学习用于量子态层析的信息丰富潜在表示
Learning Informative Latent Representation for Quantum State Tomography
AI总结：
针对量子态层析中测量数据不完美导致的不适定重建问题，提出基于transformer的自编码器，通过频率重建预训练提取ILR并预测量子态，显著提升鲁棒性。
摘要：
量子态层析（QST）是通过一系列不同测量来重建量子系统完整状态（在数学上描述为密度矩阵）的过程。这些测量在量子系统的多个相同副本上执行，其结果以频率形式收集。QST旨在从测量频率中恢复密度矩阵或量子态的性质。尽管在理想情况下，借助大量相同副本，一个信息完备的测量集合可以准确确定量子态，但在实际场景中，测量和相同副本都受到限制且并不完美，从而使QST成为高度不适定的问题。传统QST方法通常假设测量频率准确，或依赖人工设计的正则化项来处理不适定重建问题，因此在现实场景中的应用受到限制。深度神经网络（DNN）的最新进展推动了深度学习在QST中的出现。然而，现有基于深度学习的QST方法通常采用通用DNN模型，并未针对QST的不完美条件进行优化。本文提出一种专为具有不完美测量数据的QST定制的、基于transformer的自编码器架构。该方法利用基于transformer的编码器从不完美测量数据中提取信息丰富的潜在表示（ILR），并采用解码器基于ILR预测量子态。我们预期高维ILR将捕获关于量子态的更全面信息。为此，我们通过一个涉及从测量频率重建高质量频率的代理任务对编码器进行预训练。大量仿真和实验证明了信息丰富潜在表示在处理QST中不完美测量数据方面的卓越能力。
英文摘要：
Quantum state tomography (QST) is the process of reconstructing the complete state of a quantum system (mathematically described as a density matrix) through a series of different measurements. These measurements are performed on a number of identical copies of the quantum system, with outcomes gathered as frequencies. QST aims to recover the density matrix or the properties of the quantum state from the measured frequencies. Although an informationally complete set of measurements can specify the quantum state accurately in an ideal scenario with a large number of identical copies, both the measurements and identical copies are restricted and imperfect in practical scenarios, making QST highly ill-posed. The conventional QST methods usually assume accurate measured frequencies or rely on manually designed regularizers to handle the ill-posed reconstruction problem, suffering from limited applications in realistic scenarios. Recent advances in deep neural networks (DNN) led to the emergence of deep learning in QST. However, existing DL-based QST approaches often employ generic DNN models that are not optimized for imperfect conditions of QST. In this paper, we propose a transformer-based autoencoder architecture tailored for QST with imperfect measurement data. Our method leverages a transformer-based encoder to extract an informative latent representation (ILR) from imperfect measurement data and employs a decoder to predict the quantum states based on the ILR. We anticipate that the high-dimensional ILR will capture more comprehensive information about the quantum states. To achieve this, we conduct pre-training of the encoder using a pretext task that involves reconstructing high-quality frequencies from measured frequencies. Extensive simulations and experiments demonstrate the remarkable ability of the informative latent representation to deal with imperfect measurement data in QST.
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。
