耦合强度对量子绝热算法求解最大割的影响

本文分析基于量子绝热近似的不同顶点的最大割问题求解.该算法将无向图的顶点等效为量子比特,各个顶点间的边等效为两个量子比特之间的耦合,边的权重值等效为量子比特间的耦合强度.采用Python语言编写算法程序,模拟了6–13个顶点的完全无向图的最大割问题求解情况.实验结果表明,当完全无向图顶点个数取为8,12,13,同时耦合...

Influence of Coupling Strength on Quantum Adiabatic Algorithm for Solving Max-Cut

This study analyzes the solution to the max-cut problem of different vertices according to quantum adiabatic approximation.In this algorithm,the vertices of an undirected graph are equivalent to qubits,the edge between vertices to the coupling between two qubits,and the weight value of an edge to the coupling strength.The algorithm is written in the Python programming language,and the solution to the max-cut problem of a completely undirected graph with 6–13 vertices is simulated.Experimental results demonstrate that when the completely undirected graph has 8,12,and 13 vertices and coupling strength is 1.0,the expected value of Hamiltonian in the max-cut problem does not converge.Then the coupling strength between qubits is adjusted to observe the changes in the expected value.Experiments reveal that for a completely undirected graph with 12 vertices,the expected value converges when coupling strength is 0.95.For completely undirected graphs with 8 and 13 vertices,it converges with time when coupling strength is 0.75.Accordingly,it is inferred that the coupling strength between qubits can be normalized to about 0.75 when the quantum adiabatic algorithm is used to solve the max-cut problem for a completely undirected graph with more than 13 vertices,so that the expected value can eventually converge.