量子近似优化算法在约束优化问题中的应用

Application of Quantum Approximate Optimization Algorithm to Constrained Optimization Problems

结合量子近似优化算法求解约束优化问题是当前的研究热点之一,针对约束优化问题,提出了一种在量子近似优化算法框架中的改进方法;此方法融合了二次无约束二元优化和量子交替拟设这两种方法,同时将在目标算符中添加惩罚项,将不符合解的期望值降低和通过对问题进行求解得出问题的可行解,将混合操作限定在可行解空间内融合在一起;优点在于在求解约束优化问题时,能减小迭代次数,快速并准确地得到问题的最优解;以最小顶点覆盖问题为例,将提出的方法与几种已有的方法做比较,得出方法能减小量子近似优化算法的迭代次数,使得能够高质量和高效率的求解约束优化问题。

Combining quantum approximate optimization algorithm to solve the constrained optimization problem is one of the current research hotspots.In order to solve the constrained optimization problem,an improved method is proposed in the framework of the quantum approximate optimization algorithm.This method combines the quadratic unconstrained binary optimization method and the quantum alternate ansatz method,adds penalty term to the target operator,reduces the expected value of nonconforming solution and obtains feasible solution by solving the problem,and limits the mixing operation to the feasible solution space and fuses together.The advantage of this method is that it can reduce the number of iterations and get the optimal solution quickly and accurately when solving constrained optimization problems.Taking the minimum vertex coverage problem as an example,the proposed method is compared with several existing methods,and it is concluded that the proposed method can reduce the number of iterations of the quantum approximate optimization algorithm,so that the constrained optimization problem can be solved with high quality and high efficiency.