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FQ-SHAP: Fuzzy Logic Enhanced Explainability for Quantum Circuits An Extension of Q-SHAP via Fuzzy Gate Classification, Importance-Weighted Consistency, and Entanglement-Aware Pruning

Abraham Itzhak Weinberg

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.13140/rg.2.2.15355.27684

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This study explores explainability approaches that are independent of models, with a particular emphasis on Integrated Gradients (IG) and Baseline SHAP (BS) within the framework of parametrized quantum circuits (PQCs). After a thorough mathematical examination, we modify BS to a new Polynomial SHAP (qSHAP) approach optimized for PQCs; this allows us to estimate SHAP values efficiently using rankone polynomial approximations. We prove that qSHAP is resilient even in quantum contexts with noise by evaluating the stability of IG and BS in the presence of quantum noise via the central limit theorem. Tests on the Bars and Stripes dataset with one-, two-, and four-qubit classifiers confirm that our method works in different environments, such as classical simulations, noise models, and actual quantum computers. The results demonstrate that qSHAP offers consistent and dependable feature attributions, whereas IG's performance drops with noise. This suggests that qSHAP might be a useful tool for explainability in the near future of quantum machine learning, resistant to noise.

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Deep learning vision systems excel at pattern recognition yet falter when inputs are noisy or the model must explain its own confidence. Fuzzy inference, with its graded memberships and rule transparency, offers a remedy, while parameterized quantum circuits can embed features in richly entangled Hilbert spaces with striking parameter efficiency. Bridging these ideas, this study introduces a innovative Highly Quantized Fuzzy Neural Network (HQFNN) that realises the entire fuzzy pipeline inside a shallow quantum circuit and couples the resulting quantum signal to a lightweight CNN feature extractor. Each image feature is first mapped to a single qubit membership state through repeated angle reuploading. Then a compact rule layer refines these amplitudes, and a clustered CNOT defuzzifier collapses them into one crisp value that is fused with classical features before classification. Evaluated on standard image benchmarks, HQFNN consistently surpasses classical, fuzzy enhanced and quantum only baselines while using several orders of magnitude fewer trainable weights, and its accuracy degrades only marginally under simulated depolarizing and amplitude damping noise, evidence of intrinsic robustness. Gate count analysis further shows that circuit depth grows sublinearly with input dimension, confirming the model's practicality for larger images. These results position the model as a compact, interpretable and noise tolerant alternative to conventional vision backbones and provide a template for future quantum native fuzzy learning frameworks.
This study explores explainability approaches that are independent of models, with a particular emphasis on Integrated Gradients (IG) and Baseline SHAP (BS) within the framework of parametrized quantum circuits (PQCs). After a thorough mathematical examination, we modify BS to a new Polynomial SHAP (qSHAP) approach optimized for PQCs; this allows us to estimate SHAP values efficiently using rankone polynomial approximations. We prove that qSHAP is resilient even in quantum contexts with noise by evaluating the stability of IG and BS in the presence of quantum noise via the central limit theorem. Tests on the Bars and Stripes dataset with one-, two-, and four-qubit classifiers confirm that our method works in different environments, such as classical simulations, noise models, and actual quantum computers. The results demonstrate that qSHAP offers consistent and dependable feature attributions, whereas IG's performance drops with noise. This suggests that qSHAP might be a useful tool for explainability in the near future of quantum machine learning, resistant to noise.