Related papers: Particle Topology, Braids, and Braided Belts
In a topological quantum computer, universality is achieved by braiding and quantum information is natively protected from small local errors. We address the problem of compiling single-qubit quantum operations into braid representations…
Topological phases of noninteracting particles are distinguished by global properties of their band structure and eigenfunctions in momentum space. On the other hand, group theory as conventionally applied to solid-state physics focuses…
Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space,…
In the paper we give a survey on braid groups and subjects connected with them. We start with the initial definition, then we give several interpretations as well as several presentations of these groups. Burau presentation for the pure…
A method for compiling quantum algorithms into specific braiding patterns for non-Abelian quasiparticles described by the so-called Fibonacci anyon model is developed. The method is based on the observation that a universal set of quantum…
The ribbon cocycle invariant is defined by means of a partition function using ternary cohomology of self-distributive structures (TSD) and colorings of ribbon diagrams of a framed link, following the same paradigm introduced by Carter,…
Knots and links represent a fundamental motif of non-local connectivity that permeates the physical sciences from string theory to protein folds. While spectral braiding has been explored in two-band non-Hermitian models across various…
String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group $G$ and a 4-cocycle twist $\omega_4$ of $G$'s cohomology group…
Fibonacci anyons provide the simplest possible model of non-Abelian fusion rules: [1] x [1] = [0] + [1]. We propose a conformal field theory construction of topological quantum registers based on Fibonacci anyons realized as quasiparticle…
It is well-known that is spite of sharing some properties with conventional particles, topological geons in general violate the spin-statistics theorem. On the other hand, it is generally believed that in quantum gravity theories allowing…
This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…
Topological principles constitute at present an integral component of condensed matter physics, permeating the modern characterization of electronic states while also guiding materials design. In this brief Perspective, I highlight three…
Recent progress in string theory has led to a reformulation of quantum-group polynomial invariants for knots and links into new polynomial invariants whose coefficients can be understood in topological terms. We describe in detail how to…
Fractional statistics is one of the most intriguing features of topological phases in 2D. In particular, the so-called non-Abelian statistics plays a crucial role towards realizing universal topological quantum computation. Recently, the…
We apply the geometric-topology surgery theory on spacetime manifolds to study the constraints of quantum statistics data in 2+1 and 3+1 spacetime dimensions. First, we introduce the fusion data for worldline and worldsheet operators…
The topological framework of circuit topology has recently been introduced to complement knot theory and to help in understanding the physics of molecular folding. Naturally evolved linear molecular chains, such as proteins and nucleic…
Loop braid groups characterize the exchange of extended objects, namely loops, in three dimensional space generalizing the notion of braid groups that describe the exchange of point particles in two dimensional space. Their interest in…
We connect Braided Ribbon Networks to the states of loop quantum gravity. Using this connection we present the reduced link as an invariant which captures information from the embedding of the spin-networks. We also present a means of…
The spaces of triangulations of a given manifold have been widely studied. The celebrated theorem of Pachner~\cite{Pachner} says that any two triangulations of a given manifold can be connected by a sequence of bistellar moves, or Pachner…
For non-abelian simple objects in a unitary modular category, the density of their braid group representations, the #P-hard evaluation of their associated link invariants, and the BQP-completeness of their anyonic quantum computing models…