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BIMSA-Tsinghua量子对称讨论班
Operator algebra approach for topological Pauli stabilizer codes in two dimensions
Operator algebra approach for topological Pauli stabilizer codes in two dimensions
演讲者
陈昱安
时间
2024年12月25日 13:30 至 14:30
地点
A3-3-301
线上
Zoom 242 742 6089
(BIMSA)
摘要
In this talk, I will discuss the operator algebra and computational algorithms for analyzing topological Pauli stabilizer codes in two spatial dimensions. These codes underpin the study of topological phases of matter and the design of quantum codes for fault-tolerant quantum computation. Building on the generalized Pauli stabilizer codes framework, I will present algorithms for extracting topological data such as anyon types, fusion rules, topological spins, and braiding statistics. I will also introduce methods for constructing gapped boundaries and defects through boundary anyon condensation. The algebraic approach, which utilizes matrix operations such as the Hermite and Smith normal forms, allows for efficient analysis and systematic construction of surface codes. Examples, including toric codes, color codes, and bivariate bicycle codes, illustrate the versatility of these methods in revealing new insights into the bulk and boundary topological properties of quantum codes. These results deepen our understanding of two-dimensional topological stabilizer codes and pave the way for practical designs of quantum error-correcting codes in fault-tolerant quantum computing.
演讲者介绍
陈昱安，北京大学物理学院量子材料科学中心助理教授。2015 年 6 月毕业于美国麻省理工学院，获得数学、物理学学士学位；2020 年 6 月毕业于美国加州理工学院，获得物理学博士学位。曾任谷歌公司量子人工智能（Quantum AI）研究团队研究科学家。2020 年 9月至 2023 年 6 月期间，在美国马里兰大学帕克分校联合量子研究所（JQI）博士后研究员 。2023 年 7 月加入北京大学物理学院。2009年和2010年分别获第40届国际物理奥林匹克竞赛（IPhO）金牌和第51届国际数学奥林匹克竞赛铜牌。