A quantum convolution and neighborhood pixel extraction scheme based on NEQR

At the vanguard of quantum computation and quantum machine learning, the role of convolutional operations is pivotal, serving as the linchpin of image processing techniques. Currently, various quantum convolutional circuits have been proposed, but they are all based on non-ground state encoding. Quantum convolution methods based on ground state encoding, particularly NEQR, have not yet been studied. To address the aforementioned issues, a novel quantum convolutional circuit has been designed based on arithmetic operation modules and quantum amplitude estimation modules. This circuit performs convolution operations on NEQR encoded quantum images. Furthermore, considering the limitations of existing neighborhood pixel extraction methods in quantum image processing, this quantum convolutional circuit has been utilized to design a quantum neighborhood pixel extraction circuit. Neighborhood pixels from a specified pixel in NEQR encoded quantum images are accurately extracted by this circuit, providing a novel solution. Through comparative analysis, our research results show certain advantages in time and space complexity over existing technologies.