2020/08/31 by Takumi Sanno, Shunsuke Miyazaki, Takeshi Mizushima +1 · 2 citations
Physics and Astronomy · #cond-mat.supr-con
paper · pdf · doi:10.1103/physrevb.103.054504
published as Phys. Rev. B 103, 054504 (2021)
arxiv created 2021/02/14 · arxiv updated 2021/02/16
We numerically investigate non-Abelian braiding dynamics of vortices in two-dimensional topological superconductors, such as s-wave superconductors with Rashba spin-orbit coupling. Majorana zero modes (MZMs) hosted by the vortices constitute a topological qubit, which offers a fundamental building block of topological quantum computation. As the MZMs are protected by ℤ2 invariant, however, the Majorana qubit and quantum gate operations may be sensitive to intrinsic decoherence caused by quasiparticle interference. Numerically simulating the time-dependent Bogoliubov-de Gennes equation without assuming \it a priori existence of MZMs, we examine quantum noises on the unitary operators of non-abelian braiding dynamics due to interactions with neighboring MZMs and other quasiparticle states. We demonstrate that after the interchange of two vortices, the lowest vortex-bound states accumulate the geometric phase π/2, and errors stemming from dynamical phases are negligibly small, irrespective of interactions of MZMs. Furthermore, we numerically simulate the braiding dynamics of four vortices in two-dimensional topological superconductors, and discuss an optimal braiding condition for realizing the high performance of non-Abelian statistics and quantum gates operations of Majorana-based qubits.