With the rapid development of Quantum Machine Learning, quantum neural networks (QNN) have experienced great advancement in the past few years, harnessing the advantages of quantum computing to significantly speed up classical machine learning tasks. Despite their increasing popularity, the quantum neural network is quite counter-intuitive and difficult to understand, due to their unique quantum-specific layers (e.g., data encoding and measurement) in their architecture. It prevents QNN users and researchers from effectively understanding its inner workings and exploring the model training status. To fill the research gap, we propose VIOLET, a novel visual analytics approach to improve the explainability of quantum neural networks. Guided by the design requirements distilled from the interviews with domain experts and the literature survey, we developed three visualization views: the Encoder View unveils the process of converting classical input data into quantum states, the Ansatz View reveals the temporal evolution of quantum states in the training process, and the Feature View displays the features a QNN has learned after the training process. Two novel visual designs, i.e., satellite chart and augmented heatmap, are proposed to visually explain the variational parameters and quantum circuit measurements respectively. We evaluate VIOLET through two case studies and in-depth interviews with 12 domain experts. The results demonstrate the effectiveness and usability of VIOLET in helping QNN users and developers intuitively understand and explore quantum neural networks.
With the rapid development of Quantum Machine Learning, quantum neural networks (QNN) have experienced great advancement in the past few years, harnessing the advantages of quantum computing to significantly speed up classical machine learning tasks. Despite their increasing popularity, the quantum neural network is quite counter-intuitive and difficult to understand, due to their unique quantum-specific layers (e.g., data encoding and measurement) in their architecture. It prevents QNN users and researchers from effectively understanding its inner workings and exploring the model training status. To fill the research gap, we propose VIOLET, a novel visual analytics approach to improve the explainability of quantum neural networks. Guided by the design requirements distilled from the interviews with domain experts and the literature survey, we developed three visualization views: the Encoder View unveils the process of converting classical input data into quantum states, the Ansatz View reveals the temporal evolution of quantum states in the training process, and the Feature View displays the features a QNN has learned after the training process. Two novel visual designs, i.e., satellite chart and augmented heatmap, are proposed to visually explain the variational parameters and quantum circuit measurements respectively. We evaluate VIOLET through two case studies and in-depth interviews with 12 domain experts. The results demonstrate the effectiveness and usability of VIOLET in helping QNN users and developers intuitively understand and explore quantum neural networks.
Quantum computing has entered a stage of increasing practicality. Many quantum hardware vendors such as IBM, Rigetti, Honeywell, and IonQ now enable experiments on real devices in the Noisy Intermediate-Scale Quantum (NISQ) era. These platforms show computational advantages in domains such as optimization, machine learning, and materials science. However, they remain limited by hardware noise and the absence of human-interpretable information. Existing visual metaphors, such as the Bloch Sphere for single-qubit states or circuit schematics for algorithm design, struggle to convey multi-qubit entanglement or measurement probabilities in ways accessible to human reasoning. Likewise, the rise of variational quantum circuits and quantum neural networks (QNNs) introduces new layers of opacity: how data are encoded into quantum states and how parameters evolve through training remain largely under-explored. These challenges motivate a need for visual explanation frameworks that unveil the invisible processes of quantum computing visible, interpretable, and reasonable.To address these challenges, this dissertation presents a coherent sequence of visual analytics systems that progressively enhance explainability across the hardware, state, circuit, and model layers of quantum computing. First, VACSEN supports noise-aware execution by visually correlating hardware fidelity metrics with compiled quantum circuits, allowing users to identify unstable qubits, track temporal noise evolution, and select optimal execution strategies. Second, VENUS introduces a geometric representation for quantum state visualization, combining right triangles and semicircles to jointly encode amplitude and probability information, thereby enabling intuitive exploration of superposition and entanglement beyond the traditional Bloch Sphere. Third, QuantumEyes extends interpretability to quantum circuit behavior, integrating coordinated views to reveal how quantum gates transform amplitudes and probabilities during algorithm execution (e.g., Grover’s search or the Quantum Fourier Transform). Finally, VIOLET applies visual explainability to quantum neural networks, bridging concepts from explainable AI and quantum computing. It visualizes the encoding of classical data into quantum states, tracks parameter dynamics during variational training, and exposes learned features and measurement distributions, establishing the first end-to-end system for understanding QNNs.Each system was designed through iterative co-design with quantum computing experts and evaluated through case studies, task analyses, and in-depth interviews involving researchers and practitioners from academia and industry. Across evaluations, participants reported that visualization significantly enhanced their ability to reason about noise effects, understand quantum-state evolution, and interpret the learning behavior of QNNs. These findings demonstrate that visualization not only accelerates analysis and debugging but also strengthens conceptual understanding and user trust in quantum computing. To sum up, this dissertation establishes visualization
