The unitary transformation matrices of nodes expansion are analyzed by using quantum computing method for 3-puzzle problem. Element coding and node state coding are performed on a 3-puzzle problem instance. The specific node expansion unitary transformation matrices are described, and the unitary transformation matrices are realized by using the quantum controlled-NOT gate logic circuits. A logic circuit model of N-puzzle quantum computing is discussed. The preparation of ground state and optimum ground state of quabits is analyzed, and the N-puzzle heuristic search quantum computing framework is discussed.