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International Journal of Image Graphics and Signal Processing

In-depth Study of Quantum Hadamard Gate EdgeDetection: Complexity Analysis, Experiments,and Future Directions

Ridho Nur Rohman Wijaya, Budi Setiyono, Dwi Ratna Sulistyaningrum

Published Oct 1, 2025• 0 citations
Publisher

Abstract

Quantum computing is a rapidly developing field with faster computational capabilities than classical computing.The popularity of quantum computing has reached the field of image processing, particularly with a breakthrough method known as Quantum Hadamard Edge Detection.This approach represents a significant advancement in edge detection techniques using quantum computing.Quantum Hadamard Edge Detection is a method that can detect image edges more quickly than classical methods with exponential acceleration.This paper explains the Quantum Hadamard Edge Detection method in detail, including how it is implemented, a time complexity explanation, some experiments, and future research directions.Our experiments utilize a quantum computer simulator and employ four measurement metrics: Structural Similarity Index, Figure of Merit, Entropy, and a Proposed Metric with radius-based features, to detect simple binary images, MNIST images, and the Berkeley Segmentation datasets.We recognize the potential of quantum computing and believe that image processing with quantum representation will make processing more efficient and significantly valuable in the future.

DOI
10.5815/ijigsp.2025.05.02

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Quantum computing is a rapidly developing field with faster computational capabilities than classical computing.The popularity of quantum computing has reached the field of image processing, particularly with a breakthrough method known as Quantum Hadamard Edge Detection.This approach represents a significant advancement in edge detection techniques using quantum computing.Quantum Hadamard Edge Detection is a method that can detect image edges more quickly than classical methods with exponential acceleration.This paper explains the Quantum Hadamard Edge Detection method in detail, including how it is implemented, a time complexity explanation, some experiments, and future research directions.Our experiments utilize a quantum computer simulator and employ four measurement metrics: Structural Similarity Index, Figure of Merit, Entropy, and a Proposed Metric with radius-based features, to detect simple binary images, MNIST images, and the Berkeley Segmentation datasets.We recognize the potential of quantum computing and believe that image processing with quantum representation will make processing more efficient and significantly valuable in the future.
Quantum image processing is a research field that explores the use of quantum computing and algorithms for image processing tasks such as image encoding and edge detection. Although classical edge detection algorithms perform reasonably well and are quite efficient, they become outright slower when it comes to large datasets with high-resolution images. Quantum computing promises to deliver a significant performance boost and breakthroughs in various sectors. Quantum Hadamard Edge Detection (QHED) algorithm, for example, works at constant time complexity, and thus detects edges much faster than any classical algorithm. However, the original QHED algorithm is designed for Quantum Probability Image Encoding (QPIE) and mainly works for binary images. This paper presents a novel protocol by combining the Flexible Representation of Quantum Images (FRQI) encoding and a modified QHED algorithm. An improved edge outline method has been proposed in this work resulting in a better object outline output and more accurate edge detection than the traditional QHED algorithm.
Abstract Edges are image locations where the gray value intensity changes suddenly. They are among the most important features to understand and segment an image. Edge detection is a standard task in digital image processing, solved, for example, using filtering techniques. However, the amount of data to be processed grows rapidly and pushes even supercomputers to their limits. Quantum computing promises exponentially lower memory usage in terms of the number of qubits compared to the number of classical bits. In this paper, we propose a hybrid method for quantum edge detection based on the idea of a quantum artificial neuron. Our method can be practically implemented on quantum computers, especially on those of the current noisy intermediate-scale quantum era. We compare six variants of the method to reduce the number of circuits and thus the time required for the quantum edge detection. Taking advantage of the scalability of our method, we can practically detect edges in images considerably larger than reached before.
Quantum computing offers the potential to enhance computational efficiency beyond classical methods, but practical implementation remains challenging due to the limitations of Noisy Intermediate-Scale Quantum (NISQ) hardware, namely, restricted qubit counts, limited connectivity, and the presence of noise and decoherence. This study presents a novel approach to edge detection by leveraging a recently developed Quantum Fuzzy Inference Engine, implemented on a NISQ device. We introduce an optimized quantum circuit for its implementation, reducing qubit requirements and gate depth to improve execution on NISQ hardware. To overcome constraints related to large-scale image processing, a hybrid quantum–classical lookup table approach is employed. Edge detection performance is evaluated on the Berkeley Segmentation Data Set and Benchmarks 500 dataset under different conditions, including classical execution, ideal quantum simulation, noisy quantum simulation, and NISQ hardware calculation. Results demonstrate that the quantum fuzzy logic-based edge detection achieves outcomes comparable to classical methods by using fewer operations, marking a step toward practical quantum-enhanced image processing.
Abstract Quantum computing is being explored to tackle complex problems, such as image processing in this specific case. The ability of qubits to exist in multiple states at once and take advantage of quantum phenomena such as superposition and entanglement could have significant applications in a variety of fields, including image processing. Understandably, at this early stage in the development of quantum computing, quantum algorithms are not yet as efficient as classical algorithms for certain tasks. However, as quantum technology advances and becomes more accessible, we are likely to see significant improvements in terms of efficiency and problem-solving capabilities. The use of quantum computing to process images and detect specific features, such as the body contour of sheep for weight assessment or disease detection, has the potential to be a valuable tool in the agriculture and livestock industry. In this paper, we present the results of a quantum edge detector by analysing how the resolution affects the image result. Thus, a quantum edge detection model is implemented in the quantum simulator to analyse the edge recovery capability of an image as a function of the number of pixels in order to test the efficiency of quantum computers for image processing. The experiment results illustrate that edge detection times using quantum algorithms exceed 9000 seconds on 128x128 pixel images. Although the results are worse than those obtained using classical image processing models, they are promising since a resolution of 64$\times 64or12864 or 12864or128\times $128 is precise enough to determine the body contour of the sheep and can be executed in a quantum simulator. With the evolution of quantum computers, we are approaching the possibility of being able to use them for image processing tasks.
Quantum algorithms have emerged as a transformative approach to address the computational challenges of high-dimensional image processing tasks. This research investigates the integration of quantum computing principles, such as Quantum Fourier Transform (QFT) and Quantum Principal Component Analysis (QPCA), to optimize processes like edge detection, noise reduction, and image segmentation. These quantum-enhanced techniques promise significant improvements in computational efficiency and accuracy compared to classical methods, especially when handling complex visual data in real-time applications like medical imaging, satellite imagery, and autonomous systems. Additionally, the study explores hybrid quantum-classical architectures to bridge current limitations in noisy intermediate-scale quantum (NISQ) devices, ensuring resource optimization and scalability. The potential of quantum algorithms to provide faster, more precise solutions is evaluated alongside challenges like error mitigation and algorithmic stability. This research highlights the future role of quantum computing in revolutionizing image processing, paving the way for breakthroughs in computer vision and artificial intelligence.