Related papers: Braiding Fibonacci anyons
Chiral conformal blocks in a rational conformal field theory are a far going extension of Gauss hypergeometric functions. The associated monodromy representations of Artin's braid group capture the essence of the modern view on the subject,…
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons…
The paper contains enumerative combinatorics for positive braids, square free braids, and simple braids, emphasizing connections with classical Fibonacci sequence. The simple subgraph of the Cayley graph of the braid group is analyzed in…
This is a tutorial review of methods to braid the world lines of non-Abelian anyons (Majorana zero-modes) in topological superconductors. That "Holy Grail" of topological quantum information processing has not yet been reached in the…
We present microscopic, multiple Landau level, (frustration-free and positive semi-definite) parent Hamiltonians whose ground states, realizing different quantum Hall fluids, are parton-like and whose excitations display either Abelian or…
The non-Abelian braiding of Majorana fermions is one of the most promising operations providing a key building block for the realization of topological quantum computation. Recently, the chiral Majorana fermions were observed in a hybrid…
In this thesis we develop a full characterization of abelian quantum statistics on graphs. We explain how the number of anyon phases is related to connectivity. For 2-connected graphs the independence of quantum statistics with respect to…
We construct some braided quantum groups over the circle group. These are analogous to the free orthogonal quantum groups and generalise the braided quantum SU(2) groups for complex deformation parameter. We describe their irreducible…
Parafermions modes are non-Abelian anyons which were introduced as $\mathbb{Z}_N$ generalizations of $\mathbb{Z}_2$ Majorana states. In particular, $\mathbb{Z}_3$ parafermions can be used to produce Fibonacci anyons, laying a path towards…
The result of this paper is the determination of the cohomology of Artin groups of type A_n, B_n and \tilde{A}_{n} with non-trivial local coefficients. The main result is an explicit computation of the cohomology of the Artin group of type…
Parafermions, which can be viewed as a fractionalized version of Majorana modes, exhibit profound non-Abelian statistics and emerge in topologically ordered systems, while their realization in experiment has been challenging. Here we…
The possibility of realizing bosonic fractional quantum Hall effect in ultra-cold atomic systems suggests a new route to producing and manipulating anyons, by introducing auxiliary bosons of a different species that capture quasiholes and…
Braiding of anyons such as Majoranas or parafermions provides only Clifford gates which do not form a universal set of quantum gates. We propose a robust and resource-efficient scheme to perform a non-Clifford gate on a logical qudit…
We develop a full characterization of abelian quantum statistics on graphs. We explain how the number of anyon phases is related to connectivity. For 2-connected graphs the independence of quantum statistics with respect to the number of…
We propose a bottom-up approach to the building of particle physics models from string theory. Our building blocks are Type II D-branes which we combine appropriately to reproduce desirable features of a particle theory model: 1) Chirality…
The knot concordance group can be contextualized as organizing problems about 3- and 4-dimensional spaces and the relationships between them. Every 3-manifold is surgery on some link, not necessarily a knot, and thus it is natural to ask…
Topological quantum computation (TQC) is one of the most striking architectures that can realize fault-tolerant quantum computers. In TQC, the logical space and the quantum gates are topologically protected, i.e., robust against local…
Two-dimensional systems such as quantum spin liquids or fractional quantum Hall systems exhibit anyonic excitations that possess more general statistics than bosons or fermions. This exotic statistics makes it challenging to solve even a…
Recent theoretical insights into the possibility of non-Abelian phases in $\nu=2/3$ fractional quantum Hall states revived the interest in the numerical phase diagram of the problem. We investigate the effect of various kinds of two-body…
We prove that braid group representations associated to braided fusion categories and mapping class group representations associated to modular fusion categories are always semisimple. The proof relies on the theory of extensions in…