This paper concerns the theoretical model of quantum computing and the it's implementation by nuclear magnetic resonance(NMR). In the NMR quantum computing, one can get an effective pure state from the statistical mixture of a spin system by appropriate preparation process and use it as a pure input state of the computation.
I show that such a preparation process is not necessary for some special cases. Also I build up the pulse sequences for the evaluations of the two-bit binary functions which are needed in the refined Deutsch's algorithm. I implement the two-bit homo-nuclear NMR quantum computer for two-bit refined Deutsch's algorithm without usual preparation process. This work is the first implementation of the refined Deutsch's algorithm and the experimental aspects are much simpler than that of previous NMR quantum computing experiments.