BIMSA > BIMSA-Tsinghua Quantum Symmetry Seminar BIMSA-Tsinghua Quantum Symmetry Seminar Operator algebra approach for topological Pauli stabilizer codes in two dimensions
Operator algebra approach for topological Pauli stabilizer codes in two dimensions
Organizers
Linzhe Huang , Zhengwei Liu , Sebastien Palcoux , Yilong Wang , Jinsong Wu
Speaker
Yu-An Chen
Time
Wednesday, December 25, 2024 1:30 PM - 2:30 PM
Venue
A3-3-301
Online
Zoom 242 742 6089 (BIMSA)
Abstract
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.
Speaker Intro
Yu-An Chen is an Assistant Professor at the Quantum Materials Science Center, School of Physics, Peking University. He graduated from the Massachusetts Institute of Technology (MIT) in June 2015, earning bachelor's degrees in mathematics and physics. In June 2020, he completed his Ph.D. in physics at the California Institute of Technology (Caltech). He previously worked as a research scientist on the Quantum AI team at Google. From September 2020 to June 2023, he was the JQI postdoctoral fellow at the University of Maryland, College Park. In July 2023, he joined the School of Physics at Peking University.