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Quantum Convolutional Layer (QCL) is considered as one of the core of Quantum Convolutional Neural Networks (QCNNs) due to its efficient data feature extraction capability. However, the current principle of QCL is not as mathematically understandable as Classical Convolutional Layer (CCL) due to its black-box structure. Moreover, classical data mapping in many QCLs is inefficient. To this end, firstly, the Quantum Adjoint Convolution Operation (QACO) consisting of a quantum amplitude encoding and its inverse is theoretically shown to be equivalent to the quantum normalization of the convolution operation based on the Frobenius inner product while achieving an efficient characterization of the data. Subsequently, QACO is extended into a Quantum Adjoint Convolutional Layer (QACL) by Quantum Phase Estimation (QPE) to compute all Frobenius inner products in parallel. At last, comparative simulation experiments are carried out on PennyLane and TensorFlow platforms, mainly for the two cases of kernel fixed and unfixed in QACL. The results demonstrate that QACL with the insight of special quantum properties for the same images, provides higher training accuracy in MNIST and Fashion MNIST classification experiments, but sacrifices the learning performance to some extent. Predictably, our research lays the foundation for the development of efficient and interpretable quantum convolutional networks and also advances the field of quantum machine vision.

Numerous current Quantum Machine Learning (QML) models exhibit an inadequacy in discerning the significance of quantum data, resulting in diminished efficacy when handling extensive quantum datasets. Hard Attention Mechanism (HAM), anticipated to efficiently tackle the above QML bottlenecks, encounters the substantial challenge of non-differentiability, consequently constraining its extensive applicability. In response to the dilemma of HAM and QML, a Grover-inspired Quantum Hard Attention Mechanism (GQHAM) consisting of a Flexible Oracle (FO) and an Adaptive Diffusion Operator (ADO) is proposed. Notably, the FO is designed to surmount the non-differentiable issue by executing the activation or masking of Discrete Primitives (DPs) with Flexible Control (FC) to weave various discrete destinies. Based on this, such discrete choice can be visualized with a specially defined Quantum Hard Attention Score (QHAS). Furthermore, a trainable ADO is devised to boost the generality and flexibility of GQHAM. At last, a Grover-inspired Quantum Hard Attention Network (GQHAN) based on QGHAM is constructed on PennyLane platform for Fashion MNIST binary classification. Experimental findings demonstrate that GQHAN adeptly surmounts the non-differentiability hurdle, surpassing the efficacy of extant quantum soft self-attention mechanisms in accuracies and learning ability. In noise experiments, GQHAN is robuster to bit-flip noise in accuracy and amplitude damping noise in learning performance. Predictably, the proposal of GQHAN enriches the Quantum Attention Mechanism (QAM), lays the foundation for future quantum computers to process large-scale data, and promotes the development of quantum computer vision.

Self-Attention Mechanism (SAM) excels at distilling important information from the interior of data to improve the computational efficiency of models. Nevertheless, many Quantum Machine Learning (QML) models lack the ability to distinguish the intrinsic connections of information like SAM, which limits their effectiveness on massive high-dimensional quantum data. To tackle the above issue, a Quantum Kernel Self-Attention Mechanism (QKSAM) is introduced to combine the data representation merit of Quantum Kernel Methods (QKM) with the efficient information extraction capability of SAM. Further, a Quantum Kernel Self-Attention Network (QKSAN) framework is proposed based on QKSAM, which ingeniously incorporates the Deferred Measurement Principle (DMP) and conditional measurement techniques to release half of quantum resources by mid-circuit measurement, thereby bolstering both feasibility and adaptability. Simultaneously, the Quantum Kernel Self-Attention Score (QKSAS) with an exponentially large characterization space is spawned to accommodate more information and determine the measurement conditions. Eventually, four QKSAN sub-models are deployed on PennyLane and IBM Qiskit platforms to perform binary classification on MNIST and Fashion MNIST, where the QKSAS tests and correlation assessments between noise immunity and learning ability are executed on the best-performing sub-model. The paramount experimental finding is that a potential learning advantage is revealed in partial QKSAN subclasses that acquire an impressive more than 98.05% high accuracy with very few parameters that are much less in aggregate than classical machine learning models. Predictably, QKSAN lays the foundation for future quantum computers to perform machine learning on massive amounts of data while driving advances in areas such as quantum computer vision.

Self-Attention Mechanism (SAM) is good at capturing the internal connections of features and greatly improves the performance of machine learning models, espeacially requiring efficient characterization and feature extraction of high-dimensional data. A novel Quantum Self-Attention Network (QSAN) is proposed for image classification tasks on near-term quantum devices. First, a Quantum Self-Attention Mechanism (QSAM) including Quantum Logic Similarity (QLS) and Quantum Bit Self-Attention Score Matrix (QBSASM) is explored as the theoretical basis of QSAN to enhance the data representation of SAM. QLS is employed to prevent measurements from obtaining inner products to allow QSAN to be fully implemented on quantum computers, and QBSASM as a result of the evolution of QSAN to produce a density matrix that effectively reflects the attention distribution of the output. Then, the framework for one-step realization and quantum circuits of QSAN are designed for fully considering the compression of the measurement times to acquire QBSASM in the intermediate process, in which a quantum coordinate prototype is introduced as well in the quantum circuit for describing the mathematical relation between the output and control bits to facilitate programming. Ultimately, the method comparision and binary classification experiments on MNIST with the pennylane platform demonstrate that QSAN converges about 1.7x and 2.3x faster than hardware-efficient ansatz and QAOA ansatz respevtively with similar parameter configurations and 100% prediction accuracy, which indicates it has a better learning capability. QSAN is quite suitable for fast and in-depth analysis of the primary and secondary relationships of image and other data, which has great potential for applications of quantum computer vision from the perspective of enhancing the information extraction ability of models.