Quantum algorithm for edge detection in digital grayscale images

• URL: http://arxiv.org/abs/2507.06642v1
• Date: Wed, 09 Jul 2025 08:14:37 GMT
• Title: Quantum algorithm for edge detection in digital grayscale images
• Authors: Mohit Rohida, Alok Shukla, Prakash Vedula,
• Abstract summary: We propose a novel quantum algorithm for edge detection in digital grayscale images, based on the sequency-ordered Walsh-Hadamard transform.<n>The proposed method significantly improves upon existing quantum techniques for edge detection by using a quantum algorithm for the sequency-ordered Walsh-Hadamard transform.<n>Our approach for edge detection has a computational cost (both gate complexity and quantum circuit depth) of $mathcalO(log_2(N_1N_2))$ for an image of size $N_1times N
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $\mathcal{O}(n)$ (where $n$ is the number of qubits). This represents a notable enhancement over the Quantum Fourier Transform (QFT), which has a circuit depth of $\mathcal{O}(n^{2})$. Furthermore, our approach for edge detection has a computational cost (both gate complexity and quantum circuit depth) of $\mathcal{O}(\log_{2}(N_{1}N_{2}))$ 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 $\mathcal{O}(\text{poly}(\log_{2}(N_{1}N_{2})))$. 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.

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