Abstract
This thesis explores the intersection of quantum information and variational learning, focusing on classical learning for quantum information processing, tensor networks for quantum circuit simulation, and quantum variational learning. Contributions include supervised learning methods for reconstructing system Hamiltonians, deep reinforcement learning-based approaches for error reduction in quantum imaginary time evolution, and advancements in simulating noisy random quantum circuits using matrix product density operators. Furthermore, the thesis presents a noise-resilient variational quantum algorithm for discovering quantum error-correcting codes and investigates the limitations of quantum autoencoders, proposing a noise-assisted model for high-fidelity compression of mixed states. Overall, this work advances the understanding of the interplay between quantum information and variational learning, with potential applications in near-term quantum computing and condensed matter physics.