Braiding of Majorana-like corner states in electric circuits and its non-Hermitian generalization

Abstract

Braiding is a key aspect of topological quantum computations. Such a proposal has been made based on Majorana fermions. In this paper, it is shown that the braiding behavior is simulated in electric circuits by constructing Majorana-like corner states. First, we simulate the Kitaev model by an $LC$ electric circuit and the ${p}_{x}+i{p}_{y}$ model by an $LC$ circuit together with operational amplifiers. Zero-energy edge states emerge in the topological phase, which are detectable by measuring impedance. Next, we simulate the Bernevig-Hughes-Zhang model by including an effective magnetic field without breaking the particle-hole symmetry, where zero-energy corner states emerge in the topological phase. It is demonstrated that they are Ising anyons subject to braiding. Namely, we derive ${\ensuremath{\sigma}}^{2}=\ensuremath{-}1$ for them, where $\ensuremath{\sigma}$ denotes the single-exchange operation. We also study non-Hermitian generalizations of these models by requiring particle-hole symmetry. It is shown that braiding holds also in certain reciprocal non-Hermitian generalizations.