Speaker: 马海兰，澳国立大学

Title: On compression rate of quantum autoencoders: analytic analysis, numerical and experimental realization

Language: Chinese

Time & Venue: 2024.12.31 10:00-11:00 思源楼813

Abstract: Quantum autoencoders (QAEs) are at the forefront of automatic data compression within quantum information. Generally, a QAE consists of an encoder to compress high-dimensional input states into low-dimensional latent states with the discarded part denoted as the trash states, and a decoder to recover to the original space via the combination of the latent states and the reference states. The goal of QAE is to maximize the overlap between the trash state and the reference state (i.e., the encoding fidelity) or the overlap between the recovered state and the original state (i.e., the decoding fidelity). When taking a pure state as the reference state, perfect QAEs (i.e., the encoding fidelity reaching 1) can be realized when the number of linearly independent vectors among the input states is less than the dimension of the latent space. Furthermore, there exists an upper bound for the encoding fidelity, which is determined by the eigenvalues of the density matrix representation of the input states. However, the upper bound limits the compression rate for high-rank states when focusing on the density matrix representation of the input states. To address the entropy inconsistency between the input states and the reconstructed states, we allow the reference state to be a mixed state to further improve the decoding fidelity. For all these cases, numerical simulations and experimental realizations using different learning methods have been presented.