Topological superconductor from superconducting topological surface states and fault-tolerant quantum computing

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.