Witness algebra and anyon braiding. (16th March 2020)

• Record Type: Journal Article
• Authors: Blass, Andreas; Gurevich, Yuri
• Is Part Of: Mathematical structures in computer science. Volume 30:Number 3(2020)
• Page Start: 234
• Page End: 270
• Publication Date: 2020-03-16
• Subjects: Anyons, -- braiding, -- modular tensor categories, -- topological quantum computing, -- witness algebra; Computer science -- Mathematics -- Periodicals; 004.015105
• DOI: 10.1017/S0960129520000055
• Languages: English
• ISSNs: 0960-1295

Abstract

Abstract: Topological quantum computation employs two-dimensional quasiparticles called anyons. The generally accepted mathematical basis for the theory of anyons is the framework of modular tensor categories. That framework involves a substantial amount of category theory and is, as a result, considered rather difficult to understand. Is the complexity of the present framework necessary? The computations of associativity and braiding matrices can be based on a much simpler framework, which looks less like category theory and more like familiar algebra. We introduce that framework here.