关键词: 量子力学, 量子潮流计算, 变分量子线性求解器, 牛顿-拉夫逊法

Abstract: This paper proposes a hybrid quantum-classical Newton's method for solving the power flow problem in electrical power systems.The method combines Newton's method with subspace variational quantum algorithm, and employs a high-precision iterative process to reduce the impact of quantum noise on the accuracy of computational solutions. When using gradient descent algorithm to solve problems, the method replaces differential gradients by finite-difference gradients, avoiding the use of depth uncontrollable quantum circuits. In addition, by introducing a random hypothesis parameter strategy and a dynamic learning rate strategy, the risk of the algorithm getting trapped in local optimal extrema is reduced, and the ability to escape from local optimal extrema is enhanced. Experimental results show that this method can flexibly utilize limited quantum bit resources to efficiently solve high-dimensional power flow problems, and has good fault tolerance and high-precision advantages. Furthermore, a comparison between the results from real quantum hardware experiments and from noise-free virtual machines indicates that the presence of quantum noise will lead to the additional resource consumption of the algorithm.

Key words: quantum mechanics, quantum power flow calculation, variational quantum linear algorithm, Newton-Raphson method