A quantum computing method for multidimensional cycle shift transformations for quantum image processing

Konstantinos Prousalis

doi:10.1088/1402-4896/ae1d2b

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A quantum computing method for multidimensional cycle shift transformations for quantum image processing

2025-11-17

Konstantinos Prousalis *

Asimakis Kydros

N. Konofaos

DOI：10.1088/1402-4896/ae1d2b

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Abstract

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Quantum image processing in qubit-based image representations for more than two dimensions seems to offer great opportunities for advanced data analysis and processing in quantum computers. Of fundamental importance is cycle shifting an image along an arbitrary direction, as various operations are based on it. In this work, a widely used image representation scheme is generalized into a single, multidimensional encoding. Within this framework, we define a cycle shifting method capable of translating a representation along any linear combination of its dimensional axes. The algorithmic procedure is appropriately redefined to accommodate arbitrary shifts in the Hilbert space. The corresponding computational complexity is optimized, achieving an exponential reduction in quantum resource requirements with respect to the shift-step magnitude. A comparative complexity analysis substantiates the efficiency gain, while simulation results validate the proposed multidimensional framework for two- and three-dimensional representations.