Quantum-KIP: Kernel Inducing Points for Quantum Privacy

We introduce Quantum-KIP, a method that compresses a training set into a small set of kernel inducing points with soft labels. It uses a quantum feature map to compute state-fidelity overlaps and relies only on forward evaluations, avoiding backpropagation through quantum circuits. We provide a compression-induced stability analysis showing that replacing one training example changes the learned set and predictions by $O(m/n)$ . We further provide a joint analysis of this sensitivity bound with intrinsic quantum noise, showing how finite-shot measurement noise and depolarizing noise give rise to privacy-relevant distinguishability bounds for quantum-kernel observations. A circuit-execution analysis shows substantially fewer quantum runs than gradient-based approaches. On MNIST and CIFAR-10 datasets with six-qubit feature maps, Quantum-KIP achieves accuracy close to full-data training, large speedups, reduced privacy leakage, and robustness under depolarizing and measurement noise.