On exploring practical potentials of quantum auto-encoder with advantages
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Quantum auto-encoder (QAE) is a powerful tool to relieve the curse of dimensionality encountered in quantum physics, celebrated by the ability to extract low-dimensional patterns from quantum states living in the high-dimensional space. Despite its attractive properties, little is known about the practical applications of QAE with provable advantages. To address these issues, here we prove that QAE can be used to efficiently calculate the eigenvalues and prepare the corresponding eigenvectors of a high-dimensional quantum state with the low-rank property. With this regard, we devise three effective QAE-based learning protocols to solve the low-rank state fidelity estimation, the quantum Gibbs state preparation, and the quantum metrology tasks, respectively. Notably, all of these protocols are scalable and can be readily executed on near-term quantum machines. Moreover, we prove that the error bounds of the proposed QAE-based methods outperform those in previous literature. Numerical simulations collaborate with our theoretical analysis. Our work opens a new avenue of utilizing QAE to tackle various quantum physics and quantum information processing problems in a scalable way.
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