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.
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 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.
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
Abstract Quantum Haar Wavelet Transform (QHWT) methods connect multiresolution analysis with quantum information processing through reversible averaging and differencing operations that can be implemented with comparatively compact circuits. Their localized basis functions, real-valued binary structure, and compatibility with hierarchical state representations make them attractive for resource-constrained quantum processing. Nevertheless, claims of practical superiority are difficult to generalize because published studies use heterogeneous encodings, simulators, hardware platforms, noise models, and evaluation metrics. This systematic review examines scholarly work on Haar-based quantum methods published between 1997 and March 2025. A PRISMA-oriented protocol was used to search major engineering and computing databases, remove duplicates, screen records, assess eligibility, and construct a qualitative evidence corpus. The review includes peer-reviewed journal and conference studies together with a limited number of historically influential technical reports and preprints; therefore, the corpus is described as scholarly literature rather than as a uniformly peer-reviewed dataset. Because the reported experiments are not sufficiently homogeneous for statistical pooling, numerical results are treated as study-specific evidence rather than global averages. The review makes three analytical contributions. First, it introduces a unified conceptual framework that links mathematical foundations, circuit realization, application design, hardware evaluation, and research translation. Second, it develops a taxonomy spanning transform theory, quantum image and signal processing, hardware implementation, and emerging quantum artificial intelligence and security applications. Third, it critically compares QHWT with Quantum Fourier Transform and higher-order wavelet approaches by distinguishing circuit depth, gate complexity, approximation behavior, hardware assumptions, and empirical validation. The synthesis indicates that QHWT is most compelling when localization, reversible multiresolution processing, and shallow circuit structure are more important than smooth-basis approximation. Individual studies report promising compression, feature-extraction, and hardware-efficiency results, but these findings remain conditional on encoding choices and platform constraints. Important limitations include sparse cross-platform benchmarking, limited fault-tolerant analysis, noise sensitivity, uncertain scaling, and optimization difficulties in variational quantum learning, including barren plateaus. The resulting roadmap prioritizes reproducible benchmarks, hardware-aware circuit design, explicit complexity reporting, error-mitigation studies, and validation on larger quantum systems.
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.
Abstract This paper presents a quantum morphological Haar wavelet transform (QMHWT) that integrates the morphological minimum operator into the low-frequency subband of the Haar wavelet, unifying nonlinear morphological processing with multi-directional wavelet decomposition in a quantum arithmetic circuit framework. For a 2 × 2 pixel block [ a , b , c , d ] , the low-frequency subband is defined as L = min ( a , b , c , d ) , while the three directional detail subbands adopt the linear combination form of the classical Haar transform with floor division for integer-domain compatibility. We design a four-stage quantum circuit: a cascade of forward compare-swap (FCS) units extracts the four-way minimum, a reverse compare-swap recovery (FCS − 1 ) stage recycles auxiliary qubits, a modular addition/subtraction stage computes three detail subbands through separate arithmetic chains, and an arithmetic shift right stage performs integer division by two. The resulting circuit has width W ( n ) = 7 n + 12 , and the number of auxiliary qubits does not scale with image size. A D -map metric D = L mean − L min is derived from the morphological low-frequency subband, and its non-negativity, zero-value condition, and upper-bound relationship with the classical morphological gradient are established. Experiments on three standard 512 × 512 test images at 6-bit quantization confirm exact agreement between the quantum circuit output and classical reference results for all 3 × 65536 pixel blocks. The D -map achieves consistently high Pearson correlation with the morphological gradient ( r > 0.95 , mean r = 0.973 ), demonstrating the validity of the proposed transform and its potential use in quantum image edge analysis. The current large-image validation employs a hybrid quantum–classical scheme in which the per-block unitary cost is
Deep learning has transformed radiology, but the computational cost of training and deploying modern models is outpacing what classical hardware can support. Quantum computing has been proposed as one response to this bottleneck: an n-qubit system can represent 2n states simultaneously, although practical speedups require efficient algorithms, data encoding, and measurement strategies rather than superposition alone. This review introduces radiologists to five core quantum concepts, qubits, superposition, entanglement, quantum gates, and quantum circuits, and to the superconducting, trapped-ion, and photonic hardware platforms that define the current noisy intermediate-scale quantum (NISQ) era. We then summarize the quantum machine learning architectures most often applied to medical imaging (quantum support vector machines, quantum neural networks, variational quantum circuits, and quantum convolutional neural networks) and quantum image representations such as the flexible representation of quantum images (FRQI) and the novel enhanced quantum representation (NEQR). Reported applications include brain tumor classification and segmentation on MRI, pneumonia detection on chest radiographs, skin and breast lesion classification, CT and PET reconstruction, and ultrasound denoising. Nearly all published systems are hybrid quantum-classical pipelines evaluated on small, downsampled benchmark datasets or simulators, and clinical deployment is not yet feasible. We conclude with current limitations and translational priorities for radiology.