Related papers: Non-Abelian statistics and topological quantum inf…
Topological superconductors can host Majorana quasiparticles which supersede the fermion/boson dichotomy and offer a pathway to fault tolerant quantum computation. In one-dimensional systems zero-energy Majorana states are bound to the ends…
Can topological quantum entanglement between anyons in one topological medium "stray" into a different, topologically distinct medium? In other words, can quantum information encoded non-locally in the combined state of non-Abelian anyons…
We investigate a promising conformal field theory realization scheme for topological quantum computation based on the Fibonacci anyons, which are believed to be realized as quasiparticle excitations in the $\mathbb{Z}_3$ parafermion…
Theoretically, a pair of Majorana bound states in a topological superconductor forms a single fermionic level even at large separations, implying that the parity information is stored nonlocally. The nonlocality leads to a long-distance…
We introduce and develop an approach to realizing a topological phase transition and non-Abelian statistics with dynamically induced Floquet Majorana Fermions (FMFs). When the periodic driving potential does not break fermion parity…
It has been proposed that localized zero-energy Majorana states can be realized in a two-dimensional network of quasi-one-dimensional semiconductor wires that are proximity-coupled to a bulk superconductor. The wires should have strong…
It has been argued that fluctuations of fermion parity are harmful for the demonstration of non-Abelian anyonic statistics. Here, we demonstrate a striking exception in which such fluctuations are actively used. We present a theory of…
Over the last decade, there have been considerable efforts to observe non-abelian quasi-particles in novel quantum materials and devices. These efforts are motivated by the goals of demonstrating quantum statistics of quasi-particles beyond…
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…
Braiding of non-Abelian Majorana anyons is a first step towards using them in quantum computing. We propose a protocol for braiding Majorana zero modes formed at the edges of nanowires with strong spin orbit coupling and proximity induced…
We propose a platform for braiding Majorana non-Abelian anyons based on a heterostructure between a $d$-wave high-$T_c$ superconductor and a quantum spin-Hall insulator. It has been recently shown that such a setup for a quantum spin-Hall…
Exchanging particles on graphs, or more concretely on networks of quantum wires, has been proposed as a means to perform fault tolerant quantum computation. This was inspired by braiding of anyons in planar systems. However, exchanges on a…
We summarize the key ingredients required for universal topological quantum computation using Majorana zero modes in networks of topological superconductor nanowires. Particular emphasis is placed on the use of both sparse and dense logical…
We study the stability of the topological quantum computation proposals involving Majorana fermions against thermal fluctuations. We use a minimal realistic model of a spinless px+ipy superconductor and consider effect of excited midgap…
In view of the fundamental importance and many promising potential applications, non-Abelian statistics of topologically protected states have attracted much attention recently. However, due to the operational difficulties in solid-state…
Non-trivial braid-group representations appear as non-Abelian quantum statistics of emergent Majorana zero modes in one and two-dimensional topological superconductors. Here, we generate such representations with topologically protected…
Majorana fermions, quantum particles with non-Abelian exchange statistics, are not only of fundamental importance, but also building blocks for fault-tolerant quantum computation. Although certain experimental breakthroughs for observing…
A vortex in a model spinless px+ipy superconductor induces two Majorana fermions (MFs), one in the core and the other at the sample edge. In the present work, we show that edge MF can be generated, fused, transported, and braided easily by…
Non-abelian anyons are highly desired for topological quantum computation purposes, with Majorana fermions providing a promising route, particularly zero modes with non-trivial mutual statistics. Yet realizing Majorana zero modes in matter…
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…