This paper investigates several Quadratic Unconstrained Binary optimisation (QUBO) formulations for the parallel machine scheduling problem P m | | C max with the goal of assessing their suitability for quantum annealing and related heuristic optimisation methods. Three QUBO models are constructed, ranging from formulations derived from classical integer and one-hot encodings to a more compact load-balancing based representation. Extensive computational experiments using Simulated Annealing (SA) and Quantum Annealing (QA) reveal substantial differences in scalability and solution quality among the formulations. The alternative load-balanced model consistently yields near-optimal makespans, typically within 1%–3% of the theoretical lower bound, highlighting its stability and effectiveness compared to the more penalty sensitive formulations, whose performance deteriorates for larger instances. Sensitivity analyses further reveal that the appropriate selection of penalty weights and problem-specific parameter tuning significantly influences both solution accuracy and computational effort in QUBO formulations. While current quantum hardware limitations restrict experimentation to small problem sizes, the findings illustrate how compact QUBO designs can better exploit quantum optimisation frameworks. The insights gained in this study provide practical modelling guidelines for future quantum scheduling research and lay the groundwork for extending QUBO-based approaches to more complex scheduling environments. • Three QUBO formulations are compared for identical parallel machine scheduling. • A compact load-balancing QUBO avoids auxiliary variables. • Load balancing yields makespans on average within 1–3%. • Both simulated and quantum annealing produce near-optimal schedules. • Penalty selection and encoding strongly affect scalability and solution quality.
The rapid explosion of medical image data poses a significant challenge to reliable disease Classification with high-dimensional feature spaces and intricate inter-feature correlations. In this paper, a new quantum annealing-inspired framework for optimal feature subset selection, specifically tailored to improve medical image Classification. In contrast to traditional filter, wrapper, or embedded techniques that tend to ignore redundancy and feature interactions, our solution poses feature selection as a Quadratic Unconstrained Binary Optimization (QUBO) problem and solves it effectively using D-Wave quantum annealer hardware. The presented approach makes three primary contributions: (i) a QUBO formulation that captures feature importance, redundancy suppression, and interaction synergy simultaneously, (ii) a hybrid quantum-classical pipeline with embedding, decomposition, and chain strength optimization for efficient execution on existing quantum hardware, and (iii) a comprehensive evaluation on three heterogeneous medical imaging datasets—diabetic retinopathy, breast cancer histopathology, and chest X-ray pneumonia. Experimental findings exhibit uniform improvements in Classification performance (up to 12.1%), drastic feature reduction (65–80%), and much reduced computational time over six state-of-the-art classical approaches. With the exposure of clinically relevant features and robust statistical significance across benchmarks, our approach places quantum annealing as an influential and scalable tool for future medical AI applications.
Accurate carbon-emissions prediction is critical for evidence-based climate policy, where even modest improvements can influence emission–reduction targets. However, high-dimensional datasets often exhibit noise, nonlinear dependencies, and multicollinearity that degrade model stability. We propose QMICO-PCA, a hybrid dimensionality-reduction method that integrates quantum annealing (QA)-based feature selection with principal component analysis (PCA). In the selection stage, mutual information (MI) and Pearson correlation (CO) are combined multiplicatively within a QUBO formulation to jointly reward nonlinear relevance and penalize linear redundancy, enabling balanced subset optimization. The selected features are then transformed via PCA to enhance generalization and mitigate overfitting. We evaluate QMICO-PCA against classical approaches (RFE, LASSO, ELN), with and without PCA, using three regression models on the Our World in Data carbon dataset (13,706 records; 79 features; 1970–2023). Experiments are conducted on heterogeneous QA-based solvers to assess optimization robustness. QMICO-PCA achieves the strongest overall performance (average RMSE = 1134.12, MAE = 237.54,
R2 = 0.8020), corresponding to a 4-7% error reduction over classical methods. In multi-year emission prediction, such reductions can lead to lower cumulative projection errors, supporting more reliable quantitative policy design. Statistical analysis confirms significance (Friedman
p=0.0018 ) with a strong effect size (
W=0.975 ) and significant Holm-adjusted post-hoc comparisons (
pholm<0.05 ). As additional validation, the proposed method is further evaluated on small-scale carbon-emissions datasets, where it also demonstrates consistent performance. Overall, these findings suggest that the proposed method provides a competitive approach for high-dimensional carbon-emissions modeling.