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Communications in computer and information science

Explainable Variational Quantum Policy Gradient: SHAP-Based Interpretability of Quantum Reinforcement Learning Agents on CartPole

Sandeep Gupta, Sazzad Hossain, Akmal Akhatov, Mekhriddin Nurmamatov, Kanad Ray

Published Oct 23, 2026• 0 citations
Publisher

Abstract

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 $$496.4 \pm 8.1$$ over ten independent seeds (maximum 500.0), compared to $$249.7 \pm 38.6$$ for a standard Deep Q-Network (DQN) with 9 220 parameters and $$412.3 \pm 67.9$$ for a parameter-matched Tiny-MLP (30 parameters, identical training budget). SHAP analysis identifies Pole Angular Velocity as the dominant decision feature (mean $$|\phi | = 0.2859$$ , approximately $$7\times $$ 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.

DOI
10.1007/978-3-032-42348-1_3

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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±8.1496.4 \pm 8.1496.4±8.1 over ten independent seeds (maximum 500.0), compared to 249.7±38.6249.7 \pm 38.6249.7±38.6 for a standard Deep Q-Network (DQN) with 9 220 parameters and 412.3±67.9412.3 \pm 67.9412.3±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|\phi | = 0.2859∣ϕ∣=0.2859 , approximately 7×7\times 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%3.1\%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.
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.
The comparative evaluation between classical and quantum reinforcement learning (QRL) paradigms was conducted to investigate their convergence behavior, robustness under observational noise, and computational efficiency in a benchmark control environment. The study employed a multilayer perceptron (MLP) agent as a classical baseline and a parameterized variational quantum circuit (VQC) as a quantum counterpart, both trained on the CartPole-v1 environment over 500 episodes. Empirical results demonstrated that the classical MLP achieved near-optimal policy convergence with a mean return of 498.7 +/- 3.2, maintaining stable equilibrium throughout training. In contrast, the VQC exhibited limited learning capability, with an average return of 14.6 +/- 4.8, primarily constrained by circuit depth and qubit connectivity. Noise robustness analysis further revealed that the MLP policy deteriorated gracefully under Gaussian perturbations, while the VQC displayed higher sensitivity at equivalent noise levels. Despite the lower asymptotic performance, the VQC exhibited significantly lower parameter count and marginally increased training time, highlighting its potential scalability for low-resource quantum processors. The results suggest that while classical neural policies remain dominant in current control benchmarks, quantum-enhanced architectures could offer promising efficiency advantages once hardware noise and expressivity limitations are mitigated.
Quantum Machine Learning (QML) has emerged as a promising paradigm that leverages quantum mechanical principles to accelerate machine learning tasks.Despite its potential, most QML models remain opaque "black boxes," hindering their deployment in high-stakes or regulated domains where trust and accountability are essential.This work introduces two novel interpretability methods tailored for QML: Quantum Shapley Values (QSV) and Quantum Local Interpretable Model-Agnostic Explanations (Q-LIME).QSV adapts cooperative game theory to quantify the contribution of individual qubits, observables, or circuit parameters, while Q-LIME generates perturbed quantum states and trains surrogate classical models to approximate local decision boundaries.Through experiments on variational quantum classifiers and hybrid quantum-classical neural networks, we demonstrate that QSV provides rigorous attribution but suffers from scalability constraints, whereas Q-LIME yields efficient, approximate explanations suitable for near-term devices.By transforming quantum models from opaque "black boxes" into interpretable "glass boxes," this research lays the foundation for trustworthy, transparent, and human centred quantum AI.
Deep Reinforcement Learning (RL) has considerably advanced over the past decade. At the same time, state-of-the-art RL algorithms require a large computational budget in terms of training time to converge. Recent work has started to approach this problem through the lens of quantum computing, which promises theoretical speed-ups for several traditionally hard tasks. In this work, we examine a class of hybrid quantum-classical RL algorithms that we collectively refer to as variational quantum deep Q-networks (VQ-DQN). We show that VQ-DQN approaches are subject to instabilities that cause the learned policy to diverge, study the extent to which this afflicts reproducibility of established results based on classical simulation, and perform systematic experiments to identify potential explanations for the observed instabilities. Additionally, and in contrast to most existing work on quantum reinforcement learning, we execute RL algorithms on an actual quantum processing unit (an IBM Quantum Device) and investigate differences in behaviour between simulated and physical quantum systems that suffer from implementation deficiencies. Our experiments show that, contrary to opposite claims in the literature, it cannot be conclusively decided if known quantum approaches, even if simulated without physical imperfections, can provide an advantage as compared to classical approaches. Finally, we provide a robust, universal and well-tested implementation of VQ-DQN as a reproducible testbed for future experiments.
Abstract The challenge of quantum measurement, wherein observation collapses the wavefunction, hinders non-invasive study of phenomena such as entanglement and superposition. This is especially problematic when analyzing the temporal evolution of multi-qubit systems, where repeated measurement disrupts the very dynamics under investigation. Inspired by challenges in interpreting black-box machine learning models, we propose a simulation-to-explainable AI (XAI) framework for analyzing entanglement dynamics through neural network proxies and interpretability analysis. Using QuTiP-based simulations, we generate temporal correlation data from entangled two-, four-, and six-qubit systems evolving under structured Hamiltonians~\cite{johansson2013}. Classical neural networks trained on this data achieve high accuracy in reproducing entanglement metrics, with mean squared errors of 0.0196 (2 qubits), 0.025 (4 qubits), and 0.0361 (6 qubits). Applying SHAP (SHapley Additive exPlanations)~\cite{lundberg2017}, we **uniquely identify temporal features (t≈2.5t \approx 2.5t≈2.5 and 7.57.57.5) that reveal entanglement oscillation phases, enhancing interpretability beyond traditional simulation endpoints.** We propose a framework integrating neural-network proxies with explainable AI techniques to analyze quantum dynamics. Importantly, our approach is strictly \emph{collapse-free within classical simulations}: it does not address the measurement problem in quantum foundations but avoids explicit projective measurement in the numerical pipeline. The method combines QuTiP-based simulations, neural approximations of unitary dynamics, and SHAP-based interpretability applied to temporal entanglement features. **As of September 2025, this work supports NISQ-era applications with freely accessible code and data at Zenodo (DOI: \href{https://doi.org/10.5281/zenodo.17216687}{10.5281/zenodo.17216687}).**
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.