Related papers: Braid Matrices and Quantum Gates for Ising Anyons …
Topological quantum computers promise a fault tolerant means to perform quantum computation. Topological quantum computers use particles with exotic exchange statistics called non-Abelian anyons, and the simplest anyon model which allows…
In topological quantum computation, quantum information is stored in states which are intrinsically protected from decoherence, and quantum gates are carried out by dragging particle-like excitations (quasiparticles) around one another in…
We give a general proof for the existence and realizability of Clifford gates in the Ising topological quantum computer. We show that all quantum gates that can be implemented by braiding of Ising anyons are Clifford gates. We find that the…
We study topological properties of quasi-particle states in the non-Abelian quantum Hall states. We apply a skein-theoretic method to the Read--Rezayi state whose effective theory is the SU(2)_K Chern--Simons theory. As a generalization of…
The simulation of non-Abelian anyon braiding is a critical step towards fault-tolerant quantum computation. We introduce a framework for this task based on a one-dimensional Quasicrystal Inflation Code (QIC). The code is defined by a local…
Unitary braiding operators can be used as robust entangling quantum gates. We introduce a solution-generating technique to solve the $(d,m,l)$-generalized Yang-Baxter equation, for $m/2\leq l \leq m$, which allows to systematically…
Read-Rezayi fractional quantum Hall states are among the prime candidates for realizing non-Abelian anyons which in principle can be used for topological quantum computation. We present a prescription for efficiently finding braids which…
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…
We introduce a recoupling theory for virtual braided trees. This recoupling theory can be utilized to incorporate swap gates into anyonic models of quantum computation.
Topological quantum computing promises intrinsic fault tolerance by encoding quantum information in non-Abelian anyons, where quantum gates are implemented via braiding. While braiding operations are robust against local perturbations, a…
We propose a framework for topological quantum computation using newly discovered non-semisimple analogs of topological quantum field theories in 2+1 dimensions. These enhanced theories offer more powerful models for quantum computation.…
Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from…
We demonstrate that the two inequivalent spinor representations of the braid group \B_{2n+2}, describing the exchanges of 2n+2 non-Abelian Ising anyons in the Pfaffian topological quantum computer, are equivalent from computational point of…
Fibonacci anyons are attractive for use in topological quantum computation because any unitary transformation of their state space can be approximated arbitrarily accurately by braiding. However there is no known braid that entangles two…
A great part of the mathematical foundations of topological quantum computation is given by the theory of modular categories which provides a description of the topological phases of matter such as anyon systems. In the near future the…
We study the emergence of topological matter in two-dimensional systems of neutral Rydberg atoms in Ruby lattices. While Abelian anyons have been predicted in such systems, non-Abelian anyons, which would form a substrate for fault-tolerant…
Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle…
In a topological quantum computer, braids of non-Abelian anyons in a (2+1)-dimensional space-time form quantum gates, whose fault tolerance relies on the topological, rather than geometric, properties of the braids. Here we propose to…
We show that universal quantum computation can be performed within the ground state of a topologically ordered quantum system, which is a naturally protected quantum memory. In particular, we show how this can be achieved using brane-net…
We extend the topological quantum computation scheme using the Pfaffian quantum Hall state, which has been recently proposed by Das Sarma et al., in a way that might potentially allow for the topologically protected construction of a…