Segmentation-Based Regression for Quantum Neural Networks

• URL: http://arxiv.org/abs/2507.00065v1
• Date: Fri, 27 Jun 2025 20:11:43 GMT
• Title: Segmentation-Based Regression for Quantum Neural Networks
• Authors: James C. Hateley,
• Abstract summary: Recent advances in quantum hardware motivate the development of algorithmic frameworks that integrate quantum sampling with classical inference.<n>This work introduces a segmentation-based regression method tailored to quantum neural networks (QNNs)<n>By casting the regression task as a constrained problem over a structured digit lattice, the method replaces continuous inference with interpretable and tractable updates.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recent advances in quantum hardware motivate the development of algorithmic frameworks that integrate quantum sampling with classical inference. This work introduces a segmentation-based regression method tailored to quantum neural networks (QNNs), where real-valued outputs are encoded as base-b digit sequences and inferred through greedy digitwise optimization. By casting the regression task as a constrained combinatorial problem over a structured digit lattice, the method replaces continuous inference with interpretable and tractable updates. A hybrid quantum-classical architecture is employed: quantum circuits generate candidate digits through projective measurement, while classical forward models evaluate these candidates based on task-specific error functionals. We formalize the algorithm from first principles, derive convergence and complexity bounds, and demonstrate its effectiveness on inverse problems involving PDE-constrained models. The resulting framework provides a robust, high-precision interface between quantum outputs and continuous scientific inference.

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