Related papers: Engineering Yang-Lee anyons via Majorana bound sta…
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…
We investigate the composite systems consisting of topological orders separated by gapped domain walls. We derive a pair of domain-wall Verlinde formulae, that elucidate the connection between the braiding of interdomain excitations labeled…
Topological superconductivity supports exotic Majorana bound states (MBS) which are chargeless zero-energy emergent quasiparticles. With their non-Abelian exchange statistics and fractionalization of a single electron stored nonlocally as a…
Non-Abelian anyons are exotic quasiparticle excitations hosted by certain topological phases of matter. They break the fermion-boson dichotomy and obey non-Abelian braiding statistics: their interchanges yield unitary operations, rather…
We analyse the control of Majorana zero-energy states by mapping the fermionic system onto a chain of Ising spins. Although the topological protection is lost for the Ising system, the mapping provides additional insight into the nature of…
We find the coexistence of two kinds of non-abelian anyons, Majorana fermion at the geometric ends and Jackiw-Rebbi-type bound state (JRBS)at a domain-wall, in a topological superconducting phase in one-dimensional (1D) systems. Each…
Unpaired Majorana zero-modes are central to topological quantum computation schemes as building blocks of topological qubits, and are therefore under intense experimental and theoretical investigation. Their generalizations to parafermions…
Zero--energy Majorana quasiparticles can be induced at the edge of a low dimensional systems. Non--Abelian statistics of this state makes it a good candidate for the realization of quantum computing. From the practical point of view, it is…
Non-Abelian toplogical superconductors are characterized by the existence of {zero-energy} Majorana fermions bound in the quantized vortices. This is a consequence of the nontrivial bulk topology characterized by an {\em odd} Chern number.…
These lectures contain an introduction to instantons, calorons and dyons of the Yang--Mills gauge theory. Since we are interested in the mechanism of confinement and of the deconfinement phase transition at some critical temperature, the…
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…
Braiding of Majorana states demonstrates their non-Abelian exchange statistics. One implementation of braiding requires control of the pairwise couplings between all Majorana states in a trijunction device. To have adiabaticity, a…
The Yao-Lee model is an example of exactly solvable spin-orbital models that are generalizations of the original Kitaev honeycomb model with extra local orbital degrees of freedom. Similar to the Kitaev model, both spin and orbital degrees…
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…
Anyons have recently received great attention due to their promising application in topological quantum computation. The best validated system that enjoys the anyonic excitations are the Laughlin states. The quasi-particles in Laughlin…
Majorana zero-modes bound to vortices in a topological superconductor have a non-Abelian exchange statistics expressed by a non-deterministic fusion rule: When two vortices merge they may or they may not produce an unpaired fermion with…
Majorana zero-modes in a superconductor are midgap states localized in the core of a vortex or bound to the end of a nanowire. They are anyons with non-Abelian braiding statistics, but when they are immobile one cannot demonstrate this by…
Majorana bound states have been a focus of condensed matter research for their potential applications in topological quantum computation. Here we utilize two charge-qubit arrays to explicitly simulate a DIII class one-dimensional…
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…
Quantum gates built out of braid group elements form the building blocks of topological quantum computation. They have been extensively studied in $SU(2)_k$ quantum group theories, a rich source of examples of non-Abelian anyons such as the…