A Hybrid Quantum-Classical Framework for Utility-Scale Edge Detection of Real-World Medical and Geospatial Data

Abstract

We present a hybrid quantum-classical framework designed to achieve utility-scale performance for Quantum Hadamard Edge Detection (QHED) on Noisy Intermediate-Scale Quantum (NISQ) devices. The framework utilizes a Two-Level Decomposition strategy: (1) Problem-Level Decomposition (PLD), which partitions high-resolution real-world data into buffered sub-images, and (2) Circuit-Level Decomposition (CLD), which employs circuit-cutting to reduce complexity for near-term hardware. This approach, combined with a depth-efficient QHED^M decrement gate, achieves a 62% reduction in circuit depth and 93% fewer two-qubit operations. We demonstrate the framework's domain-agnostic utility by processing real-world data from Medical Image Computing (MIC) and Geospatial Information Systems (GIS). Crucially, we investigate the resilience crossover point by comparing a [[3,1,1]] bit-flip repetition code against passive Quantum Error Mitigation (QEM). Our results indicate that for current coherence times, passive mitigation offers a superior utility advantage by bypassing the gate-overhead penalties inherent in active encoding, recovering nearly 99% of the ideal signal.