Non-Abelian braiding has attracted substantial attention because of its pivotal role in describing the exchange behaviour of anyons—candidates for realizing quantum logics. The input and outcome of non-Abelian braiding are connected by a unitary matrix
Non-Abelian Thouless pumps are periodically driven systems designed by the non-Abelian holonomy principle, in which quantized transport of degenerate eigenstates emerges, exhibiting noncommutative features such that the outcome depends on the pumping seq
However, discussions of complex-energy braids have been largely limited to the Abelian braid group B 2 \mathbb{B}_2 for its relative simplicity, while identifying topological non-Abelian braiding is still difficult since it has no universal topological invariant for characterization. Here, we ...
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 (braiding) operators of anyons by adiabatically varying pairwise...
With braiding simulated numerically as nonequilibrium quench processes, we verify that the MFs in our spin ladder model obey non-Abelian braiding statistics. Our scheme provides a promising platform to study exotic properties of MFs and a broad range of applications in topological quantum computation....
Also, some topological photonic systems are candidates for quantum computing such as non-Abelian anyon statistics [21]. Topological photonic crystals can be also combined to machine learning, for example, training the artificial neural network to get the parameters of topological photonic crystals or ...
Wave functions describing quasiholes and electrons in non-Abelian quantum Hall states are well known to correspond to conformal blocks of certain coset conformal field theories. In this paper we explicitly analyse the algebraic structure underlying the braiding properties of these conformal blocks. We ...
Non-Abelian braiding is regarded as an essential process for realizing quantum logic. Its realizations in quantum systems often rely on the dynamic winding of anyons, which can be challenging to obtain. Implementing braiding in a classical system could, therefore, assist the experimental study of ...
It has been proposed that anyons could be used to encode and manipulate information in a topologically protected manner that is immune to local noise, with quantum gates performed by braiding and fusing anyons. Unfortunately, realizing non-Abelian topologically ordered states is challenging, and it ...
Here we briefly review the relevant properties of nonabelian quantum Hall states and discuss some of the methods we have found for finding specific braiding patterns which can be used to carry out universal quantum computation using them. Recent work on one-dimensional chains of interacting ...