Ultra-cold atomic gases have many important potential applications ranging from emulation of condensed matter physics to building a quantum computer. In this talk, I will discuss topological quantum states and the architecture of topological quantum computation (TQC) using a p-wave fermionic cold atom system. TQC proposes to use the topologically robust braiding statistics of a p-wave superfluid to perform quantum computation. I will give a general introduction to p-wave cold atom physics, the relevant topological properties, and discuss the physics behind TQC using the p-wave fermionic cold atoms.