【时间】2021年10月27日（周三） 14:00

【地点】量子院526报告厅   

【主持】刘东  量子院兼聘研究员，清华大学副教授

【题目】Quantized Graphs and Quantum Error Correction

【摘要】Graph theory has been widely used in classical error corrections. In this talk, we introduce quantized graphs and apply them to quantum error corrections. Various graphical concepts for classical error corrections can be quantized in a natural way. The quon language provides a mathematical theory to study such quantized graphs in a general framework. For any quantized graph, we construct a family of graphical quantum error correcting codes and we characterize all optimal [[n,k,d]] codes among them. Computing the distance d reduced to two classical problems on bits. This phenomenon is similar to CSS codes, but our methods work for non CSS codes as well, such as the optimal [[5,1,3]] code. From a better choice of quantized graphs, we can ensure that logical qubits are implemented by the ground states of “translation-invariant” local Hamiltonians, which are gapped in the large scale limit.

【报告人简介】

刘正伟，清华大学丘成桐数学科学中心数学科学系教授，北京雁栖湖应用数学研究院副院长。海外高层次引进人才。曾解决多个重要数学公开问题，提出量子傅里叶分析理论。在2017年PNAS文章中，与Arthur Jaffe和Alex Woznikwoski提出Quon语言研究量子信息。2019年获得华人数学家大会（ICCM）银奖。