Abstract: Based on the physical model of two qubit NMR quantum processor，using the spin-1/2 algebra theory proposed by Raedt group，according to the definition of quantum controlled not gate and principle of Grover quantum algorithm，the design process of four different pulse sequences of quantum controlled not gate and two different pulse sequences of two qubit Grover quantum algorithm are introduced. The time-dependent Schrdinger equation is numerically calculated for simulating quantum controlled not gate and two-qubit Grover quantum algorithm， which is equivalent to executing quantum controlled not gate and two-qubit Grover quantum algorithm operations， we demonstrate and analyze the quantum programming problem of quantum controlled not gate and two-qubit Grover quantum algorithm nuclear magnetic resonance pulse sequence design.

Key words: quantum programming problem, quantum algorithm, NMR pulse sequence, numerical computation