中文摘要：

针对3-puzzle问题，运用量子计算方法分析了节点扩展的酉变换矩阵。对一个3-puzzle问题实例进行了元素编码和节点状态编码，描述了具体的节点扩展酉变换矩阵，并运用量子受控非门逻辑线路实现了酉变换矩阵。讨论了N-puzzle量子计算的线路模型，对量子位的基态和最佳基态的制备作了分析，阐述了N-puzzle启发式搜索量子计算框架。

英文摘要：

The unitary transformation matrices of nodes expansion are analyzed by using quantum com- puting 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 uni- tary 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.