Advancing Computational Frontiers in Noisy Quantum Systems with Transformative Quantum Neural Network Classifiers

Date of Award

5-2026

Degree Name

Doctor of Philosophy

Department

Computer Science

First Advisor

Alvis Fong, Ph.D.

Second Advisor

Elise de Doncker, Ph.D.

Third Advisor

Dean Johnson, Ph.D.

Keywords

Quantum enhanced entanglement, quantum evolutionary algorithm, quantum machine learning, quantum natural language processing, quantum neural networks

Abstract

The advancement of Quantum Machine Learning (QML) in the Noisy Intermediate-Scale Quantum (NISQ) era is fundamentally constrained by the interplay between limited hardware fidelity, unstable optimization dynamics, and the absence of structurally aligned quantum representations. While variational quantum circuits offer a promising framework for learning, they are hindered by barren plateaus, measurement-induced stochasticity, and architectures that fail to fully exploit the intrinsic representational advantages of quantum systems. This dissertation addresses these challenges through a unified framework that integrates optimization, representation, architectural search, and application-specific design into a coherent, noise-aware quantum learning paradigm.

At the core of this work is the development of Adaptive Quantum Gradient Descent (AQGD), a novel optimization algorithm that departs from fixed learning-rate strategies by introducing a state-dependent update mechanism governed by quantum-state divergence. By leveraging fidelity-based feedback, AQGD dynamically modulates step size in response to the geometry of quantum state space and the statistical properties of measurement, enabling stable and efficient training under both noiseless and noisy conditions. Theoretical analysis and simulation results demonstrate that AQGD mitigates gradient instability and accelerates convergence relative to conventional quantum and classical optimizers.

To address representational limitations, this dissertation introduces Quantum Enhanced Entanglement (QEE) and Self-Stabilizing Topological Protection (SSTP), a framework for constructing entanglement structures aligned with hierarchical and compositional data domains, particularly natural language. QEE formalizes the mapping between linguistic structure and entanglement patterns through a Linguistic Entanglement Graph (LEG), while SSTP embeds these states within topologically constrained subspaces to enhance robustness against decoherence and noise. Together, these mechanisms preserve meaningful quantum correlations in NISQ environments without requiring full fault-tolerant error correction.

Building on these foundations, the dissertation presents a complete Quantum Natural Language Processing (QNLP) system that integrates structured encoding, topological stabilization, and adaptive optimization. This system models linguistic meaning as trajectories on a stabilized quantum manifold, providing a principled and interpretable alternative to classical distributional approaches.

Recognizing the challenges of circuit design in high-dimensional and noise-constrained settings, this work further develops a Quantum Evolutionary Algorithm (QEA) for architecture search and initialization. By combining evolutionary strategies with quantum representations and hardware-aware constraints, QEA explores entanglement configurations and parameter landscapes to identify high-quality initializations that improve subsequent gradient-based optimization. These components are synthesized into a unified framework and evaluated through extensive simulations using both ideal and noise-injected quantum models.

Collectively, this dissertation advances the state of QML by establishing a unified, noise-aware framework that aligns quantum optimization, representation, and system design with the realities of NISQ hardware.

Access Setting

Dissertation-Abstract Only

Restricted to Campus until

5-1-2028

This document is currently not available here.

Share

COinS