探索量子自编码器在学习量子系统方面的潜力
On exploring the potential of quantum auto-encoder for learning quantum systems
AI总结：
本文提出三种基于 QAE 的学习协议，用于低秩态保真度估计、量子 Fisher 信息估计和 Gibbs 态制备，并通过误差界分析与数值模拟验证其近期量子可行性。
摘要：
量子计算与机器学习之间的频繁互动正在为这两个领域带来革命性变化。一个典型成果是量子自编码器（QAE），它是缓解量子世界中普遍存在的维数灾难的领先策略。尽管 QAE 具有引人注目的能力，但其实际应用在很大程度上仍未得到探索。为缩小这一知识空白，本文设计了三种有效的、基于 QAE 的学习协议，以解决学习量子系统时三个经典计算困难的学习问题，即低秩态保真度估计、量子 Fisher 信息估计和 Gibbs 态制备。得益于 QAE 的多功能性，我们提出的方案可以在近期量子机器上直接执行。此外，我们分析了训练后协议的误差界，并从复杂性理论角度展示了其提供实际效用所需的条件。我们进行了数值模拟，以验证所提出的三种协议的有效性。本工作为开发先进的量子学习算法以完成困难的量子物理和量子信息处理任务提供了新的思路。
英文摘要：
The frequent interactions between quantum computing and machine learning revolutionize both fields. One prototypical achievement is the quantum auto-encoder (QAE), as the leading strategy to relieve the curse of dimensionality ubiquitous in the quantum world. Despite its attractive capabilities, practical applications of QAE have yet largely unexplored. To narrow this knowledge gap, here we devise three effective QAE-based learning protocols to address three classically computational hard learning problems when learning quantum systems, which are low-rank state fidelity estimation, quantum Fisher information estimation, and Gibbs state preparation. Attributed to the versatility of QAE, our proposals can be readily executed on near-term quantum machines. Besides, we analyze the error bounds of the trained protocols and showcase the necessary conditions to provide practical utility from the perspective of complexity theory. We conduct numerical simulations to confirm the effectiveness of the proposed three protocols. Our work sheds new light on developing advanced quantum learning algorithms to accomplish hard quantum physics and quantum information processing tasks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
