Non-Abelian braiding has attracted significant attention because of its pivotal role in describing the exchange behaviors anyons--a candidate for realizing quantum logics. The input and outcome non-Abelian are connected by a unitary matrix which can also physically emerge as geometric-phase classical systems. Hence it is predicted that should have analogues photonics, but feasible platform expe...

Majorana zero modes (MZMs) are prime candidates for robust topological quantum bits, holding a great promise for quantum computing. Semiconducting nanowires with strong spin orbit coupling offer a promising platform to harness one-dimensional electron transport for Majorana physics. Demonstrating the topological nature of MZMs relies on braiding, accomplished by moving MZMs around each other in...

The perturbative expression of Chern-Simons theory for links in Euclidean 3-space is a linear combination of integrals on configuration spaces. This has successively been studied by Guadagnini, Martellini and Mintchev, Bar-Natan, Kontsevich, Bott and Taubes, D. Thurston, Altschuler and Freidel, Yang. . .We give a self-contained version of this study with a new choice of compactification, and we...

We give an alternative presentation of braided monoidal categories. Instead of the usual associativity and braiding we have just one constraint (the b-structure). In the unital case, the coherence conditions for a b-structure are shown to be equivalent to the usual associativity, unit and braiding axioms. We also discuss the next dimensional version, that is, b-structures on bicategories. As an...

Textile technology and resin transfer molding (RTM) process have been combined to manufacture composites coil springs. Preforms for coil springs were made by braiding process, in which axial yarns are located in the central region and braiding yarns covered them circumferentially. The geometric and process parameters that are related with the fiber orientation and fiber volume fraction of the b...

Anyons are exotic quasiparticles living in two dimensions that do not fit into the usual categories of fermions and bosons, but obey a new form of fractional statistics. Following a recent proposal [Phys. Rev. Lett. 98, 150404 (2007)], we present an experimental demonstration of the fractional statistics of anyons in the Kitaev spin lattice model using a photonic quantum simulator. We dynamical...

In this paper we propose, firstly, a categorification of virtual braid groups and groupoids in terms of “locally” braided objects in a symmetric category (SC), and, secondly, a definition of self-distributive structures (SDS) in an arbitrary SC. SDS are shown to produce braided objects in a SC. As for examples, we interpret associativity and the Jacobi identity in a SC as generalized selfdistri...

A rank-2 toric code (R2TC) Hamiltonian in two dimensions can be constructed as a Higgsed descendant of U(1) lattice gauge theory. As noted by the authors recently, [Y.-T. Oh, J. Kim, E.-G. Moon, and H. Han, Phys. Rev. B {\bf 105}, 045128] quasiparticles that model shows unusual braiding statistics depends on initial locations particles which participate braiding. We show this new kind statistic...