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arXiv:2512.16960

QSMOTE-PGM/kPGM: QSMOTE Based PGM and kPGM for Imbalanced Dataset Classification

Bikash K. Behera, Giuseppe Sergioli, Robert Giuntini

cs.LGquant-phSubmitted Dec 18, 2025• Announced Dec 19, 2025• 0 citations
v1 · Dec 18, 2025v2 · May 12, 2026
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Abstract

Quantum-inspired machine learning (QiML) leverages mathematical frameworks from quantum theory to enhance classical algorithms, with particular emphasis on inner product structures in high-dimensional feature spaces. Among the prominent approaches, the Kernel Trick, widely used in support vector machines, provides efficient similarity computation, while the Pretty Good Measurement (PGM), originating from quantum state discrimination, enables classification grounded in Hilbert space geometry. Building on recent developments in kernelized PGM (KPGM) and direct PGM-based classifiers, this work presents a unified theoretical and empirical comparison of these paradigms. We analyze their performance across synthetic oversampling scenarios using Quantum SMOTE (QSMOTE) variants. Experimental results show that both PGM and KPGM classifiers consistently outperform a classical random forest baseline, particularly when multiple quantum copies are employed. Notably, PGM with stereo encoding and n_copies=2 achieves the highest overall accuracy (0.8512) and F1-score (0.8234), while KPGM demonstrates competitive and more stable behavior across QSMOTE variants, with top scores of 0.8511 (stereo) and 0.8483 (amplitude). These findings highlight that quantum-inspired classifiers not only provide tangible gains in recall and balanced performance but also offer complementary strengths: PGM benefits from encoding-specific enhancements, whereas KPGM ensures robustness across sampling strategies. Our results advance the understanding of kernel-based and measurement-based QiML methods, offering practical guidance on their applicability under varying data characteristics and computational constraints.

