatorial optimization problems, especially those formulated as Quadratic Unconstrained Binary Optimization (QUBO). In this work, we propose PDQUBO (Performance-Driven Quadratic Unconstrained Binary Optimization), a QUBO-based feature selection method that is directly executable on quantum annealers. Unlike prior QUBO-based feature selection approaches on quantum annealers, PDQUBO explicitly quantifies the performance impact of both individual features and feature pairs on recommender system models. This alignment between QUBO optimization objectives and model performance ensures that the solution direction is closely tied to recommendation quality, making it well-suited for practical deployment on quantum hardware. Moreover, by leveraging counterfactual analysis, PDQUBO is model-agnostic and evaluation-metric-independent, making it broadly applicable across diverse recommender architectures and assessment criteria. In addition, we investigate the instability of quantum annealing on real quantum devices with respect to varying problem sizes and problem difficulties. Extensive experiments on real-world datasets demonstrate that PDQUBO consistently outperforms prior QUBO-based feature selection methods on quantum annealers. Furthermore, we compare PDQUBO against classical feature selection baselines on click-through rate (CTR) prediction tasks, showing its strong performance and highlighting the potential of using quantum annealers for real-world feature selection applications. Our findings suggest that integrating quantum optimization with counterfactual analysis provides a promising direction for effective feature selection in recommender systems.