Related papers: Introduction to topological quantum computation wi…
Anyons obtained from a finite gauge theory have a computational power that depends on the symmetry group. The relationship between group structure and computational power is discussed in this paper. In particular, it is shown that anyons…
We study the implementation of a universal quantum gate set via multiple-braiding within $SU(2)_k$ ($k > 2$, $k \neq 4$) anyon models. The multiple elementary braiding matrices (MEBMs) are derived from the $q$-deformed representation theory…
Anyons are quasiparticles in two-dimensional systems that show statistical properties very distinct from those of bosons or fermions. While their isolated observation has not yet been achieved, here we perform a quantum simulation of anyons…
Electrons are indivisible elementary particles, yet paradoxically a collection of them can act as a fraction of a single electron, exhibiting exotic and useful properties. One such collective excitation, known as a topological Majorana…
The Fibonacci topological order is the simplest platform for a universal topological quantum computer, consisting of a single type of non-Abelian anyon, $\tau$, with fusion rule $\tau\times\tau=1+\tau$. While it has been proposed that the…
This set of lecture notes forms the basis of a series of lectures delivered at the 48th IFF Spring School 2017 on Topological Matter: Topological Insulators, Skyrmions and Majoranas at Forschungszentrum Juelich, Germany. The first part of…
The surface code is currently the primary proposed method for performing quantum error correction. However, despite its many advantages, it has no native method to fault-tolerantly apply non-Clifford gates. Additional techniques are…
In topology, a torus remains invariant under certain non-trivial transformations known as modular transformations. In the context of topologically ordered quantum states of matter, these transformations encode the braiding statistics and…
We show that non-abelian quantum statistics can be studied using certain topological invariants which are the homology groups of configuration spaces. In particular, we formulate a general framework for describing quantum statistics of…
Quantum computers are predicted to utilize quantum states to perform memory and to process tasks far faster than those of conventional classical computers. In this paper we show a new road towards building fault tolerance quantum computer…
These extended lecture notes survey a novel derivation of anyonic topological order (as seen in fractional quantum Hall systems) on single magnetized M5-branes probing Seifert orbi-singularities ("geometric engineering" of anyons), which we…
We describe the chiral Kondo chain model based on the symplectic Kondo effect and demonstrate that it has a quantum critical ground state populated by non-Abelian anyons. We show that the fusion channel of two arbitrary anyons can be…
Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid…
There are two schools of "measurement-only quantum computation". The first ([11]) using prepared entanglement (cluster states) and the second ([4]) using collections of anyons, which according to how they were produced, also have an…
A convenient and effective way in the quantum double model to study anyons in a topological space with a tensor product structure is to create and braid anyons using ribbon operators connected to a common base site [A. Kitaev Ann.\ Phys.…
In this paper, we give a description of a recent quantum algorithm created by Aharonov, Jones, and Landau for approximating the values of the Jones polynomial at roots of unity of the form exp(2$\pi$i/k). This description is given with two…
We study an efficient algorithm to hash any single qubit gate (or unitary matrix) into a braid of Fibonacci anyons represented by a product of icosahedral group elements. By representing the group elements by braid segments of different…
Holonomic quantum computation is the idea to use non-Abelian geometric phases to implement universal quantum gates that are robust to fluctuations in control parameters. Here, we propose a compact design for a holonomic quantum computer…
Topological quantum computing has recently proven itself to be a powerful computational model when constructing viable architectures for large scale computation. The topological model is constructed from the foundation of a error correction…
While topological quantum computation is intrinsically fault-tolerant at zero temperature, it loses its topological protection at any finite temperature. We present a scheme to protect the information stored in a system supporting…