  The chiral $p$-wave superconductor/superfluid in two dimensions (2D) is the
simplest and most robust system for topological quantum computation .
Candidates for such topological superconductors/superfluids in nature are very
rare. A widely believed chiral $p$-wave superfluid is the Moore-Read state in
the $\nu=\frac{5}2$ fractional quantum Hall effect, although experimental
evidence are not yet conclusive. Experimental realizations of chiral $p$-wave
superconductors using quantum anomalous Hall insulator-superconductor hybrid
structures have been controversial. Here we report a new mechanism for
realizing 2D chiral $p$-wave superconductors on the surface of 3D $s$-wave
superconductors that have a topological band structure and support
superconducting topological surface states (SC-TSS), such as the iron-based
superconductor Fe(Te,Se). We find that tunneling and pairing between the SC-TSS
on the top and bottom surfaces in a thin film or between two opposing surfaces
of two such superconductors can produce an emergent 2D time-reversal symmetry
breaking chiral topological superconductor. The topologically protected anyonic
vortices with Majorana zero modes as well as the chiral Majorana fermion edge
modes can be used as a platform for more advantageous non-abelian braiding
operations. We propose a novel device for the CNOT gate with six chiral
Majorana fermion edge modes, which paves the way for fault-tolerant universal
quantum computing.
