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

Hierarchical problem reduction via SLIC superpixels enables full-resolution quantum-annealer-compatible segmentation of mammography images

Mohammad Chalhoub; Mahdi Chehimi; Laia Domingo; Omar Alhussein; Ahmed Farouk; Saif Al-Kuwari· 2026· DOI 10.48550/arXiv.2607.24288

The core problem

Quadratic unconstrained binary optimization (QUBO) has emerged as a powerful framework for medical computing problems, where binary decision variables naturally represent clinical choices and map well onto quantum annealing hardware. However, a fundamental scalability challenge limits practical deployment: problem size grows rapidly with input dimensionality. In medical image segmentation, pixel-level QUBO formulations create over 65,000 variables for a 256\times256 image, forcing existing approaches to downsample to 42\times42 resolution and discard 97% of pixel information. This paper addresses the challenge through hierarchical problem reduction, demonstrated on breast cancer segmentation in mammography images. The central research question is whether perceptually meaningful region grouping can preserve segmentation quality while shrinking the QUBO to a size compatible with current quantum annealer connectivity limits.

On INbreast mammography images, the superpixel-based QUBO achieved a mean IoU of 0.76 versus 0.73 for the pixel-level baseline, a 4.2% improvement in segmentation quality. Computational time dropped from 21.97s to 0.67s, a 33\times speedup. Problem size fell by 97.3%, from 1764 to 48 variables. Critically, these gains were obtained while processing full-resolution images rather than downsampled versions, meaning the 97% of pixel information discarded by prior approaches is retained. The reduced problem size also fits within current quantum annealer connectivity limits, removing the embedding overhead that has historically blocked direct deployment of pixel-level QUBO segmentation on quantum hardware.

Quadratic unconstrained binary optimization (QUBO) has emerged as a powerful framework for medical computing problems, where binary decision variables naturally represent clinical choices and map well onto quantum annealing hardware. However, a fundamental scalability challenge limits practical deployment: problem size grows rapidly with input dimensionality. In medical image segmentation, pixel-level QUBO formulations create over 65,000 variables for a 256\times256 image, forcing existing approaches to downsample to 42\times42 resolution and discard 97% of pixel information. This paper addresses the challenge through hierarchical problem reduction, demonstrated on breast cancer segmentation in mammography images. The central research question is whether perceptually meaningful region grouping can preserve segmentation quality while shrinking the QUBO to a size compatible with current quantum annealer connectivity limits.

The proposed framework uses simple linear iterative clustering (SLIC) to group pixels into perceptually meaningful superpixels, then formulates segmentation as a QUBO over a region adjacency graph (RAG). The objective combines a min-cut term and a smoothness term:

The results indicate that hierarchical problem reduction via superpixels is an effective strategy for making QUBO-based medical image segmentation tractable on near-term quantum annealers. By operating on perceptually meaningful regions rather than individual pixels, the formulation preserves clinically relevant structure while drastically reducing variable count. The 48-variable problem is small enough to avoid the embedding overhead that dominates pixel-level approaches, suggesting a path toward direct quantum hardware execution. The 33\times speedup and 4.2% IoU improvement on INbreast data demonstrate that scalability gains need not come at the cost of segmentation quality. Limitations include validation on a single mammography dataset and reliance on SLIC hyperparameters; future work could extend the framework to other imaging modalities and multi-class segmentation tasks.

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