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As quantum computing transitions from theory to implementation, understanding the practicality of quantum algorithms on current hardware is essential. This thesis explores two key challenges in the advancement of quantum computation, namely the application of quantum algorithms to solving linear systems of equations and optimizing quantum circuit architectures. Specifically, the study investigates the Harrow–Hassidim–Lloyd (HHL) and Variational Quantum Linear Solver (VQLS) algorithms, analyzing their scalability, accuracy, and suitability for near-term noisy intermediate-scale quantum (NISQ) devices. Using AC power flow as a representative engineering case study, results highlight that while HHL offers a theoretical exponential speedup, its circuit depth and hardware demands remain prohibitive for practical use. In contrast, VQLS demonstrates reliable convergence and adaptability on simulated hybrid quantum–classical systems, albeit with sensitivity to ansatz design and optimizer performance.
Beyond quantum linear solvers, this thesis extends to the intersection of quantum machine learning (QML) and reinforcement learning (RL) for quantum circuit optimization. Variational QML algorithms are surveyed for their potential to learn expressive models with shallow quantum circuits. A deep reinforcement learning framework is then implemented to automate quantum architecture search, showing that adaptive agents, particularly those trained with Advantage Actor-Critic (A2C) and Proximal Policy Optimization (PPO), can discover high-fidelity quantum circuits. Together, these studies demonstrate that data-driven and learning-based methods can bridge the gap between theoretical quantum algorithms and their real-world implementation.
Overall, this work analyzes the potential of variational and reinforcement learning approaches to enhance the efficiency, scalability, and practicality of quantum algorithms. It establishes a foundation for applying such techniques to engineering problems, while pointing toward future research in hybrid quantum–classical optimization and noise-resilient circuit design.