  Majorana fermions feature non-Abelian exchange statistics and promise
fascinating applications in topological quantum computation. Recently,
second-order topological superconductors (SOTSs) have been proposed to host
Majorana fermions as localized quasiparticles with zero excitation energy,
pointing out a new avenue to facilitate topological quantum computation. We
provide a minimal model for SOTSs and systematically analyze the features of
Majorana zero modes with analytical and numerical methods. We further construct
the fundamental fusion principles of zero modes stemming from a single or
multiple SOTS islands. Finally, we propose concrete schemes in different setups
formed by SOTSs, enabling us to exchange and fuse the zero modes for
non-Abelian braiding and holonomic quantum gate operations.
