The rigorous solutions of Bloch and Schr?dinger equations for spin-1/2 particle under the rotating magnetic field are obtained. The exact expressions of AA geometric and dynamic phases have been obtained. Using an orthogonal method,non-adiabatic geometric quantum gates are obtained with all advantages of holonomic geometric quantum gates. Based on the cyclic condition of general evolution,the universal topological gates are constructed only by the winding number and knot number. Finally,we propose with asymmetric Josephson junction nano-circuit(JJNC)experiment to implement all topological quantum gates.