On exploring the potential of quantum auto-encoder for learning quantum systems

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.