Juan Maldacena在2001年的一篇研究在AdS(Anti-de Sitter space)空间中的永久可穿越的黑洞的文章中初次提出了Thermofield Double State（TFD）的思想。Thermofield Double State在holography中有重要的意义,因为它可以对偶到一个AdS空间中的永久的黑洞中，同时，它也给对纠缠、黑洞、量子信息等方面的研究提供了一个很好的出发点。本文介绍了Thermofield Double State（TFD）的基本定义以及几种等价定义，总结归纳了TFD的基本性质，介绍了TFD的几个重要应用，以及介绍了制备TFD的基本思想，包括介绍了几个基态可以被证明是TFD的特例；如何构造体系的哈密顿量使其基态是一个TFD的方法，以及如何从数值模拟的角度近似构造一个TFD。本文从简单的耦合谐振子模型验证了构造哈密顿量的基本方式的正确性；总结了证明耦合SYK模型基态是TFD的证明思路，对于制备TFD与量子信息和机器学习的交叉也给出了一定解释。

Juan Maldacena first proposed the idea of Thermofield Double State (TFD) in a 2001 paper on the eternal traversable black holes in Anti-de Sitter space. Thermofield Double State is of great significance in holography because it dual to an eternal black hole in AdS space. At the same time, it also provides a good starting point for the study of entanglement, black hole, quantum information and so on. This paper introduces the basic definition and several equivalent definitions of TFD, summarizes the basic properties of TFD, introduces several important applications of TFD, and introduces the basic ideas of preparing TFD, including introducing several special cases whose ground states can be proved to be TFD, introducing how to construct the Hamiltonian of the system to make its ground state a TFD, and how to construct a TFD using quantum simulation. This paper verifies the correctness of the basic way to construct a general Hamiltonian from a simple coupled harmonic oscillator model, summarizes the idea of proving that the ground state of the coupled SYK model is TFD, and gives some explanations for the intersection of TFD preparation with quantum information and machine learning.

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