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.
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.
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 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=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.
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 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.
Abstract Quantum information theory, and in particular, the theory of quantum state discrimination, has enabled the development of a supervised multi-class classification algorithm. Inspired by the Pretty Good Measurement (PGM), a quantum-inspired classifier named the PGM Classifier has been designed, capable of classifying among multiple classes without resorting to the One versus One or One versus Rest strategy. In the recent past, several approaches of quantum machine learning have been introduced to classify entangled and separable states. In this article, we apply the PGM Classifier to discriminate among factorized states, separable states, and entangled states. We analyze from the simplest case ( 2 qubits) up to a system of ( 5 qubits) and offer a comparison between our quantum-inspired classifier and other classical classifiers. Finally, we propose a refined classification of non-locality based on the violation of the Mermin and Svetlichny inequalities.
Subtyping of lung cancer is crucial for individualized treatment and optimizing outcomes. Computational modeling allows data analysis over large scales, which helps in making precision classification in large datasets or high-dimensional datasets. Conventional machine learning methods perform well, but integration of multi-omic data (DNA, RNA, miRNA) is challenging in cancer subtyping because of high dimensionality and complex inter-omic relationships. To bypass this Quantum machine learning (QML) provides better ability to navigate high-dimensional biological data with many variables using quantum computational concepts that can identify fine patterns or small-scale patterns beyond the capability of classical approaches. Through the integration of quantum computing principles with the machine learning framework, the study highlights the improvement of computer technology. The framework shows how the system is optimized with the help of quantum principles, how it can improve accuracy, parallel processing and reducing latency. In this work, we have combined data on miRNA, RNA expression, and DNA methylation to create a complete workflow for classifying cancer. This method uses a wide variety of feature selection techniques, such as random forest-based selection, chi-square, mutual information(MI), and principal component analysis(PCA).In order to illustrate the notion of quantum advantage, we carefully compare the performance metrics of the Quantum Support Vector Classifier (QSVC) to the classical Support Vector Machine (SVM), using a ZZ feature map quantum kernel as our baseline for analysis. Using five-fold crossvalidation, we have also verified that the quantum has an advantage with consistently lower variance and higher accuracy.
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.