  We propose a platform for braiding Majorana non-Abelian anyons based on a
heterostructure between a $d$-wave high-$T_c$ superconductor and a quantum
spin-Hall insulator. It has been recently shown that such a setup for a quantum
spin-Hall insulator leads to a pair of Majorana zero modes at each corner of
the sample, and thus can be regarded as a higher-order topological
superconductor. We show that upon applying a Zeeman field in the region, these
Majorana modes split in space and can be manipulated for braiding processes by
tuning the field and pairing phase. We show that such a setup can achieve full
braiding, exchanging, and arbitrary phase gates (including the $\pi/8$ magic
gates) of the Majorana zero modes, all of which are robust and protected by
symmetries. As many of the ingredients of our proposed platform have been
realized in recent experiments, our results provide a new route toward
universal topological quantum computation.
