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
26: (1) create an anyon pair; (2) verify the rules that govern the ‘collision’ of two anyons, known as the fusion rules; (3) verify the non-Abelian braiding statistics reflected in the matrix structureR2and (4) realize controlled entanglement...
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 that can also physically emerge as a geometric-...
doi:10.1103/PhysRevB.88.180402He, Yin-ChenChen, YanPhysical Review BYin-Chen He and Yan Chen, Measuring fermions qubit state and non-Abelian braiding statistics in quenched inhomogeneous spin ladders, arXiv: 1210.5139 (2013).
We analyze a system composed by four anyons whose couplings define a T junction, and we show that the braiding operator of two of them can be obtained through a particular adiabatic cycle in the space of the coupling parameters. We also discuss how to couple this scheme with anyonic chains ...
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 Pfaffian state is an attractive candidate for the observed quantized Hall plateau at a Landau-level filling fraction nu=5/2. This is particularly intriguing because this state has unusual topological properties, including quasiparticle excitations with non-Abelian braiding statistics. In order to de...
{it non-Abelian braiding statistics}. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations which are necessary for quantum computation are carried out by braiding quasiparticles, and then measuring the multi-quasiparticle ...
In this talk, I will reveal how we demonstrate MZM non-Abelian statistics through fusion and braiding in planar Josephson Junctions (JJs) with gate, phase, or magnetic texture control [1-4]. Our proposals to identify non-Abelian statistics are supported by dynamical simulations and experimental ...
In non-Abelian semimetals, the topological charges of band nodes are converted through the braiding of nodes in adjacent gaps, and their behaviour cannot be captured by conventional topological band theory. By controlling the geometry of the acoustic metamaterials, topological transitions are induced ...