Grover's quantum walk on segmented complete graphs

We study Grover's quantum walk on a new class of graphs, termed segmented complete graphs, which combine high symmetry with detailed spectral properties. Using these graphs, we implement Grover's search algorithm and investigate its performance, focussing on the relationship between graph volume, optimal search time and success probabilities. Our results generalize classical findings for directed weighted graphs and provide new insights into enhancing quantum search algorithms on complex graph structures.This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.