Multidimensional Quantum Convolution with Arbitrary Filtering and Unity Stride

Convolution is a fundamental operation in many critical algorithms across various domains, such as digital image processing, convolutional neural networks, and quantum machine learning. Existing implementations of the convolution operator, for example, in quantum neural networks, usually approximate the operation by applying filters with a stride equal to the filter window size. Therefore, it becomes challenging to accurately capture the spatial and temporal locality of the input features, particularly for data of higher dimensions than the commonly-investigated 1-D or 2-D data. Moreover, performing quantum convolution with a unity stride on data of higher dimensions typically requires deep quantum circuits that risk exceeding decoherence constraints. In this work, we propose depth-optimized techniques of implementing multidimensional quantum convolution operations with arbitrary filtering and unity stride. We present theoretical analysis of our techniques and provide the corresponding optimized quantum circuits. We also experimentally demonstrate the applicability of our techniques by using real-world, high-resolution, multidimensional image data on a state-of-the-art quantum simulator from IBM Quantum.