Towards Explainable Quantum AI: Informing the Encoder Selection of Quantum Neural Networks via Visualization

© 2025 IEEE. This is the author’s version of the article that has been published in IEEE Transactions on Visualization and Computer Graphics. The final version of this record is available at: xx.xxxx/TVCG.201x.xxxxxxx/ Towards Explainable Quantum AI: Informing the Encoder Selection of Quantum Neural Networks via Visualization Shaolun Ruan , Feng Liang , Rohan Ramakrishna , Chao Ren , Rudai Yan , Qiang Guan , Jiannan Li and Yong Wang C A D F G J B E H Fig. 1: The interface of XQAI-Eyes supports the reasoning and selection of the encoder’s quality in QNNs. The Original Data View (C) visualizes the input dataset. The Encoded Data Evolution View (E) illustrates the quantum circuit used for encoding together with the illustration of the encoding process in each step. The Encoder Map View (F) displays the encoded data as a heatmap, facilitating a direct comparison with the original data. The Quantum Distribution Map (J) provides an intuitive representation to show how well the encoder distinguishes the data points with different classes. The Trained Map View (G) visualizes the final learned patterns after training, while the Performance Analysis View (H) uses line charts to depict the training loss and accuracy. Abstract—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. Index Terms—Data visualization, quantum neural network, explainable artificial intelligence (XAI), quantum data encoder. 1 INTRODUCTION • Shaolun Ruan and Jiannan Li are with Singapore Management University. E-mail: slruan.2021@phdcs.smu.edu.sg, jiannanli@smu.edu.sg • Feng Liang, Rohan Ramakrishna, Rudai Yan and Yong Wang are with Nanyang Technological University. E-mail: {feng011 | roha0012 | rudai011}@e.ntu.edu.sg, yong-wang@ntu.edu.sg. Yong Wang is the corresponding author. • Chao Ren is with KTH Royal Institute of Technology. E-mail: renc0003@e.ntu.edu.sg • Qiang Guan is with Kent State University. E-mail: qguan@kent.edu. 1 arXiv:2512.14181v1 [quant-ph] 16 Dec 2025 Quantum computing is an emerging field that harnesses the principles of quantum mechanics to achieve advantages beyond the capabilities of classical computation. Building on this foundation, quantum neu- ral networks (QNNs) integrate quantum operations with neural net- work architectures to tackle complex optimization problems [9,19,25]. Compared to their classical counterparts, QNNs demonstrate the po- tential for exponential speed-ups and are particularly well-suited for processing high-dimensional and entangled data [1, 10, 40, 51]. Fur- thermore, by exploiting quantum parallelism, QNNs facilitate more efficient learning and optimization processes [3,53]. Meanwhile, visu- alization, which has proven to be a suitable scientific educational tool, has seen an increasing proliferation in research [5,34,35,46] and appli- cations [12,29,30] of quantum computing in recent years, significantly enhancing the transparency of black-box quantum algorithms. Typically, a QNN consists of three basic components: the encoder, the ansatz, and the measurement. As the first component, the encoder plays a crucial role in transforming classical input data into quantum states, enabling the encoded data to be recognized and trained by the subsequent ansatz layer. Due to the fact that different encoders can produce completely different results, the selection and design of the encoder significantly affect the final performance of the QNN [22,26]. More specifically, the model could achieve optimal performance only if the original data features can be ef

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