Year: 2025
Type: conference-paper
Abstract: We present a quantum algorithm for sampling random spanning trees from a weighted graph in Õ(√{mn}) time, where n and m denote the number of vertices and edges, respectively. Our algorithm has sublinear runtime for dense graphs and achieves a quantum speedup over the best-known classical algorithm, which runs in Õ(m) time. The approach carefully combines, on one hand, a classical method based on "large-step" random walks for reduced mixing time and, on the other hand, quantum algorithmic techniques, including quantum graph sparsification and a sampling-without-replacement variant of Hamoudi’s multiple-state preparation. We also establish a matching lower bound, proving the optimality of our algorithm up to polylogarithmic factors. These results highlight the potential of quantum computing in accelerating fundamental graph sampling problems.
Source: HAL
Authors: Apers, Simon, Gao, Minbo, Ji, Zhengfeng, Liu, Chenghua
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: Etude de la pile quantique : Algorithmes, modèles de calcul et simulation pour l’informatique quantique, G2838674790, G2896165731, Initiative Nationale Hybride HPC Quantique – R&D et Support des communautés, G5528670684, Quantum algorithms for optimization, Quantum algorithms for modern optimization and sampling
OpenAlex ID: W7109963305