Related papers: Topological quantum computing
The boundary of topological superconductors might lead to the appearance of Majorana edge modes, whose non-trivial exchange statistics can be used for topological quantum computing. In branched nanowire networks one can exchange Majorana…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…
We remove the need to physically transport computational anyons around each other from the implementation of computational gates in topological quantum computing. By using an anyonic analog of quantum state teleportation, we show how the…
Topological quantum computation with Fibonacci anyons relies on the possibility of efficiently generating unitary transformations upon pseudoparticles braiding. The crucial fact that such set of braids has a dense image in the unitary…
Majorana fermions feature non-Abelian exchange statistics and promise fascinating applications in topological quantum computation. Recently, second-order topological superconductors (SOTSs) have been proposed to host Majorana fermions as…
This is a series of lecture notes explaining topos theory and its application in physics.
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…
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…
A universal quantum computer can be constructed using abelian anyons. Two qubit quantum logic gates such as controlled-NOT operations are performed using topological effects. Single-anyon operations such as hopping from site to site on a…
These notes provide an introduction to standard topics on quantum computation and communication for those who already have a basic knowledge of quantum mechanics. The main target audience are professional physicists as well as advanced…
Topological quantum computation by way of braiding of Majorana fermions is not universal quantum computation. There are several attempts to make universal quantum computation by introducing some additional quantum gates or quantum states.…
Finding physical realizations of topologically ordered states in experimental settings, from condensed matter to artificial quantum systems, has been the main challenge en route to utilizing their unconventional properties. We show how to…
Topological quantum computation employs two-dimensional quasiparticles called anyons. The generally accepted mathematical basis for the theory of anyons is the framework of modular tensor categories. That framework involves a substantial…
Harnessing non-abelian statistics of anyons to perform quantum computational tasks is getting closer to reality. While the existence of universal anyons by braiding alone such as the Fibonacci anyon is theoretically a possibility,…
The common approach to topological quantum computation is to implement quantum gates by adiabatically moving non-Abelian anyons around each other. Here we present an alternative perspective based on the possibility of realizing the exchange…
We examine how best to design qubits for use in topological quantum computation. These qubits are topological Hilbert spaces associated with small groups of anyons. Op- erations are performed on these by exchanging the anyons. One might…
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…
In this paper we study a Clifford algebra generalization of the quaternions and its relationship with braid group representations related to Majorana fermions. The Fibonacci model for topological quantum computing is based on the fusion…
We study the non-abelian statistics characterizing systems where counter-propagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity-coupling to superconductors and ferromagnets. The most transparent…
We consider universal statistical properties of systems that are characterized by phase states with macroscopic degeneracy of the ground state. A possible topological order in such systems is described by non-linear discrete equations. We…