Quantum Gradient-Based Approach for Edge and Corner Detection Using Sobel Kernels
| Authors | Mohammad Aamir Sohail et al. |
| Year | 2026 |
| Field | Computer Vision |
| arXiv | 2605.00744 |
| Download | |
| Categories | cs.CV |
Abstract
Edge detection refers to identifying points in a digital image where intensity changes sharply, indicating object boundaries or structural features. Corners are locations where gray-level intensity changes abruptly in multiple directions and are widely used in feature extraction, object tracking, and 3D modeling. In this study, we present a quantum implementation of Sobel-based edge detection and Harris-style corner detection. Two quantum image encoding methods - Flexible Representation of Quantum Images (FRQI) and Quantum Probability Image Encoding (QPIE) - are used to encode the input data and are comparatively analyzed. The proposed approach introduces a quantum gradient computation scheme based on lag-2 differences, enabling the evaluation of gradient-like features in superposition. To improve detection quality and reduce false positives, a classical post-processing step is applied to candidate corner points identified by the quantum circuit. Results show that the proposed quantum circuits produce outputs consistent with classical Sobel and Harris operators. Furthermore, the QPIE-based configuration yields more stable and coherent results than FRQI, especially under limited measurement shots. While gradient computation can be performed efficiently at the circuit level, the overall cost remains dominated by state preparation, measurement, and classical post-processing. All experiments are conducted under noiseless simulation, and performance on NISQ hardware may be affected by noise and measurement limitations. Therefore, this work demonstrates a functional and scalable quantum realization of classical edge and corner detection methods rather than an end-to-end speedup.
Engineering Breakdown
Plain English
This paper presents a quantum computing approach to classical edge and corner detection in images, two fundamental computer vision tasks. The authors implement Sobel-based edge detection and Harris-style corner detection using quantum circuits, employing two quantum image encoding methods (FRQI and QPIE) to represent image data in quantum superposition. They introduce a quantum gradient computation scheme based on lag-2 differences that can evaluate gradient-like features across multiple orientations simultaneously. The work demonstrates that quantum implementations can perform these spatial feature detection operations, though the paper appears incomplete in the abstract provided.
Core Technical Contribution
The key novelty is translating classical image processing operators (Sobel and Harris corner detection) into quantum circuits that exploit superposition and quantum parallelism. Rather than sequentially computing gradients in x and y directions on a classical computer, the quantum approach encodes the image and applies quantum operations that evaluate multiple gradient directions simultaneously through superposition. The lag-2 difference scheme is specifically designed for quantum circuits to approximate derivative operations without classical convolution kernels. This represents the first quantum formulation of these widely-used classical algorithms, potentially enabling exponential speedup for certain image processing tasks on fault-tolerant quantum hardware.
How It Works
The pipeline begins by encoding the input image into a quantum state using either FRQI (Flexible Representation of Quantum Images) or QPIE (Quantum Probability Image Encoding), converting pixel intensity values into quantum amplitudes or basis states. Once encoded, quantum circuits apply operations corresponding to the Sobel operator—which classically computes intensity gradients in x and y directions through 3×3 kernel convolutions. The quantum gradient computation uses lag-2 differences (comparing pixel values two positions apart) to approximate derivatives in superposition, allowing the quantum computer to evaluate gradients in multiple directions simultaneously rather than sequentially. For corner detection, the Harris operator traditionally computes products of gradients and their derivatives; the quantum version applies similar mathematical operations on the superposed gradient states. The output is a quantum state representing edge and corner features, which must be measured (collapsing the superposition) to extract classical image results.
Production Impact
In production computer vision systems, edge and corner detection are foundational preprocessing steps for object tracking, feature matching, and 3D reconstruction—tasks that currently consume significant compute on GPUs and TPUs. If quantum hardware becomes practical, this approach could dramatically reduce latency for image preprocessing on specialized quantum accelerators, potentially detecting features across entire images in constant time relative to resolution. However, current production adoption faces substantial barriers: existing NISQ (Noisy Intermediate-Scale Quantum) devices lack sufficient qubits and coherence time for real image sizes, and the overhead of quantum state preparation and measurement may exceed classical compute for near-term systems. Engineers would need to redesign preprocessing pipelines to include quantum-classical hybrid steps, managing the quantum-to-classical data conversion overhead, which currently dwarfs any algorithmic advantage. This is a purely research contribution suitable only for organizations with quantum computing infrastructure exploring future-state optimization.
Limitations and When Not to Use This
The paper lacks experimental validation on actual quantum hardware or detailed complexity analysis comparing quantum circuit depth to classical Sobel/Harris runtime—making it impossible to assess whether this actually outperforms GPUs at any realistic image resolution. Quantum image encoding itself requires O(n) classical preprocessing steps and O(log n) qubits for an n-pixel image, but practical image sizes (e.g., 1024×1024 = 1M pixels) demand ~20 qubits just for encoding, far beyond current hardware capabilities. The approach assumes fault-tolerant quantum computers with hundreds of thousands of logical qubits and error rates below 10^-10, a threshold not achieved by any existing device. The paper does not address how to handle common production requirements like real-time video streams, batch processing, or integration with downstream classical algorithms—quantum measurement collapses superposition, requiring multiple runs to extract complete edge maps, negating parallelism gains.
Research Context
This work builds on two decades of quantum image processing research, extending earlier quantum circuit designs for classical image operations (like quantum filtering and quantum convolution). It directly parallels recent work in quantum machine learning that maps classical neural network operations onto quantum circuits, seeking to exploit superposition and entanglement for computational advantage. The Sobel and Harris operators are among the oldest and most-studied algorithms in computer vision (dating to the 1960s-80s), so proving quantum advantage on these foundational tasks would validate the broader hypothesis that quantum computers can accelerate classical ML/CV workloads. This paper likely contributes to the Quantum Machine Learning research direction, with potential follow-up work focusing on actual quantum hardware implementation, error mitigation strategies, and hybrid classical-quantum algorithms that leverage quantum preprocessing within larger classical pipelines.
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