Comments
14 pages, 10 figures

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Quantum-inspired machine learning (QiML) leverages mathematical frameworks from quantum theory to enhance classical algorithms, with particular emphasis on inner product structures in high-dimensional feature spaces. Among the prominent approaches, the Kernel Trick, widely used in support vector machines, provides efficient similarity computation, while the Pretty Good Measurement (PGM), originating from quantum state discrimination, enables classification grounded in Hilbert space geometry. Building on recent developments in kernelized PGM (KPGM) and direct PGM-based classifiers, this work presents a unified theoretical and empirical comparison of these paradigms. We analyze their performance across synthetic oversampling scenarios using Quantum SMOTE (QSMOTE) variants. Experimental results show that both PGM and KPGM classifiers consistently outperform a classical random forest baseline, particularly when multiple quantum copies are employed. Notably, PGM with stereo encoding and n_copies=2 achieves the highest overall accuracy (0.8512) and F1-score (0.8234), while KPGM demonstrates competitive and more stable behavior across QSMOTE variants, with top scores of 0.8511 (stereo) and 0.8483 (amplitude). These findings highlight that quantum-inspired classifiers not only provide tangible gains in recall and balanced performance but also offer complementary strengths: PGM benefits from encoding-specific enhancements, whereas KPGM ensures robustness across sampling strategies. Our results advance the understanding of kernel-based and measurement-based QiML methods, offering practical guidance on their applicability under varying data characteristics and computational constraints.
Abstract Quantum-inspired machine learning (QiML) employs mathematical principles from quantum theory, such as Hilbert-space representations and quantum state discrimination, to enhance classical learning algorithms. In this work, we investigate the integration of Quantum Synthetic Minority Oversampling Technique (QSMOTE) variants with two quantum-inspired classifiers: the Pretty Good Measurement (PGM) classifier and the kernelized Pretty Good Measurement (KPGM) classifier. We propose and analyze three QSMOTE variants, namely KNN-based, Fidelity-based, and Margin-based QSMOTE, designed to improve minority-class representation in imbalanced datasets through quantum-inspired similarity and sampling mechanisms. A unified theoretical and empirical comparison of PGM and KPGM is presented under amplitude and stereo encoding strategies with multiple quantum copies. Experimental evaluations on the Telco Customer Churn dataset demonstrate that the proposed quantum-inspired approaches consistently outperform a classical Random Forest baseline, particularly in terms of recall and balanced F1-score. Among all configurations, PGM with stereo encoding and ncopies=2n_{\textrm{copies}}=2ncopies​=2 n copies = 2 achieves the best performance with an accuracy of 0.8512 and an F1-score of 0.8234, while KPGM exhibits competitive and more stable behavior across different QSMOTE variants, reaching accuracies of 0.8511 under stereo encoding and 0.8483 under amplitude encoding. The results further show that increasing the number of quantum copies systematically improves classification performance, especially for minority-class detection. This work highlights the effectiveness of combining quantum-inspired oversampling and classification strategies for imbalanced learning, while providing practical insights into the complementary strengths of measurement-based and kernel-based quantum-inspired machine learning frameworks.
Class imbalance remains a major challenge in industrial condition monitoring and fault classification, where minority fault patterns can be poorly represented during machine learning. This work develops a noise-aware quantum-inspired oversampling framework and systematically evaluates its effectiveness and robustness for industrial and energy-system fault diagnosis. The principal artificial-intelligence contribution is a noise-aware extension of the Quantum Synthetic Minority Oversampling Technique (QSMOTE), in which quantum-inspired perturbations are introduced directly into the compact-swap-test-based similarity estimation used during synthetic minority-sample generation. Consequently, noise propagates through overlap estimation and angle computation to the generated samples, enabling direct assessment of the robustness of the oversampling mechanism rather than perturbing only the downstream classifier. The engineering application is evaluated on four public datasets covering solar-panel faults, bearing condition monitoring, engine failures, and industrial fault detection. Five classical classifiers are used to compare performance on the original imbalanced data, after QSMOTE-based balancing, and under noisy-QSMOTE. The results show substantial classifier-dependent benefits from QSMOTE, including improvements of up to 170% on the engine-failure dataset and accuracy exceeding 0.99 on the industrial fault-detection dataset. Robustness experiments across six quantum-inspired noise channels further demonstrate that perturbations in similarity estimation can produce markedly different downstream effects depending on the noise model and classifier. The proposed framework therefore provides a reproducible approach for jointly assessing class-imbalance mitigation and noise robustness of quantum-inspired oversampling in practical industrial artificial-intelligence applications.
We investigate a quantum-inspired approach to supervised multi-class classification based on the Pretty Good Measurement (PGM), viewed as an operator-valued decision rule derived from quantum state discrimination. The method associates each class with an encoded mixed state and performs classification through a single POVM construction, thus providing a genuinely multi-class strategy without reduction to pairwise or one-vs-rest schemes. In this perspective, classification is reformulated as the discrimination of a finite ensemble of class-dependent density operators, with performance governed by the geometry induced by the encoding map and by the overlap structure among classes. To assess the practical scope of this framework, we apply the PGM-based classifier to two biomedical radiomics case studies: histopathological subtyping of non-small-cell lung carcinoma (NSCLC) and prostate cancer (PCa) risk stratification. The evaluation is conducted under protocols aligned with previously reported radiomics studies, enabling direct comparison with established classical baselines. The results show that the PGM-based classifier is consistently competitive and, in several settings, improves upon standard methods. In particular, the method performs especially well in the NSCLC binary and three-class tasks, while remaining competitive in the four-class case, where increased class overlap yields a more demanding discrimination geometry. In the PCa study, the PGM classifier remains close to the strongest ensemble baseline and exhibits clinically relevant sensitivity--specificity trade-offs across feature-selection scenarios.
Abstract We investigate a quantum-inspired approach to supervised multi-class classification based on the Pretty Good Measurement (PGM), viewed as an operator-valued decision rule derived from quantum state discrimination. The method associates each class with an encoded mixed state and performs classification through a single POVM construction, thus providing a genuinely multi-class strategy without reduction to pairwise or one-vs-rest schemes. In this perspective, classification is reformulated as the discrimination of a finite ensemble of class-dependent density operators, with performance governed by the geometry induced by the encoding map and by the overlap structure among classes. To assess the practical scope of this framework, we apply the PGM-based classifier to two biomedical radiomics case studies: histopathological subtyping of non-small-cell lung carcinoma (NSCLC) and prostate cancer (PCa) risk stratification. The evaluation is conducted under protocols aligned with previously reported radiomics studies, enabling direct comparison with established classical baselines. The results show that the PGM-based classifier is consistently competitive and, in several settings, improves upon standard methods. In particular, the method performs especially well in the NSCLC binary and three-class tasks, while remaining competitive in the four-class case, where increased class overlap yields a more demanding discrimination geometry. In the PCa study, the PGM classifier remains close to the strongest ensemble baseline and exhibits clinically relevant sensitivity–specificity trade-offs across feature-selection scenarios. These findings support the relevance of PGM-based quantum-inspired decision rules as a mathematically well-motivated and practically viable extension of quantum state discrimination techniques to genuinely multi-class learning problems and provide further evidence of their applicability in high-dimensional biomedical settings.
Data scarcity and class imbalance are persistent challenges in machine learning that degrade model generalization and introduce predictive bias. We present a hybrid quantum-classical framework for synthetic data generation using a Quantum Circuit Born Machine (QCBM) to address these limitations. The proposed approach exploits quantum mechanical properties -- superposition and entanglement -- within a parameterized variational quantum circuit to model complex probability distributions that are difficult for classical generative methods to capture. Experiments are conducted on two tabular benchmark datasets: the Iris dataset and the Telco Customer Churn dataset. Preprocessing includes normalization and PCA-based dimensionality reduction to enable efficient basis encoding for quantum circuits. The QCBM is trained by minimizing Kullback-Leibler (KL) divergence between real and generated data distributions using a gradient-based parameter-shift optimization rule. Augmenting training data with QCBM-generated synthetic samples at 40-50% of the minority class improves F1-score by approximately 5-15% and minority-class recall by 10-25%. Cross-domain evaluations (Train on Synthetic, Test on Real; and Train on Real, Test on Synthetic) reveal a performance gap of only 3-10%, indicating strong distributional fidelity. Comparative analysis against classical oversampling methods -- SMOTE, Borderline-SMOTE, KMeansSMOTE, and SVM-SMOTE -- shows that QCBM achieves competitive classification performance and produces lower Maximum Mean Discrepancy (MMD) on the Telco dataset, suggesting superior structural similarity in certain imbalanced settings. These findings establish QCBM as a viable complementary tool for data augmentation, particularly for low-dimensional structured tabular data with class imbalance.
We present algorithms for supervised classification tasks in machine learning that are inspired by quantum mechanics. They rely on the so-called problem of quantum state discrimination, which consists in identifying which one of a known set of quantum states has been prepared based on the outcome of a quantum measurement on the state. After building the quantum states associated with the training data, which are encoded as density matrices, we explore various quantum measurement strategies suited for the classification task, including those based on semi-definite programming and on the so-called Pretty GoodMeasurement.We also consider how the measurement performs on multiple copies of the quantum state, since this in principle improves quantum state discrimination at the price of a higher computational cost. For the Pretty Good Measurement classifier, an analogue of the well-known Kernel Trick in learning theory can be devised, so that the cost scales only with the number of examples in the training dataset. This allows to study the performance of this classifier on tensor products of the quantum state. Finally, thedifferent classifiers are benchmarked on the MNIST and MNIST-1D datasets.