Abstract: An adaptive quantum genetic algorithm based on Bloch sphere is proposed based on the quantum genetic algorithm which is based on Bloch coordinates of qubits. The algorithm uses two ways to select a part of the Bloch sphere for searching：along the warp direction and weft direction. The paper proves that the two methods are able to contain all the solutions of the continuous optimization problem in theory, and proposes a method of approximately equal-area to search the selected Bloch sphere, and derives the inverse relationship between the two-phase. The chromosomes mutation is modified to meet the restrictions of selected region. The simulation results show that the approach is equal to quantum genetic algorithm based on Bloch coordinates of qubits in search capability, but the optimization efficiency is significantly improved.

Key words: quantum computation, quantum genetic algorithm, Bloch coordinates, optimization problem

摘要： 在基于量子位Bloch坐标的量子遗传算法的基础上，提出一种自适应Bloch球面的量子遗传算法。该算法按两种方式自适应地选取Bloch球面的一部分进行搜索：沿经线方向选取和沿纬线方向选取，并在理论上证明了这两种选取方式都能够包含所求连续优化问题的所有可行解。在对选取的Bloch球面进行搜索时，提出了近似等面积搜索的方法，进而推导出两个相位转角大小之间的反比例关系，染色体的变异操作也作了相应的修改以适应选取区域的限制。实验表明该算法在搜索能力方面与基于量子位Bloch坐标的量子遗传算法基本相当，但优化效率方面有明显提高。

关键词: 量子计算, 量子遗传算法, Bloch球面坐标, 优化问题