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

Abstract

This thesis studies the intersection of quantum computing and artificial intelligence in two directions: quantum methods for machine learning and machine learning methods for quantum systems. For quantum machine learning, Neural Quantum Embedding learns data representations that increase the trace distance between embedded class ensembles, lowering an embedding-dependent bound on empirical risk and improving classification on noisy quantum hardware. A training objective based on the Hilbert-Schmidt inner product extends this approach to deterministic quantum computation with one qubit (DQC1) and is demonstrated on an NMR quantum processor. A margin-based generalization analysis then connects quantum neural network performance to quantum state discrimination. In the studied benchmarks, margin distributions predict generalization more reliably than parameter-count metrics. For quantum systems, a Mamba-based neural decoder for surface codes matches a reproduced Transformer baseline in memory experiments while reducing inference-cost scaling from quartic to quadratic in code distance. Under an explicit decoder-induced-noise model, it achieves lower logical error rates and a higher effective threshold. For neural quantum states, stochastic reconfiguration is interpreted as tangent-space ridge regression, with its diagonal shift controlling the bias-variance trade-off under finite Monte Carlo sampling. Multi-shift stochastic reconfiguration reduces checkpoint-local validation residuals and update variance relative to fixed-shift SR, at additional computational cost. Together, these contributions show how learned representations, statistical control, and hardware constraints shape the exchange between quantum computing and machine learning.