This paper augments the edge-detecting Sobel Filter with quantum calculations.This implementation replaces the classical stencil operation, which calculates the horizontal and vertical gradients at each pixel through a dot product of edge detection kernels and its neighbors, with a quantum operation that allows each pixel address to gain access to all neighboring values simultaneously.This was done by encoding shifted versions of the original image into a quantum circuit using QCrank and performing the weighted sum calculation within the quantum circuit using the EHands protocol, both developed by LBNL.This thesis also developed a novel reversible version of the EHands parity flip gate.As an additional optimization, this Sobel implementation added functionality to break the input image into tiles on which smaller quantum circuits would act, with their results reassembled into a final image.The experiments of this paper verify the effectiveness of the EHands blocks and gradient calculation circuits, and compare simulation runtime and circuit structure for various combinations of circuit variants and quantum calculations needed for the Sobel Filter.These experiments found the optimal circuit variant for calculating Sobel stencil operations, that GPU nodes outperform CPU nodes at all images sizes, and that divide-and-conquer tiling is superior to processing the input image in its entirety for circuit simulations with larger image sizes.Future work aims to extend the study of this implementation on real quantum hardware and introduce further optimizations to the implementation.v
This paper augments the edge-detecting Sobel Filter with quantum calculations.This implementation replaces the classical stencil operation, which calculates the horizontal and vertical gradients at each pixel through a dot product of edge detection kernels and its neighbors, with a quantum operation that allows each pixel address to gain access to all neighboring values simultaneously.This was done by encoding shifted versions of the original image into a quantum circuit using QCrank and performing the weighted sum calculation within the quantum circuit using the EHands protocol, both developed by LBNL.This thesis also developed a novel reversible version of the EHands parity flip gate.As an additional optimization, this Sobel implementation added functionality to break the input image into tiles on which smaller quantum circuits would act, with their results reassembled into a final image.The experiments of this paper verify the effectiveness of the EHands blocks and gradient calculation circuits, and compare simulation runtime and circuit structure for various combinations of circuit variants and quantum calculations needed for the Sobel Filter.These experiments found the optimal circuit variant for calculating Sobel stencil operations, that GPU nodes outperform CPU nodes at all images sizes, and that divide-and-conquer tiling is superior to processing the input image in its entirety for circuit simulations with larger image sizes.Future work aims to extend the study of this implementation on real quantum hardware and introduce further optimizations to the implementation.v
Quantum image processing is a system where both quantum computing and image processings are key. Now it is required to investigate how to apply image processing concepts such as image edge detection and improved Sobel operator, to quantum image processing. Just as traditional image processing helps to image manipulation, our efforts in quantum image processing contribute to the further development of quantum algorithm and quantum information theory. Edge detection is an important problem in traditional image processing, and image edge detection algorithm can filter image edge features and retain important attributes. We proposed a quantum edge detection algorithm, which employs improved Sobel operator to improve the performance, so as to solve the problem of unsatisfactory traditional image edge detection methods. In practical application, the amount of image data to be processed increases sharply, and the computing power of classical computer becomes a limitation. Quantum information processing can effectively accelerate many classical problems by virtue of quantum mechanical characteristics, such as quantum superposition, entanglement, parallelism. Our proposed method uses the novel enhanced quantum representation to store quantum images, which stores all the pixels in the image in a superimposed state, realizing parallel computation. The improved eight-direction Sobel operator is used to calculate the gray gradient, and the quantum circuit is designed to realize quantum edge detection. Simulation results have shown that our algorithm can extract edge with dimension 2n× 2nwhen the computational complexity is O(n2+ 2q+3). The improved algorithm can detect more edge details and has strong adaptability.
This work introduces a novel quantum algorithm for gradient-based edge detection that operates entirely within the quantum circuit model. Grayscale images are encoded using the Novel Enhanced Quantum Representation (NEQR), allowing exact arithmetic on pixel intensities. Directional gradients are computed by generating superpositions of neighboring pixels via cyclic shift operations and performing subtraction with an exact quantum arithmetic circuit. To refine accuracy, we introduce a direction-aware shifting mechanism that aligns edges with the darker side of intensity transitions. Our novel Quantum Partitioning Algorithm enables efficient in-place thresholding of edge candidates. This work exhibits polynomial-time improvements and optimizes the ancilla count compared to previous NEQR-based quantum edge detection algorithms. These results demonstrate a resource-efficient and fully quantum approach to edge detection, highlighting a practical quantum advantage in image processing.
