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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | https://arxiv.org/abs/2507.06642 |
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| _version_ | 1866911047188742144 |
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| author | Rohida, Mohit Shukla, Alok Vedula, Prakash |
| author_facet | Rohida, Mohit Shukla, Alok Vedula, Prakash |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06642 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum algorithm for edge detection in digital grayscale images Rohida, Mohit Shukla, Alok Vedula, Prakash Quantum Physics 81P68, 68U10, 94A12, 42C10 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. |
| title | Quantum algorithm for edge detection in digital grayscale images |
| topic | Quantum Physics 81P68, 68U10, 94A12, 42C10 |
| url | https://arxiv.org/abs/2507.06642 |