Quantum Neural Networks (QNNs) represent a promising fusion of quantum computing and neural network architectures, offering speed-ups and efficient processing of high-dimensional, entangled data. A crucial component of QNNs is the encoder, which maps classical input data into quantum states. However, choosing suitable encoders remains a significant challenge, largely due to the lack of systematic guidance and the trial-and-error nature of current approaches. This process is further impeded by two key challenges: (1) the difficulty in evaluating encoded quantum states prior to training, and (2) the lack of intuitive methods for analyzing an encoder's ability to effectively distinguish data features. To address these issues, we introduce a novel visualization tool, XQAI-Eyes, which enables QNN developers to compare classical data features with their corresponding encoded quantum states and to examine the mixed quantum states across different classes. By bridging classical and quantum perspectives, XQAI-Eyes facilitates a deeper understanding of how encoders influence QNN performance. Evaluations across diverse datasets and encoder designs demonstrate XQAI-Eyes's potential to support the exploration of the relationship between encoder design and QNN effectiveness, offering a holistic and transparent approach to optimizing quantum encoders. Moreover, domain experts used XQAI-Eyes to derive two key practices for quantum encoder selection, grounded in the principles of pattern preservation and feature mapping.
Quantum computing offers significant speedup compared to classical computing, which has led to a growing interest among users in learning and applying quantum computing across various applications. However, quantum circuits, which are fundamental for implementing quantum algorithms, can be challenging for users to understand due to their underlying logic, such as the temporal evolution of quantum states and the effect of quantum amplitudes on the probability of basis quantum states. To fill this research gap, we propose QuantumEyes, an interactive visual analytics system to enhance the interpretability of quantum circuits through both global and local levels. For the global-level analysis, we present three coupled visualizations to delineate the changes of quantum states and the underlying reasons: a Probability Summary View to overview the probability evolution of quantum states; a State Evolution View to enable an in-depth analysis of the influence of quantum gates on the quantum states; a Gate Explanation View to show the individual qubit states and facilitate a better understanding of the effect of quantum gates. For the local-level analysis, we design a novel geometrical visualization dandelion chart to explicitly reveal how the quantum amplitudes affect the probability of the quantum state. We thoroughly evaluated QuantumEyes as well as the novel dandelion chart integrated into it through two case studies on different types of quantum algorithms and in-depth expert interviews with 12 domain experts. The results demonstrate the effectiveness and usability of our approach in enhancing the interpretability of quantum circuits.
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.
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 performance of quantum neural network models depends strongly on architectural decisions, including circuit depth, placement of parametrized operations, and data-encoding strategies. Selecting an effective architecture is challenging and closely related to the classical difficulty of choosing suitable neural-network topologies, which is computationally hard. This work investigates automated quantum-circuit construction for regression tasks and introduces a genetic-algorithm framework that discovers Reduced Regressor QNN architectures. The approach explores depth, parametrized gate configurations, and flexible data re-uploading patterns, formulating the construction of quantum regressors as an optimization process. The discovered circuits are evaluated against seventeen classical regression models on twenty-two nonlinear benchmark functions and four analytical functions. Although classical methods often achieve comparable results, they typically require far more parameters, whereas the evolved quantum models remain compact while providing competitive performance. We further analyze dataset complexity using twelve structural descriptors and show, across five increasingly challenging meta-learning scenarios, that these measures can reliably predict which quantum architecture will perform best. The results demonstrate perfect or near-perfect predictive accuracy in several scenarios, indicating that complexity metrics offer powerful and compact representations of dataset structure and can effectively guide automated model selection. Overall, this study provides a principled basis for meta-learning-driven quantum architecture design and advances the understanding of how quantum models behave in regression settings--a topic that has received limited exploration in prior work. These findings pave the way for more systematic and theoretically grounded approaches to quantum regression.