  We numerically demonstrate that the topological corner states residing in the
corners of higher-order topological insulator possess non-Abelian braiding
properties. Such topological corner states are Dirac fermionic modes other than
Majorana zero-modes. We claim that Dirac fermionic modes protected by
nontrivial topology also support non-Abelian braiding. An analytical
description on such non-Abelian braiding is conducted based on the
vortex-induced Dirac-type fermionic modes. The braiding operator for Dirac
fermionic modes is also analytically derivated and compared with the Majorana
zero-modes. Experimentally, such non-Abelian braiding operation on Dirac
fermionic modes is proposed to be testified through topological electric
circuit.
