Analytical Quantum-Inspired Kernels for Hybrid Learning in Precision Medicine

We explore analytical quantum-inspired kernel methods for hybrid quantum-classical learning, with applications to massive, high-dimensional datasets in healthcare. Comparing analytically derived quantum feature maps to classical support-vector machines, we address limitations of noisy quantum processors for large datasets. Our formulation enables efficient evaluation of quantum kernels on realistic clinical data, showing that hybrid ensembles achieve competitive predictive accuracy by leveraging quantum-inspired representations.

Pure quantum support-vector models face key challenges in high-dimensional spaces: variance loss from dimensionality reduction and exponential decay of kernel amplitudes due to multiplicative quantum operations. We introduce a hybrid architecture fusing quantum and classical models leveraging a clinically proven feature engineering strategy, meta-learning to optimize hyper parameters, and a geometric-mean kernel normalization method to stabilize amplitude and prevent collapse.

Our analytical kernel implementation achieves efficient polynomial scaling, enabling extensive benchmarking intractable via circuit-based simulation. The results confirm that quantum-inspired kernels uncover patterns complementary to classical ones, remaining computationally practical. This establishes a framework for evaluating hybrid quantum algorithms in data-driven physics and life sciences applications.