When Quantum Meets AI: Quantum Methods for Machine Learning and Machine Learning Methods for Quantum Systems

Summary

This PhD dissertation (Yonsei University, 2026) compiles four contributions at the quantum computing–AI interface. Part I (quantum for AI): Chapter 2 introduces Neural Quantum Embedding (NQE), where a classical neural network learns preprocessing that maximizes trace distance between embedded class ensembles, provably lowering a Helstrom-type lower bound on empirical risk; on binary MNIST via IBM hardware, trace distance rises from about 0.27 to 0.84 and accuracy from 52.7% to 96.1% (PCA-NQE). The objective is reformulated with Hilbert-Schmidt inner products for DQC1 execution, demonstrated on an NMR processor (98% vs 54% accuracy) with cross-platform transfer to IBM devices. Chapter 3 derives margin-based generalization bounds for quantum neural networks; in studied benchmarks, margin metrics track generalization gaps better than parameter-count metrics. Part II (AI for quantum): Chapter 4 presents a Mamba-based surface-code decoder matching a reproduced Transformer baseline while reducing inference scaling from quartic to quadratic in code distance, with a higher effective threshold (0.0104 vs 0.0097) under an explicit decoder-induced-noise model. Chapter 5 recasts stochastic reconfiguration as tangent-space ridge regression and proposes multi-shift SR. Main limitations: narrow benchmarks (binary MNIST, small codes), thin classical-only baselines, and a reproduced rather than original Transformer reference.