张量网络，量子纠错码与时空间结构

The study of quantum entanglement and the AdS/CFT correspondence has led to many breakthroughs. One notable example is the derivation of Einstein equation via properties of entanglement, suggesting a profound connection between these structures. At the same time, the Ryu-Takayanagi formula also suggests that the tensor network is a concrete realization of the AdS/CFT correspondence -- gravity encodes entanglement in the same way as the tensor network. Based on these successes, we propose to further explore the correspondence between gravity and the tensor network, particularly in the context with real time evolution, an area which is only at its infancy. We would like to understand phenomenology such as the formation of black holes and Hawking radiation from the perspective of the tensor networks. In addition to their theoretical significance, it could provide a platform for experiment verification and implications in error correcting codes.

近年AdS/CFT与纠缠熵的研究带来了许多突破性的成果。其中一个重要的发展，就是从纠缠的结构，推导出爱因斯坦引力方程，揭示量子纠缠与引力的深刻关系。这系列研究，同时指向AdS/CFT与张量网络的关系。一个CFT态的量子纠缠在张量网络中体现的形式与AdS/CFT的Ryu-Takayanagi公式极为相似。所以了解量子纠缠以及张量网络描述量子纠缠的方式成为解开（量子）引力的一个重要的新蹊径。本项目的目的就是在这些基础上进一步厘清AdS/CFT以及量子引力的具体特性，以及如何在适当的张量网络中体现出来。尤其是含时演化的时空间，包括黑洞生成与霍金辐射，怎样在张量网络中描述。这一类含时的研究，到目前为止在整个领域里仍然非常初步。新的进展将对AdS/CFT与张量网络和量子纠错码的准确关系带来重要启示，同时在张量网络这种可控有限的系统中，非常有可能找到实验验证并带来实现量子纠错码的技术提升。