Quantum Edge Detection on Industrial X-ray Data via Quantum Circuits

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.