Comparing Classical and Quantum Machine Learning for Regression in High Energy Physics Collision Data

Tariq Mahmood; Zain ul Abidin; Itzel Luviano Soto; Alfredo Raya

cs.LGAug 28, 2026

Comparing Classical and Quantum Machine Learning for Regression in High Energy Physics Collision Data

Authors: Tariq Mahmood, Zain ul Abidin, Itzel Luviano Soto, Alfredo Raya

Organizations: Centre for High Energy Physics, University of the Punjab, Lahore, Pakistan. · Facultad de Ingenier´ıa Civil, Universidad Michoacana de San Nicol´as de Hidalgo, Morelia, Michoac´an, M´exico · Facultad de Ingenier´ıa El´ectrica, Universidad Michoacana de San Nicol´as de Hidalgo, Morelia, Michoac´an, M´exico · Centro de Ciencias Exactas, Universidad del B´ıo-B´ıo. Chill´an, Chile

Abstract

The classification and regression of particle collision events constitute a persistent computational challenge in experimental high energy physics, where large volumes of simulated data must be processed with both speed and precision. This work carries out a systematic comparison of four classical machine learning architectures, support vector machines (SVM), artificial neural networks (ANN), convolutional neural networks (CNN), and long short-term memory (LSTM) networks against their quantum counterparts: quantum SVM (QSVM), quantum neural networks (QNN), quantum CNN (QCNN), and quantum LSTM (QLSTM). All models are trained on simulated proton-proton collision events with electron-positron and muon-antimuon final states from the CERN Open Data portal, using transverse-momentum components as input features and transverse-momentum magnitude as the regression target. Classical architectures, and in particular the CNN and LSTM, achieve marginally better quantitative performance under current hardware and dataset constraints. Quantum models, however, reach competitive accuracy with substantially fewer trainable parameters: the QCNN reproduces the performance of the deep classical CNN using only four qubits and a circuit of depth three, pointing to a genuine parameter-efficiency advantage on near-term quantum devices. A baseline analysis confirms that the regression problem is non-trivial for shallow polynomial fits, supporting the relevance of the architectural comparison. These results characterize the trade-offs between classical and quantum approaches under realistic, resource-constrained conditions and provide a benchmark for future studies on actual quantum hardware.

Figures & tables

Figure 1: Schematic illustration of the SVM decision boundary and margin. The support vectors (filled symbols) are the training points closest to the hyperplane that jointly determine the optimal boundary.

Panel of Figure 2 — Figure 2: Feedforward ANN architecture. (Top) A single artificial neuron applies a weighted sum to its inputs and passes the result through a nonlinear activation. (Bottom) A multilayer network stacks such units into input, hidden, and output layers.

Figure 3: Block diagram of a one-dimensional CNN architecture as used in this study: convolutional layers extract local features from kinematic sequences, pooling reduces dimensionality, and a dense output layer produces the regression estimate.

Architecture	Parameters	Notes
SVM	–	Kernel-based
ANN	30,401	4 layers $\times$ 100 neurons
CNN	3,265	32 filters
LSTM	66,049	128 units
QSVM	–	Quantum kernel
QNN	96	8 qubits $\times$ 6 layers

Table 1: Trainable parameters.

Category	Parameter	Value
Physics	Collision type	$pp$
	Final states	$e^{+}e^{-}$ , $\mu^{+}\mu^{-}$
Dataset	Input features	$p_{x1}$ , $p_{y1}$
	Target	$p_{tl1}$
Preprocessing	Scaling	Min-max normalization
	Split	80/20 hold-out

Table 2: General experimental configuration.

Model	Parameter	Value
SVM	Kernel	RBF
	$C$	$[1.0,\,420]$ (grid search)
	$\gamma$	$[10^{-4},\,10^{-2}]$
ANN	Hidden layers	1–4 FC layers, 100 neurons
	Activation	ReLU (hidden), linear (output)
CNN	Filters / kernel	32, size 2–4

Table 3: Model hyperparameters. Quantum parameters refer to circuit configuration; classical parameters refer to architectural choices used in the final trained models.

Model	MAE	MSE	RMSE	$\bm{R^{2}}$	Acc. (%)
Linear	11.3082	268.9931	16.4010	0.0008	37.1
Poly. deg. 4	2.0898	8.8501	2.9749	0.9671	7.27
SVM	0.6379	1.7329	1.3164	0.9936	99.63
ANN	0.0234	0.00104	0.0323	0.999996	99.99
CNN	0.0051	0.0050	0.0707	1.0000	99.997
LSTM	0.0011	0.0001	0.0012	0.9942	99.999

Table 4: Regression metrics for all architectures on the test set, together with polynomial baselines. The accuracy column is defined as

100\,(1-\text{MAE}/\bar{p}_{tl1})

, where

\bar{p}_{tl1}

is the mean of the target variable.

Figure 4: True vs. predicted transverse momentum for classical (a–d) and quantum (e–h) models. Points aligned with the diagonal indicate accurate regression; deviations reveal the characteristic error patterns of each architecture.

Figure 5: Kernel density estimates of actual (blue) and predicted (orange) transverse-momentum distributions for the four classical architectures. High overlap indicates that each model has learned the statistical structure of the target variable, not only its mean behavior.

Figure 6: Kernel density estimates for quantum architectures, following the same format as Fig. 5 . Tail divergences for QSVM and QLSTM are consistent with their higher MSE values and with the optimization challenges typical of shallow variational circuits on this regression landscape.

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Hybrid Quantum-Classical ML High-Energy Physics Quantum Convolutional Neural Networks Quantum Kernel Methods

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Event triggering sits at the heart of high-energy physics, where the rare events of interest must be retained while an overwhelming background is discarded under tight latency and bandwidth budgets. This work compares four classical machine learning models, namely a support vector machine, an artificial neural network, a convolutional network and a long short-term memory network, with four hybrid quantum counterparts, on a trigger-like binary classification task built from CMS open data. The label is defined by an invariant-mass window, and the inputs combine reconstructed kinematics with physics-motivated derived variables: the pseudorapidity difference, the wrapped azimuthal difference, the angular separation and the total transverse momentum. The quantum models run under a fixed resource budget of eight qubits, a principal-component compression to sixteen features and state-vector simulation. Every model shares the same stratified split, the same preprocessing and a common decision threshold, and performance is reported through accuracy, ROC-AUC, F1-score, precision and recall. The strongest classical model is the artificial neural network, at 93.53 percent accuracy and 0.9819 ROC-AUC, while the strongest quantum model is the quantum convolutional network, at 90.89 percent accuracy and 0.9731 ROC-AUC, with the quantum neural network close behind. The quantum-kernel and recurrent quantum approaches trail both, which places the trainable hybrid embeddings ahead within this budget. The study is meant as a controlled reference point rather than a claim of quantum advantage.

Abstract

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