Abstract Capsule networks (CapsNets), which incorporate the paradigms of connectionism and symbolism, have brought fresh insights into artificial intelligence (AI). The capsule, as the building block of CapsNets, is a group of neurons represented by a vector to encode different features of an entity. The information is extracted hierarchically through capsule layers via routing algorithms. Here, we introduce a quantum capsule network (dubbed QCapsNet) together with an efficient quantum dynamic routing algorithm. To benchmark the performance of the QCapsNet, we carry out extensive numerical simulations on the classification of handwritten digits and symmetry-protected topological phases, and show that the QCapsNet can achieve an enhanced accuracy and outperform conventional quantum classifiers evidently. We further unpack the output capsule state and find that a particular subspace may correspond to a human-understandable feature of the input data, which indicates the potential explainability of such networks. Our work reveals an intriguing prospect of QCapsNets in quantum machine learning, which may provide a valuable guide towards explainable quantum AI.
Abstract Capsule networks (CapsNets), which incorporate the paradigms of connectionism and symbolism, have brought fresh insights into artificial intelligence (AI). The capsule, as the building block of CapsNets, is a group of neurons represented by a vector to encode different features of an entity. The information is extracted hierarchically through capsule layers via routing algorithms. Here, we introduce a quantum capsule network (dubbed QCapsNet) together with an efficient quantum dynamic routing algorithm. To benchmark the performance of the QCapsNet, we carry out extensive numerical simulations on the classification of handwritten digits and symmetry-protected topological phases, and show that the QCapsNet can achieve an enhanced accuracy and outperform conventional quantum classifiers evidently. We further unpack the output capsule state and find that a particular subspace may correspond to a human-understandable feature of the input data, which indicates the potential explainability of such networks. Our work reveals an intriguing prospect of QCapsNets in quantum machine learning, which may provide a valuable guide towards explainable quantum AI.
A capsule network (CapsNet) provides a richer hierarchical representation than conventional neural networks through vector-shaped capsules and intercapsule routing. However, most CapsNet designs still rely on classic matrix-multiplication-based vote transformations, which limit the formation of the prediction vector to linear mappings in Euclidean space. In this article, we propose the hybrid quantum capsule network (HQCapsNet), an architecture that replaces classical vote transformations with a quantum transformation circuit (QTC) based on a parameterized quantum circuit (PQC). We introduce a QTC in two schemes: classwise QTC and fully connected QTC. Furthermore, the routing agreement mechanism is extended via hybrid quantum routing, leveraging various quantum similarity metrics. The evaluation was conducted on several binary image classification datasets, with MNIST, TMNIST, and MNIST-M used as the primary datasets. The experimental analysis included benchmarking of quantum embedding variations, the PQC ansatz, qubit-count analysis, circuit depth, and routing iterations. The experimental results show that the fully connected QTC is the best configuration, achieving consistent accuracy improvements over the classwise QTC, with the most significant improvement from 92.86% to 97.62% on the MNIST-M dataset. Compared to the classical CapsNet, the HQCapsNet also achieves higher performance across all primary datasets, achieving 99.95% accuracy on MNIST and competing with quantum–classical models on comparable split data. These results indicate that integrating quantum computing at the voting transformation step is a promising approach to improving CapsNet’s representation and generalization capabilities.
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.
Quantum Neural Networks (QNNs) represent a promising paradigm shift in artificial intelligence, leveraging the unique properties of quantum mechanics to enhance computational capabilities. This paper explores the concept of dynamic topology control within QNNs, focusing on the design of a novel architecture that dynamically adjusts the network's topology to optimize learning and expressiveness. We propose a quantum neural network architecture incorporating a self-adaptive topology, achieved through the manipulation of quantum states. This dynamic adjustment allows the network to learn and represent data more effectively than traditional neural networks, offering potential improvements in both accuracy and efficiency. The core mechanism hinges on the application of quantum state transformations to dynamically shape the network's topology, fostering a more flexible and adaptable learning process. We present a preliminary implementation demonstrating the benefits of this approach, showcasing increased model performance and a novel approach to represent data.
This paper introduces the Topological Quantum Machine Learning Algorithm (TQMA), a novel approach to machine learning that leverages the inherent properties of topology and quantum mechanics to enhance model identification and prediction capabilities. Traditional machine learning methods often rely on extensive parameter tuning, hindering model adaptability and robustness. TQMA overcomes this limitation by incorporating a dynamically evolving, topologically structured representation within the model, enabling it to better capture complex relationships within data. We present a framework that integrates a quantum-inspired optimization process within a topological graph, allowing for exploration of intricate feature spaces and improved generalization. The algorithm's core mechanism centers around the construction and application of a quantum-enhanced topological graph, which facilitates the identification of subtle patterns and correlations often missed by conventional methods. We demonstrate the efficacy of TQMA through a series of benchmark datasets, showcasing significant improvements in classification accuracy and predictive performance compared to existing state-of-the-art techniques. This paper provides a comprehensive investigation into the potential of TQMA as a paradigm shift in machine learning, offering a pathway towards more intelligent and adaptable models.
Quantum Machine Learning (QML) represents a paradigm shift in computational neuroscience, offering the potential to surpass classical machine learning in certain tasks. This paper explores the application of hierarchical feature extraction, a core concept within QML, to enhance the performance of machine learning models. We propose a quantum algorithm for feature extraction that leverages quantum superposition and entanglement to identify and represent complex patterns within data, followed by a quantum neural network to learn from these representations. This approach aims to improve model accuracy and accelerate training through the integration of quantum computation and machine learning. The core claim is that the combined approach will yield superior results compared to traditional machine learning methods. This work addresses the limitations of current machine learning techniques by introducing a novel quantum approach to feature representation, ultimately facilitating a more robust and efficient learning process. We present a theoretical framework and initial implementation demonstrating the potential of this hybrid architecture.
At the nexus of artificial intelligence (AI) and quantum computing lies the emerging field of quantum machine learning (QML). By speeding up the computation of intricate algorithms, quantum computers have the potential to transform a number of fields, including machine learning, by outperforming classical computers by an exponential amount in specific tasks. This essay examines the fundamental ideas of quantum computing, how it applies to machine learning, and the potential advantages and difficulties of QML. We examine several quantum algorithms, including quantum versions of support vector machines, clustering, and neural networks, that can improve machine learning models. We also go over QML's drawbacks, present research directions, and potential future developments, providing insights into how quantum technologies might transform AI in the ensuing decades. With the potential to outperform traditional supercomputers in resolving important issues in a variety of fields, including machine learning, quantum computing has become a ground-breaking technology. This study investigates the fascinating nexus between artificial intelligence and quantum computing, looking at how quantum machine learning might revolutionize classification, pattern recognition, and data processing.