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.