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.
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.
Parametrized Quantum Circuits (PQCs) enable a novel method for machine learning (ML). However, from a computational point of view they present a challenge to existing eXplainable AI (xAI) methods. On the one hand, measurements on quantum circuits introduce probabilistic errors which impact the convergence of these methods. On the other hand, the phase space of a quantum circuit expands exponentially with the number of qubits, complicating efforts to execute xAI methods in polynomial time. In this paper we will discuss the performance of established xAI methods, such as Baseline SHAP and Integrated Gradients. Using the internal mechanics of PQCs we study ways to speed up their computation.
Variational quantum classifiers (VQCs) are a leading approach for near-term quantum machine learning, but explaining their specific decisions remains a growing challenge. Classical ML has established tools for self-explanation, such as gradient-based heatmaps. However, quantum circuits trained on real hardware cannot use classical backpropagation, requiring quantum-native methods instead. This study applies one such method, the parameter-shift rule, to compute input gradients, resulting in saliency scores using two circuit evaluations per input feature. Using a small, controlled 2x2 image classification task with known ground-truth pixels, this study evaluates whether the model's explanations align with the features truly driving its predictions. The trained 4-qubit VQC achieves 100% test accuracy and identifies the correct causal pixels in 62.5% of test cases. To assess faithfulness more directly, ablation experiments show that masking saliency-identified pixels reduces model confidence by 3.97%, compared to 0.014% for random masking, a raw improvement of roughly 274x. Additional multi-seed analyses suggest the method remains reasonably consistent across different model initializations, helping show that explanation results are not from just one lucky training run. Overall, these results suggest that input parameter-shift saliency is a promising approach for Quantum explainability and motivate testing it on larger, more complex datasets.
This study investigates classification performance and trainability of variational quantum classifiers on near-term noisy quantum hardware across circuit depth and qubit count regimes within the context of quantum computing and machine learning, an area of growing scientific importance given its implications for hybrid quantum-classical algorithm design and practical NISQ hardware benchmarking for near-term quantum advantage assessment. Using gradient-based parameter optimization of parameterized quantum circuits with hardware noise modeling via density matrix simulation and physical execution on IBM Eagle processors, we examine expressibility of parameterized circuits enabling nonlinear decision boundaries in feature Hilbert space, with trainability constrained by barren plateau gradients at large qubit counts in 96 circuit architectures (4 qubit counts x 4 depths x 6 ansatz families) evaluated across 5 classification datasets with 20 random initialization seeds each drawn from IBM Quantum Eagle (127-qubit) and Falcon (27-qubit) processors with noise mitigation via zero-noise extrapolation. Results indicate that 10-qubit, 4-layer VQC achieves 84.2% classification accuracy on the best benchmark, within 3.8 percentage points of classical SVM, but gradient variance decays exponentially with qubit count (variance halving per 2 added qubits), confirming barren plateau scaling (p < 0.001), with 84.2% accuracy, 3.8 pp gap to classical SVM baseline as the primary quantitative benchmark. Concordance between primary and confirmatory measurement approaches exceeded 93%, validating the analytical framework. These findings contribute empirically to quantum computing and machine learning and carry actionable implications for the design of programs and policies targeting hybrid quantum-classical algorithm design and practical NISQ hardware benchmarking for near-term quantum advantage assessment.
Abstract As machine learning grows increasingly complex due to big data and deep learning, model explainability has become essential to fostering user trust. Quantum machine learning (QML) has emerged as a promising field, leveraging quantum computing to enhance classical machine learning methods, particularly through quantum representation learning (QRL). QRL aims to provide more efficient and powerful machine learning capabilities on noisy intermediate-scale quantum (NISQ) devices. However, interpreting QRL models poses significant challenges due to the reliance on quantum gate-based parameterized circuits, which, while analogous to classical neural network layers, operate in the quantum domain. To address these challenges, we propose an explainable QRL framework combining a quantum autoencoder (QAE) with a variational quantum classifier (VQC) and incorporating theoretical and empirical explainability for image data. Our dual approach enhances model interpretability by integrating visual explanations via local interpretable model-agnostic explanations (LIME) and analytical insights using Shapley Additive Explanations (SHAP). These complementary methods provide a deeper understanding of the model’s decision-making process based on prediction outcomes. Experimental evaluations on simulators and superconducting quantum hardware validate the effectiveness of the proposed framework for classification tasks, underscoring the importance of explainable representation learning in advancing QML towards more transparent and reliable applications.
Quantum machine learning (QML) has emerged as a promising paradigm for solving complex classification problems by leveraging the computational advantages of quantum systems. While most traditional machine learning models focus on clean, balanced datasets, real-world data is often noisy, imbalanced and high-dimensional, posing significant challenges for scalability and generalisation. This paper conducts an extensive experimental evaluation of five supervised classifiers- Decision Tree, K nearest neighbour, Random Forest, linear regression and support vector machines in comparison with Quantum machine learning classifiers- quantum Support vector machine, quantum k- nearest neighbor and variational quantum classifier-across five diverse datasets, including iris, wine quality, Breast cancer, UCI human activity recognition, and Pima diabetes. To simulate real-world challenges, we introduce class imbalance using SMOTE and ADASYN Sampling, inject Gaussian noise into the features, and assess the impact of dimensionality reduction through ANOVA-based feature selection. Additionally, we utilise explainable AI tools, such as SHAP and LIME, to interpret model decisions. Our results demonstrate that Logistic Regression consistently performs well under various complexities, while Quantum Support Vector Machines show resilience to feature noise and class imbalance. The study also highlights the current capabilities and limitations of QML models, offering valuable insights into building generalisable and interpretable ML systems for deployment in complex environments. These insights are crucial for building robust, interpretable, and generalisable ML models for practical deployment.
The decisions of variational quantum reinforcement learning agents remain largely opaque, limiting trust in safety-critical deployments. We present the first application of SHapley Additive exPlanations (SHAP) to a Variational Quantum Policy Gradient (VQPG) agent trained on CartPole-v1. Our 4-qubit hybrid quantum-classical policy uses only 46 trainable parameters and achieves a mean evaluation score of 496.4±8.1 over ten independent seeds (maximum 500.0), compared to 249.7±38.6 for a standard Deep Q-Network (DQN) with 9 220 parameters and 412.3±67.9 for a parameter-matched Tiny-MLP (30 parameters, identical training budget). SHAP analysis identifies Pole Angular Velocity as the dominant decision feature (mean ∣ϕ∣=0.2859 , approximately 7× the next feature), consistent with classical control theory for inverted pendulum stabilisation. This attribution is stable across five independently sampled background sets (coefficient of variation 3.1% ), confirming the reliability of the explanation. We emphasise that all results are obtained under noiseless simulation; no claim of quantum advantage in the complexity-theoretic sense is made. The complete experimental package is deposited on https://zenodo.org/ under CC-BY 4.0.