Quantum algorithm for edge detection in digital grayscale images
Published in arXiv, 2025
In this work, we propose a novel quantum algorithm for edge detection in digital grayscale images, based on the sequency-ordered Walsh-Hadamard transform. The proposed method significantly improves upon existing quantum techniques for edge detection by using a quantum algorithm for the sequency-ordered Walsh-Hadamard transform, achieving a circuit depth of \(O(n)\) (where \(n\) is the number of qubits). This represents a notable enhancement over the Quantum Fourier Transform (QFT), which has a circuit depth of \(O(n^2)\). Furthermore, our approach for edge detection has a computational cost \(O(\text{log}_2(N_1 N_2))\) (both gate complexity and quantum circuit depth) of for an image of size \(N_1\times N_2\), offering a considerable improvement over the Quantum Hadamard Edge Detection (QHED) algorithm, which incurs a cost of \(O(\text{poly}(\text{log}_2(N_1 N_2)))\). By integrating a quantum high-pass filter with the sequency-ordered Walsh-Hadamard transform, the algorithm effectively extracts edge information from images. Computational examples are provided to demonstrate the efficacy of the proposed algorithm which provides a better performance in comparison to QHED.
Recommended citation: M. Rohida, A. Shukla, and P. Vedula, Quantum algorithm for edge detection in digital grayscale images, 2025. arXiv: 2507.06642 [quant-ph].
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