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The European Physical Journal C

On the integration of quantum machine learning into hybrid frameworks for high energy particle physics

Ş. Yalçın, Ayben Karasu Uysal

Published Dec 22, 2025• 1 citation
Publisher

Abstract

Abstract In this study, the potential of quantum machine learning (QML) techniques based on trainable quantum circuits was explored for vector boson identification at the large hadron collider (LHC). Specifically, the compact muon solenoid (CMS) experiment dataset was employed to reconstruct the Z boson through the muon–antimuon ( $$\mu ^{+}\mu ^{-}$$ μ + μ - ) decay channel using variational quantum circuits (VQC). To examine the effect of data structure on QML performance, various preprocessing strategies were applied, including different train/test splits, feature selection, dimensionality reduction, and class balancing techniques. The dataset was evaluated under two train/test configurations, namely a balanced split (70:30) and an imbalanced split (80:20), in order to examine the effect of class distribution on QML outcomes. Feature selection based on Random Forest (RF) was used to extract the most informative variables, while principal component analysis (PCA) was utilized to reduce input dimensionality and optimize qubit usage. To mitigate class imbalance, resampling techniques such as the Synthetic Minority Over-sampling Technique (SMOTE), SMOTE combined with edited nearest neighbors (SMOTEENN), and SMOTE with Tomek Links (SMOTETomek) were implemented. A comparative evaluation using stratified cross-validation was conducted to assess model performance and generalization ability across different configurations. The findings indicated that integrating PCA with resampling methods substantially improves the generalization capacity of the VQC model, especially in imbalanced settings. Among all configurations, SMOTE and SMOTEENN delivered the highest classification performance, boosting sensitivity to the minority class and enhancing model stability. These results highlight the significance of data structure, feature reduction, and resampling in classical quantum (CQ) data processing for high energy physics applications.

