2022/08/24 by Eric C. Rowell, Rowell, Eric C.
Computer Science · Mathematics · Physics and Astronomy · #18D10 #20F36 #58D30 #FOS: Mathematics #FOS: Physical sciences #Parallel Computing and Optimization Techniques #Quantum Algebra (math.QA) #Quantum Physics (quant-ph) #Topological Materials and Phenomena #Topological and Geometric Data Analysis #math.QA #msc:18D10 #msc:20F36 #msc:58D30 #quant-ph
paper · pdf · doi:10.48550/arxiv.2208.11762
arxiv created 2022/08/24 · openalex publication_date 2022/08/24 · arxiv updated 2022/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The topological model for quantum computation is an inherently fault-tolerant model built on anyons in topological phases of matter. A key role is played by the braid group, and in this survey we focus on a selection of ways that the mathematical study of braids is crucial for the theory. We provide some brief historical context as well, emphasizing ways that braiding appears in physical contexts. We also briefly discuss the 3-dimensional generalization of braiding: motions of knots.