Quantum algorithm for minimum dominating set problem with circuit design

Using quantum algorithms to solve various problems has attracted widespread attention with the development of quantum computing.Researchers are particularly interested in using the acceleration properties of quantum algorithms to solve NP-complete problems.This paper focuses on the well-known NP-complete problem of finding the minimum dominating set in undirected graphs.To expedite the search process,a quantum algorithm employing Grover’s search is proposed.However,a challenge arises from the unknown number of solutions for the minimum dominating set,rendering direct usage of original Grover’s search impossible.Thus,a swap test method is introduced to ascertain the number of iterations required.The oracle,diffusion operators,and swap test are designed with achievable quantum gates.The query complexity is O(1.414^(n))and the space complexity is O(n).To validate the proposed approach,qiskit software package is employed to simulate the quantum circuit,yielding the anticipated results.

量子计算加速的解法器算法及应用综述

量子计算作为一种基于量子力学原理的全新计算模型,具有强大的并行性和潜在的颠覆性影响力,为解决复杂问题提供了新的思路。本文的主要目标是对量子计算在大规模科学与工程计算领域中数值计算问题的解法器算法和应用进行综述。重点介绍量子计算在线性方程组、特征值问题、微分方程、哈密顿量与图计算、量子机器学习、量子解法器平台以及实际数值模拟等领域的具体应用。针对不同的数值计算问题,详细讨论当前主流的量子计算算法,并总结近年来国内外相关算法的研究进展。最后,对量子计算在数值计算求解相关研究方向的未来发展趋势进行展望。