Edge detection is a vital component of industrial image-processing and evaluation workflows, particularly in X-ray computed tomography (XCT), where it underpins segmentation, feature extraction, and defect localization. Quantum computing provides powerful building blocks for image processing by exploiting superposition and entanglement, even on today’s noisy hardware. In this work, we focus on edge detection for industrial XCT data and translate two widely used classical approaches, which are the Haar wavelet filter and the Sobel operator, into the quantum domain, while keeping the design intentionally simple: overlapping 2 × 2 patches with angle-based RY encoding, a compact bidirectional quantum Haar transform, and small spectral phase shifts (φ = π/8) applied to the HL/LH subbands to mimic Sobel-like directional selectivity. Each patch compiles into a shallow four-qubit circuit with a logical depth of 20 or less, rendering the approach feasible for both simulation and actual quantum hardware implementation. We evaluate the method on three 64 × 64 grayscale XCT radiographs, each decomposed into 63 × 63 = 3969 overlapping 2 × 2 patches, corresponding to one quantum circuit per patch. Across ideal and noise-aware simulations, the quantum Haar and Sobel operators closely follow their classical reference maps for all 2x2 patches. We additionally executed the whole pipeline for Test Case 1 on the IBM EU-DE backend (ibm_aachen) using Runtime V2 (SamplerV2). The experiment required 20 min 59 s for the quantum Haar configuration and 21 min 22 s for the quantum Sobel configuration (3969 circuits each), demonstrating that the shallow-circuit design is compatible with current superconducting hardware. Different simulation backends, as well as the real IBM device, execute the same circuit structure without modification, and edge strength is reconstructed using a hardware-robust and straightforward metric, E = 1 − P(|0 . . . 0⟩), where P(|0 . . . 0⟩) denotes the probability of observing the all-zero measurement outcome. The combination of a small Haar circuit and π/8 phase modulation yields a hardware-friendly quantum edge detector that aligns well with classical benchmarks on industrial XCT data. The results indicate that meaningful edge information can be extracted within NISQ constraints, providing a reproducible pathway for deploying quantum image-processing pipelines on present-day devices.
Quantum edge detection is one of the important part of quantum image processing. In this paper, a quantum edge detection algorithm is designed for the quantum representation of multi-wavelength image (QRMW) model. The algorithm includes all stages of filtering, enhancement and detection. The proposed algorithm is also designed to apply any filtering operation to QRMW images, not only for a particular filtering operation. The proposed algorithm aims to solve the problems that quantum edge detection algorithms in the literature have processing only for a particular operator and noise reduction. Moreover, the algorithm aims to perform operations more efficiently by using less resources. Low-pass filter (LPF) smoothing operators are applied in the filtering stage for the noise reduction problem. In order to apply all filtering operations to the image, arithmetic operators that can operate with all signed integers are used in the algorithm. The operators Sobel, Prewitt and Scharr in the enhancement stage and the gradient method in the detection stage are used for both verification of the proposed algorithm and comparisons with the existing algorithms. A method with quantitative outcomes is shown to evaluate the performance of the edge detection algorithms. Analysis of the simulations performed on sample images with different operators. The circuit complexity of the algorithm is presented and the comparisons are made with the existing studies. The superiority of the proposed algorithm and its flexibility to be used in other studies are clearly demonstrated by analysis.
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.
边缘检测是图像处理中的基本问题之一，边缘检测的许多算法是基于经典的图像处理技术。本文将介绍基于量子力学框架下的边缘检测量子算法，及其图像特征向量技术在图像检测中的应用。量子算法基于图像经典信息的量子化，通过图像处理中各类元素与量子力学基本物理量一一对应，通过图像特征构造的系统的哈密顿量，应用量子演化技术学习图像的轮廓，从而，给出我们期望的图像轮廓。我们应用像素灰度梯度、像素灰度的二阶差分、Sobel算子卷积等方法作为特征向量来构造哈密顿量。通过一组标准图(从BSDS500公开数据集的图片)测试我们的量子算法，结果显示我们的量子算法的灵敏度比传统Canny算法提高了25%，而且具有更强的抗噪声能力。 Edge detection is one of the fundamental problems in the image processing. Many algorithms of edge detection are based on the classical image processing technology. In this paper, we introduce the quantum algorithm of edge detection based on quantum mechanics and its application in image detection. Quantum algorithm is based on the quantization of the classical information of the image and one-to-one correspondence between various elements of the image processing and the concept and variables of quantum mechanics. By constructing the Hamiltonian for the image features, the quantum evolution technology for the quantum information of images learns the profile of the image, so as to give the desired image contour. We use the techniques of the pixel gray gradient, second order difference of pixel gray, Sobel operator convolution as the feature vectors to construct Hamiltonian. Our quantum algorithms are tested by a set of standard pictures (coming from BSDS500 exposed database). The testing results show that our quantum algorithm has a 25% higher sensitivity than the traditional Canny algorithm and has a stronger denoise ability.