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European Physical Society Conference on High Energy Physics (EPS-HEP)

Group Invariance in Quantum Fidelity Kernels for Vector Boson Scattering at the LHC

Väinö Mehtola, S. Laurila, Michele Grossi

Published Jan 8, 2026• 0 citations
Publisher

Abstract

In this work, we study permutation-invariance and bandwidth-tuning in quantum fidelity kernels for classifying vector boson scattering (VBS) against QCD multijet background using proton-proton collisions simulated at $\sqrt{s}=13.6$ TeV, with detector simulation corresponding to Run-2 CMS detector. We employ partially and fully symmetrized hardware-efficient kernel variants that embed $S_n$ symmetry of the final-state jets. In noiseless simulation, some symmetry-enhanced kernels outperform a non-invariant HEA kernel, a classical Gaussian kernel baseline, and a product state quantum kernel in terms of the area under the curve (AUC) of the receiver operator characteristic curve. The bandwidth $\gamma$ crucially affects the classification performance, and its optimal value is noticeably affected by the introduction of finite-shot estimation (10 000 shots) leading to the vanishing of the AUC gains over the classical baseline. Finally, accompanying runs on VTT’s Q50 quantum computer exhibit increased noise challenges for the symmetrized entanglement pattern.

DOI
10.22323/1.485.0634

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In this work, we study permutation-invariance and bandwidth-tuning in quantum fidelity kernels for classifying vector boson scattering (VBS) against QCD multijet background using proton-proton collisions simulated at s=13.6\sqrt{s}=13.6s​=13.6 TeV, with detector simulation corresponding to Run-2 CMS detector. We employ partially and fully symmetrized hardware-efficient kernel variants that embed SnS_nSn​ symmetry of the final-state jets. In noiseless simulation, some symmetry-enhanced kernels outperform a non-invariant HEA kernel, a classical Gaussian kernel baseline, and a product state quantum kernel in terms of the area under the curve (AUC) of the receiver operator characteristic curve. The bandwidth γ\gammaγ crucially affects the classification performance, and its optimal value is noticeably affected by the introduction of finite-shot estimation (10 000 shots) leading to the vanishing of the AUC gains over the classical baseline. Finally, accompanying runs on VTT’s Q50 quantum computer exhibit increased noise challenges for the symmetrized entanglement pattern.
Quantum kernels offer a valid procedure for learning quantum phase transitions on quantum processing devices, yet issues on the scalability of the learning strategy in connection with the symmetry of the critical model have not been clarified. We derive a link between model symmetry and fidelity-kernel resource scaling. We quantify the measurement resources required to estimate fidelity-based quantum kernels for many-body ground states while preserving the structure of the resulting Gram matrix under finite-shot sampling. Crucially, we show that increasing symmetry in the underlying spin model systematically amplifies these shot requirements. Moving from the Z2\mathbb{Z}_2Z2​-symmetric Ising/XY regimes to the U(1)U(1)U(1)-symmetric XX (and XXZ) regimes leads to stronger kernel concentration and therefore substantially larger shot costs under the same bounds. We consider a tunable one-dimensional spin-12\tfrac{1}{2}21​ Hamiltonian spanning the transverse-field Ising, XY, XX, and XXZ limits, and define the kernel as the ground-state fidelity. Kernel entries are estimated using a SWAP-test estimator with SSS shots, and we adapt the ensemble spread and concentration-avoidance shot bounds to obtain practical shot requirements in terms of the interquartile range of kernel values and a representative kernel magnitude. For the free-fermion XY/XX family, we use the closed-form Bogoliubov-angle fidelity, while for the interacting XXZ chain we compute fidelities by exact diagonalization and benchmark shot-noise effects. Our symmetry-aware bounds provide a pragmatic procedure for physics-informed quantum machine learning.
Abstract We report on a consistent comparison between techniques of quantum and classical machine learning applied to the classification of signal and background events for the Vector Boson Scattering processes, studied at the Large Hadron Collider installed at the CERN laboratory. Quantum machine learning algorithms based on variational quantum circuits are run on freely available quantum computing hardware, showing very good performances as compared to deep neural networks run on classical computing facilities. In particular, we show that such kind of quantum neural networks is able to correctly classify the targeted signal with an Area Under the characteristic Curve (AUC) that is very close to the one obtained with the corresponding classical neural network, but employing a much lower number of resources, as well as less variable data in the training set. Albeit giving a proof-of-principle demonstration with limited quantum computing resources, this work represents one of the first steps towards the use of near term and noisy quantum hardware for practical event classification in High Energy Physics experiments.
