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Simulation-Based Explainable AI for Quantum Dynamics: Neural Proxies and SHAP for Entanglement Analysis

Muhammad Shaharyar Nasir

Published Mar 4, 2026• 0 citations
Publisher

Abstract

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 ($t \approx 2.5$ and $7.5$) 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}).**

DOI
10.21203/rs.3.rs-8584766/v1

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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}).
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 rapid advancement of Artificial Intelligence (AI) has heightened concerns about the opacity of decision-making processes in complex models, particularly deep neural networks. This research explores a novel paradigm that integrates quantum computing principles into Explainable AI (XAI) to enhance interpretability without compromising predictive accuracy. The study introduces a Quantum-inspired Interpretable Model (QIIM) framework that leverages Hilbert space embeddings, unitary transformations, and operator-based learning to represent knowledge in a mathematically transparent form. The proposed model computes interpretability through the expectation values of observable operators, enabling the decomposition of decisions into quantifiable, human-understandable components. To capture hierarchical relationships, a Tensor Network Interpretable Model (TNIM) is further developed, offering scalable insights into complex dependencies among features. Experimental evaluations—performed on benchmark datasets for decision-making tasks—demonstrate that the quantum-inspired models achieve competitive accuracy while significantly improving local and global interpretability metrics compared to classical XAI techniques. The findings underscore the potential of quantum formalism as a new foundation for transparent AI systems, bridging the gap between computational efficiency and explainability. This study contributes to both theoretical understanding and practical advancement in interpretable machine learning, paving the way for ethically aligned, transparent, and human-trustworthy AI-driven decision support systems.
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In recent years, machine learning has achieved remarkable success in tasks such as image classification and solving complex real-world problems. The achievements of deep neural networks (DNNs) have led to the widespread adoption of block-based architectures. However, as the demand for Explainable AI (XAI) grows, there is a need for models that provide greater transparency and interpretability. Our work addresses this need by exploring the potential of quantum-classical hybrid models. By integrating classical neural networks (ClaNNs) with quantum neural networks (QNNs), we aim to develop AI systems that are not only powerful but also interpretable. We propose a framework that combines parameterized quantum circuits (PQCs) with classical layers to create a hybrid block design for QNNs. By adding a linear layer after the PQCs, the flexibility of the block design is increased. This architecture enhances the adaptability of QNN design and facilitates the integration of XAI principles through the comparison of the loss function planes. Our training method, inspired by knowledge distillation, addresses existing challenges in PQC-based QNN designs, providing insights into the optimization landscape. We validate the effectiveness of our hybrid block through experiments on standard datasets, demonstrating its potential to achieve comparable accuracy to traditional DNNs while providing improved interpretability.
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 Methods of artificial intelligence (AI) and especially machine learning (ML) have been growing ever more complex, and at the same time have more and more impact on people’s lives. This leads to explainable AI (XAI) manifesting itself as an important research field that helps humans to better comprehend ML systems. In parallel, quantum machine learning (QML) is emerging with the ongoing improvement of quantum computing hardware combined with its increasing availability via cloud services. QML enables quantum-enhanced ML in which quantum mechanics is exploited to facilitate ML tasks, typically in the form of quantum-classical hybrid algorithms that combine quantum and classical resources. Quantum gates constitute the building blocks of gate-based quantum hardware and form circuits that can be used for quantum computations. For QML applications, quantum circuits are typically parameterized and their parameters are optimized classically such that a suitably defined objective function is minimized. Inspired by XAI, we raise the question of the explainability of such circuits by quantifying the importance of (groups of) gates for specific goals. To this end, we apply the well-established concept of Shapley values. The resulting attributions can be interpreted as explanations for why a specific circuit works well for a given task, improving the understanding of how to construct parameterized (or variational) quantum circuits, and fostering their human interpretability in general. An experimental evaluation on simulators and two superconducting quantum hardware devices demonstrates the benefits of the proposed framework for classification, generative modeling, transpilation, and optimization. Furthermore, our results shed some light on the role of specific gates in popular QML approaches.