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 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-...
5,24. In other words,R2does not simplify to a scalar, but remains a unitary matrix. Therefore,R2is a fundamental characteristic of anyon braiding. The topological approach to quantum computation26aims to leverage these non-Abelian anyons and their topological nature to enable gate...
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....
R. Akhmerov, Braiding of non-Abelian anyons using pairwise interactions, Phys. Rev. A 87, 022343 (2013), doi:10.1103/PhysRevA.87.022343.M. Burrello, B. van Heck and A. R. Akhmerov, Braiding of non-Abelian anyons using pair- wise interactions, Phys. Rev. A 87, 022343 (2013), ...
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 ...
This is particularly intriguing because this state has unusual topological properties, including quasiparticle excitations with non-Abelian braiding statistics. In order to determine the nature of the nu=5/2 state, one must measure the quasiparticle braiding statistics. Here, we propose an experiment ...
{it Non-Abelian anyons}, meaning that they obey {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 ...
This facilitates non-abelian "braiding" of nodal-line rings inside the momentum space, that has not been previously reported. The geometric arguments presented in the main text are supplemented in the appendices with formal mathematical derivations. 展开 ...
However, despite intensive efforts, experimental evidence for MZM remains indirect and does not probe their crucial non-Abelian statistics. 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...