Superpixel-Based QUBO for Scalable Quantum-Enhanced Medical Image Segmentation

Quadratic unconstrained binary optimization (QUBO) has emerged as a powerful framework for medical computing problems. Binary decision variables naturally represent clinical choices, making QUBO formulations well-suited for quantum annealing hardware. However, a fundamental scalability challenge limits practical deployment: problem size grows rapidly with input dimensionality, creating computational bottlenecks that restrict applications to simplified scenarios. This paper addresses this challenge through hierarchical problem reduction, as demonstrated in medical image segmentation, where pixel-level QUBO formulations create over 65,000 variables for a 256x256 image, forcing existing approaches to downsample to 42x42 resolution and discard 97% of pixel information. A superpixel-based QUBO framework is proposed using simple linear iterative clustering (SLIC) to group pixels into perceptually meaningful regions, then formulate segmentation as QUBO over a region adjacency graph (RAG) combining min-cut and smoothness objectives. Validation on INbreast mammography breast cancer images demonstrates a 4.2% improvement in segmentation quality (mean IoU 0.76 vs 0.73) with 33 computational speedup (0.67s vs 21.97s) and a 97.3% reduction in problem size (1764 to 48 variables), all achieved while processing full-resolution images rather than downsampled versions. The reduced problem size also fits well within current quantum annealer connectivity limits, removing the embedding overhead that has historically blocked direct deployment of pixel-level QUBO segmentation on quantum hardware.