Quantum ansatz learning

Abstract

Quantum ansatz plays a pivotal role in the efficacy of quantum algorithms, notably within variational quantum algorithms (VQAs), such as quantum neural networks (QNNs), variational quantum eigensolvers (VQE), and the quantum approximate optimization algorithm (QAOA). Although recent progress in tailoring quantum ansätze for specific tasks, has nudged quantum advantages closer to practical realization, fully exploiting the quantum ansatz’s potential remains a formidable challenge, due to inherent hardware limitations and optimization hurdles. This thesis delves into the realm of quantum ansatz learning, aiming to evaluate and augment the performance of quantum ansätze across a spectrum of problems and devices. Initially, the study assesses the trainability and generalization of quantum ansätze of QNNs, revealing a critical dilemma for QNNs in processing classical data. Addressing this challenge, the thesis advances the performance of quantum ansatz through dual avenues: ansatz parameter optimization and architectural refinement. In terms of parameter optimization, the thesis introduces Shuffle-QUDIO, a quantum distributed optimization algorithm that both theoretically and empirically accelerates convergence and reduces estimation errors. On the architectural front, the thesis proposes an automated ansatz generator termed MG-Net which adeptly tailors the optimal ansatz architecture to the demands of any given task and hardware limitations, with enhanced performance. To validate the efficacy of quantum ansatz learning on actual quantum hardware, the thesis employs an automatic ansatz design technique, quantum architecture search (QAS), on an 8-qubit superconducting quantum processor, demonstrating that ansätze crafted through QAS outshine those devised via heuristic methods. These findings broaden the understanding of quantum ansatz learning towards the practical application, narrowing the gap between theoretical quantum computing and its real-world implementation.