Tailor Made Embeddings for Quantum Machine Learning

Many practically relevant applications of quantum machine learning involve classical data, for which performance depends critically on how inputs are embedded into quantum states. Yet the use of a fixed embedding circuit ansatz remains standard practice. We propose an energy-based generative learning framework that synthesizes gate sequences to optimize embedding structures and refine data-tailored parameters, using a fidelity-based surrogate objective to guide the search toward improved class distinguishability. Empirically, the method improves classification performance across diverse settings, while also revealing datasets where architecture search within the present embedding family yields only limited additional gains. We explain this saturation by deriving bounds on the achievable empirical risk in terms of the Wasserstein distance in the input space, showing that classical data geometry provides an \emph{a priori} diagnostic for regimes in which substantial gains from embedding optimization are unlikely. The results establish a practically useful and theoretically motivated framework for searching effective quantum data embeddings through generative optimization, with the attainable gains diagnosed through the geometry of the underlying classical data.

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.

Large language and sentence-embedding models provide rich semantic representations, but their high dimensionality poses a challenge for near-term quantum machine learning (QML), where quantum circuits can process only a limited number of input features. We investigate a hybrid quantum-classical pipeline that transforms high-dimensional sentence embeddings into compact representations for variational quantum classification. The workflow combines a pretrained sentence-embedding model, dimensionality reduction, angle encoding, a variational quantum circuit (VQC), and a classical decision layer. We systematically compare principal component analysis (PCA), neighborhood components analysis (NCA), and linear discriminant analysis (LDA), covering both unsupervised and supervised dimensionality reduction. Using the TREC question-classification dataset, we study the relationship between representation dimensionality, information retention, qubit count, and classification performance. Preliminary PCA experiments reveal a strong information bottleneck: reducing 768-dimensional embeddings to 3, 4, 5, and 8 dimensions retains about 8.2%, 10.2%, 11.9%, and 16.4% of the variance, with corresponding classification accuracies of 50.3%, 51.2%, 57.9%, and 63.4%. In contrast, supervised reduction is substantially more efficient. LDA reaches 85.3% accuracy and NCA reaches 83.1% using only 5 dimensions, under a leakage-free cross-validation protocol, compared with 85.1% for a full 384-dimensional classical baseline. These results indicate that supervised dimensionality reduction can preserve task-relevant information far more effectively than variance-based compression, making compact representations a promising route toward practical hybrid quantum-classical NLP models.