DOI
10.1140/epjc/s10052-025-15189-4

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Abstract In this study, the potential of quantum machine learning (QML) techniques based on trainable quantum circuits was explored for vector boson identification at the large hadron collider (LHC). Specifically, the compact muon solenoid (CMS) experiment dataset was employed to reconstruct the Z boson through the muon–antimuon ( μ+μ−\mu ^{+}\mu ^{-}μ+μ− μ + μ - ) decay channel using variational quantum circuits (VQC). To examine the effect of data structure on QML performance, various preprocessing strategies were applied, including different train/test splits, feature selection, dimensionality reduction, and class balancing techniques. The dataset was evaluated under two train/test configurations, namely a balanced split (70:30) and an imbalanced split (80:20), in order to examine the effect of class distribution on QML outcomes. Feature selection based on Random Forest (RF) was used to extract the most informative variables, while principal component analysis (PCA) was utilized to reduce input dimensionality and optimize qubit usage. To mitigate class imbalance, resampling techniques such as the Synthetic Minority Over-sampling Technique (SMOTE), SMOTE combined with edited nearest neighbors (SMOTEENN), and SMOTE with Tomek Links (SMOTETomek) were implemented. A comparative evaluation using stratified cross-validation was conducted to assess model performance and generalization ability across different configurations. The findings indicated that integrating PCA with resampling methods substantially improves the generalization capacity of the VQC model, especially in imbalanced settings. Among all configurations, SMOTE and SMOTEENN delivered the highest classification performance, boosting sensitivity to the minority class and enhancing model stability. These results highlight the significance of data structure, feature reduction, and resampling in classical quantum (CQ) data processing for high energy physics applications.
One of the major objectives of the experimental programs at the Large Hadron Collider (LHC) is the discovery of new physics. This requires the identification of rare signals in immense backgrounds. Using machine learning algorithms greatly enhances our ability to achieve this objective. With the progress of quantum technologies, quantum machine learning could become a powerful tool for data analysis in high energy physics. In this study, using IBM gate-model quantum computing systems, we employ the quantum variational classifier method in two recent LHC flagship physics analyses: (Higgs boson production in association with a top quark pair, probing the Higgs boson couplings to the top quark) and H → μ + μ − (Higgs boson decays to two muons, probing the Higgs boson couplings to second-generation fermions). We have obtained early results with 10 qubits on the IBM quantum simulator and the IBM quantum hardware. With small training samples of 100 events on the quantum simulator, the quantum variational classifier method performs similarly to classical algorithms such as SVM (support vector machine) and BDT (boosted decision tree), which are often employed in LHC physics analyses. On the quantum hardware, the quantum variational classifier method has shown promising discrimination power, comparable to that on the quantum simulator. This study demonstrates that quantum machine learning has the ability to differentiate between signal and background in realistic physics datasets. We foresee the usage of quantum machine learning in future high-luminosity LHC physics analyses, including measurements of the Higgs boson self-couplings and searches for dark matter.
High-Energy Physics (HEP) experiments, such as those at the Large Hadron Collider (LHC), generate massive datasets that challenge classical computational limits. Quantum Machine Learning (QML) offers a potential advantage in processing high-dimensional data; however, finding the optimal architecture for current Noisy Intermediate-Scale Quantum (NISQ) devices remains an open challenge. This study investigates the performance of Variational Quantum Classifiers (VQC) in detecting Higgs Boson signals using the ATLAS Higgs Boson Machine Learning Challenge 2014 experiment dataset. We implemented a dimensionality reduction pipeline using Principal Component Analysis (PCA) to map 30 physical features into 4-qubit and 8-qubit latent spaces. We benchmarked three configurations: (A) a shallow 4-qubit circuit, (B) a deep 4-qubit circuit with increased entanglement layers, and (C) an expanded 8-qubit circuit. Experimental results demonstrate that increasing circuit depth significantly improves performance, yielding the highest accuracy of 56.2% (Configuration B), compared to a baseline of 51.9%. Conversely, simply scaling to 8 qubits resulted in a performance degradation to 50.6% due to optimization challenges associated with Barren Plateaus in the larger Hilbert space. These findings suggest that for near-term quantum hardware, prioritizing circuit depth and entanglement capability is more critical than increasing qubit count for effective anomaly detection in HEP data.
Quantum machine learning offers new approaches to multivariate event classification in high-energy physics, but its performance relative to optimized classical methods remains uncertain under limited training data and restricted quantum resources. We investigate the sample-size scalability and representation sensitivity of a quantum support vector machine and a variational quantum classifier for Higgs-boson signal--background discrimination using simulated events from the ATLAS Higgs Machine Learning Challenge. The models are trained on balanced subsets ranging from 250 to 4000 events and evaluated on held-out samples preserving the original class distribution. Principal component analysis (PCA) and autoencoder (AE) representations are examined to reduce the input dimensionality and quantum-resource requirements. Four optimized classical classifiers are used as benchmarks under a common preprocessing, validation, and evaluation protocol. We assess training-sample scalability in classical and quantum classifiers using a four-component PCA representation and examine representation sensitivity through a secondary matched-event comparison of four- and eight-component PCA representations. Within the evaluated Higgs-boson classification setting, the QSVM showed stronger performance than the VQC at larger training sample sizes, while remaining below the best-performing classical classifiers.
Current quantum systems have significant limitations affecting the processing of large datasets with high dimensionality, typical of high energy physics. In the present paper, feature and data prototype selection techniques were studied to tackle this challenge. A grid search was performed and quantum machine learning models were trained and benchmarked against classical shallow machine learning methods, trained both in the reduced and the complete datasets. The performance of the quantum algorithms was found to be comparable to the classical ones, even when using large datasets. Sequential Backward Selection and Principal Component Analysis techniques were used for feature's selection and while the former can produce the better quantum machine learning models in specific cases, it is more unstable. Additionally, we show that such variability in the results is caused by the use of discrete variables, highlighting the suitability of Principal Component analysis transformed data for quantum machine learning applications in the high energy physics context.
Quantum Machine Learning (QML) has emerged as a promising paradigm for addressing increasing computational and representational demands in materials informatics. While classical models such as Support Vector Machines (SVM) achieve strong predictive performance, they often struggle to capture complex, highly correlated interactions in high-dimensional materials data. QML addresses this challenge by leveraging quantum-mechanical principles to construct expressive feature embeddings, where prospective quantum advantage lies in generating feature spaces that are difficult to approximate classically. In this study, 1,000 crystalline compounds from the Open Quantum Materials Database (OQMD) are evaluated in a binary classification task based on formation-energy stability. The dataset is normalized, reduced to four dimensions via Principal Component Analysis (PCA), and encoded into quantum circuits. Three QML models—QSVM, VQC, and QNN—are benchmarked against a classical SVM using repeated stratified evaluation. Results show that the classical SVM achieves the highest accuracy (91.8% ± 0.012), followed by QSVM (60.8% ± 0.035), while VQC and QNN perform significantly worse. This gap is driven by limited qubit capacity, encoding inefficiencies, restricted circuit expressivity, and optimization challenges. Nevertheless, QSVM demonstrates stable performance, suggesting that potential quantum advantage may emerge from improved feature encoding and kernel design rather than deeper variational circuits.
The class imbalance problem presents a critical challenge in real-world applications, particularly in high-stakes domains such as healthcare, finance, disaster management, and fault diagnosis, where accurate anomaly detection is paramount. Class imbalance often disrupts the inherent symmetry of data distributions, resulting in suboptimal performance of traditional machine learning models. Conventional approaches such as undersampling and oversampling are commonly employed to address this issue; however, these methods can introduce additional asymmetries, including information loss and overfitting, which ultimately compromise model efficacy. This study introduces an innovative approach leveraging quantum machine learning (QML), specifically the Variational Quantum Classifier (VQC), to restore and capitalize on the symmetrical properties of data distributions without relying on resampling techniques. By employing quantum circuits optimized to mitigate the asymmetries inherent in imbalanced datasets, the proposed method demonstrates consistently superior performance across diverse datasets, with notable improvements in Recall for minority classes. These findings underscore the potential of quantum machine learning as a robust alternative to classical methods, offering a symmetry-aware solution to class imbalance and advancing QML-driven technologies in fields where equitable representation and symmetry are of critical importance.