Factorization Machine (FM) is the most commonly used model to build a recommendation system since it can incorporate side information to improve performance. However, producing item suggestions for a given user with a trained FM is time-consuming. To address this problem, we propose a quadratic unconstrained binary optimization (QUBO) scheme to combine with FM and apply quantum annealing (QA) computation. Compared to classical methods, this hybrid algorithm provides a fast sub-optimal sampling of good user suggestions. We then demonstrate the aforementioned computational behavior on current noisy intermediate-scale quantum (NISQ) hardware by experimenting with a real example on a D-Wave annealer.
Factorization Machine (FM) is the most commonly used model to build a recommendation system since it can incorporate side information to improve performance. However, producing item suggestions for a given user with a trained FM is time-consuming. To address this problem, we propose a quadratic unconstrained binary optimization (QUBO) scheme to combine with FM and apply quantum annealing (QA) computation. Compared to classical methods, this hybrid algorithm provides a fast sub-optimal sampling of good user suggestions. We then demonstrate the aforementioned computational behavior on current noisy intermediate-scale quantum (NISQ) hardware by experimenting with a real example on a D-Wave annealer.
Using Quantum Computers to solve problems in Recommender Systems that classical computers cannot address is a worthwhile research topic. In this paper, we use Quantum Annealers to address the feature selection problem in recommendation algorithms. This feature selection problem is a Quadratic Unconstrained Binary Optimization(QUBO) problem. By incorporating Counterfactual Analysis, we significantly improve the performance of the item-based KNN recommendation algorithm compared to using pure Mutual Information. Extensive experiments have demonstrated that the use of Counterfactual Analysis holds great promise for addressing such problems.
Collaborative filtering models generally perform better than content-based filtering models and do not require careful feature engineering. However, in the cold-start scenario collaborative information may be scarce or even unavailable, whereas the content information may be abundant, but also noisy and expensive to acquire. Thus, selection of particular features that improve cold-start recommendations becomes an important and non-trivial task. In the recent approach by Nembrini et al., the feature selection is driven by the correlational compatibility between collaborative and content-based models. The problem is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) which, due to its NP-hard complexity, is solved using Quantum Annealing on a quantum computer provided by D-Wave. Inspired by the reported results, we contend the idea that current quantum annealers are superior for this problem and instead focus on classical algorithms. In particular, we tackle QUBO via TTOpt, a recently proposed black-box optimizer based on tensor networks and multilinear algebra. We show the computational feasibility of this method for large problems with thousands of features, and empirically demonstrate that the solutions found are comparable to the ones obtained with D-Wave across all examined datasets.
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 ( P erformance- D riven Q uadratic U nconstrained B inary O ptimization), 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.
Black-box optimization (BBO) is used in materials design, drug discovery, and hyperparameter tuning in machine learning. The world is experiencing several of these problems. In this review, a factorization machine with quantum annealing or with quadratic-optimization annealing (FMQA) algorithm to realize fast computations of BBO using Ising machines (IMs) is discussed. The FMQA algorithm uses a factorization machine (FM) as a surrogate model for BBO. The FM model can be directly transformed into a quadratic unconstrained binary optimization model that can be solved using IMs. This makes it possible to optimize the acquisition function in BBO, which is a difficult task using conventional methods without IMs. Consequently, it has the advantage of handling large BBO problems. To be able to perform BBO with the FMQA algorithm immediately, we introduce the FMQA algorithm along with Python packages to run it. In addition, we review examples of applications of the FMQA algorithm in various fields, including physics, chemistry, materials science, and social sciences. These successful examples include binary and integer optimization problems, as well as more general optimization problems involving graphs, networks, and strings, using a binary variational autoencoder. We believe that BBO using the FMQA algorithm will become a key technology in IMs, including quantum annealers.
Machine learning model training, which ultimately optimizes a model’s cost function is usually a time- consuming and computationally intensive process on classical computers. This has been more intense due to the in- creased demand for large-scale data analysis, requiring unconventional computing paradigms like quantum computing to enhance training efficiency. Adiabatic quantum computers have excelled at solving optimization problems, which require the quadratic unconstrained binary optimization (QUBO) format of the problem of interest. In this study, the squared error minimization in the multiple linear regression model is reformulated as a QUBO problem enabling it to be solved using D-wave adiabatic quantum computers. Same formulation was used to obtain a solution using gate-based algorithms such as quantum approximate optimization algorithm (QAOA) and sampling variational quantum eigensolver (VQE) im- plemented via IBM Qiskit. The results obtained through these approaches in the context of runtime and mean squared error(MSE) were analyzed and compared to the classical approaches. Our experimental results indicate a runtime ad- vantage in the D-wave annealing approach over the classical Scikit learn regression approach. The time advantage can be observed when N>524288 compared to Sklearn Linear Regression and when N>65536 compared to Sklearn SGDRegressor. Support vector machine induced neural networks, where the margin-based entropy loss is converted into a QUBO with Lagrangian approach is also focused in this study concerning the applicability for nonlinear models.
This paper explores the applications of quantum annealing (QA) and classical simulated annealing (SA) to a suite of combinatorial optimization problems in machine learning, namely feature selection, instance selection, and clustering. We formulate each task as a Quadratic Unconstrained Binary Optimization (QUBO) problem and implement both quantum and classical solvers to compare their effectiveness. For feature selection, we propose several QUBO configurations that balance feature importance and redundancy, showing that quantum annealing (QA) produces solutions that are computationally more efficient. In instance selection, we propose a few novel heuristics for instance-level importance measures that extend existing methods. For clustering, we embed a classical-to-quantum pipeline, using classical clustering followed by QUBO-based medoid refinement, and demonstrate consistent improvements in cluster compactness and retrieval metrics. Our results suggest that QA can be a competitive and efficient tool for discrete machine learning optimization, even within the constraints of current quantum hardware.