Segmentation-Based Regression for Quantum Neural Networks

TL;DR

This paper presents a segmentation-based regression method for quantum neural networks that encodes real-valued outputs as digit sequences and uses a hybrid quantum-classical approach for efficient, interpretable inference in scientific applications.

Contribution

It introduces a novel digitwise optimization framework for QNN regression tasks, formalizes the algorithm with theoretical bounds, and demonstrates its effectiveness on PDE-constrained inverse problems.

Findings

Effective high-precision inference for quantum neural networks.

The method achieves convergence with tractable complexity bounds.

Successful application to inverse PDE problems.

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.