Quantum kernel estimation (QKE) lets a quantum computer supply the similarity values a classical support vector machine needs, but the original hardware demonstration is hard to reproduce and gives little guidance on the number of shots a usable kernel requires. This study implements QKE on a two-qubit simulator and quantifies its shot and noise requirements. A second-order ZZ feature map encodes each data point, kernel entries are measured from an overlap circuit, and a classical support vector machine is trained on the resulting matrix. An artificial dataset of 40 training and 40 test points was generated with a separation gap of 0.3, the shot count was varied from 128 to 50,000, and a depolarising and readout noise model was applied; classical kernels and a variational classifier served as baselines. With an exactly computed kernel the classifier labels every training and test point correctly using 12 support vectors. Perfect test accuracy is reached at 1,024 shots per pair, far below the 50,000 used on hardware, and the deviation from the exact kernel decays with a fitted exponent of -0.52. The weight of negative eigenvalues falls from 2.019 to 0.096 as shots increase, making it a practical warning sign of too few shots. Under noise the kernel values drop by 0.014 on average, yet accuracy stays at 100% because the drop is nearly uniform. Classical kernels reach at most 70% test accuracy and the variational classifier 98.3%. The work contributes a reproducible open-source procedure and shot-budget guidance for quantum kernel experiments.
This paper examines the application of a Quantum Support Vector Machine (QSVM) for radarbased aerial target classification using micro-Doppler signatures. Classical features are extracted and reduced via Principal Component Analysis (PCA) to enable efficient quantum encoding. The reduced feature vectors are embedded into a quantum kernel-induced feature space using a fully entangled ZZFeatureMap and classified using a kernel based QSVM. Performance is first evaluated on a quantum simulator and subsequently validated on NISQ-era superconducting quantum hardware, specifically the IBM Torino (133-qubit) and IBM Fez (156-qubit) processors. Experimental results demonstrate that the QSVM achieves competitive classification performance relative to classical SVM baselines while operating on substantially reduced feature dimensionality. Hardware experiments reveal the impact of noise and decoherence and measurement shot count on quantum kernel estimation, and further show improved stability and fidelity on newer Heron r2 architecture. This study provides a systematic comparison between simulator-based and hardware-based QSVM implementations and highlights both the feasibility and current limitations of deploying quantum kernel methods for practical radar signal classification tasks.
Quantum kernel methods are the most concrete near-term proposal for quantum machine learning on classical data, yet published benchmarks disagree on whether they outperform tuned classical kernels, and the disagreement cannot be resolved from the literature because the comparisons are not protocol-controlled. We argue that the obstacle is one of measurement, not theory: the usual setup fixes the quantum feature map's data scaling while grid-searching the classical kernel's hyperparameters, recomputes nothing per fold, and reports cost in simulator time. We therefore treat the comparison itself as the object of study and impose three controls. The bandwidth is tuned on the same grid budget as the classical γγγ, the kernel is recomputed inside every fold from fold-fitted preprocessing, and cost is counted in hardware circuit evaluations. On top of these we run a factorial design of 324 cells in which dimensionality, training size, class separability and data structure are explicit covariates, together with four standard datasets, a shots-versus-gate-noise ablation, and a cost sweep. The dominant effect we measure is not quantum: tuning the feature map's bandwidth is worth 0.120 accuracy on synthetic data and 0.339 on real data, exceeding every quantum-classical difference we observe. Tuned quantum kernels are then statistically indistinguishable from a tuned RBF on all four real datasets. The advantage on synthetic data is confined almost entirely to data generated by the feature map itself, and it shrinks with dimensionality (-0.0045 per qubit) while growing with sample size. Finite sampling costs an order of magnitude more accuracy than gate and readout noise, and a fidelity kernel needs 5×1075\times10^{7}5×107 circuits at n = 10,000. Protocol variance is thus sufficient to explain the field's contradictory conclusions.
We present a systematic design for large-scale quantum kernel classification, demonstrated through a quantum support vector classifier (QSVC) for particle-track classification using centroid-based CLAS12 drift-chamber features. Each event is encoded into a six-qubit state via a fully entangled ZZFeatureMap, whose fidelities define a quantum kernel within a standard SVM framework. By decoupling state preparation from kernel construction and distributing evaluation across a multi-node MPI-based HPC allocation, the approach scales to 1.0x10^5 training and 4.0x10^5 test events with an exactly constructed kernel matrix, to our knowledge more than an order of magnitude larger than prior high-energy-physics quantum-kernel studies. Benchmarked against linear, polynomial, RBF, and sigmoid SVM kernels and extremely randomized trees (ERT), the ideal QSVC achieves the highest recall (99.99%) among all models. Under a calibrated hardware noise model (FakeMumbaiV2, 500 training / 2,000 test events), AUC falls from 0.9985 to 0.9671 and peak significance improvement falls from 17.5 to ~3.5, yet recall remains at 99.51% -- indicating this signal-retention advantage is attenuated but not eliminated by circuit-level decoherence. Geometric analysis of the quantum embedding shows near-orthogonal inter-class states with coherent intra-class neighborhoods under ideal simulation; under noise this structure compresses toward the maximally mixed state while preserving its relative ordering. These results demonstrate a scalable, reproducible workflow for quantum kernel experimentation at HEP-relevant scale, quantifying the practical cost of realistic hardware noise on quantum-enhanced classification.