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Quantum Speedup for Sampling Random Spanning Trees

Year: 2025

Type: preprint

Abstract: We present a quantum algorithm for sampling random spanning trees from a weighted graph in $\widetilde{O}(\sqrt{mn})$ 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 $\widetilde{O}(m)$ 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: arXiv (Cornell University)

Authors: Apers, Simon, Gao, Minbo, Ji, Zhengfeng, Liu, Chenghua

Institutions: Centre National de la Recherche Scientifique, Université Paris Cité, Institut de Recherche en Informatique Fondamentale, Chinese Academy of Sciences, Institute of Software, University of Chinese Academy of Sciences, Tsinghua University

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, National Natural Science Foundation of China, QuantERA, National Key Research and Development Program of China

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 modern optimization and sampling

OpenAlex ID: W6979329447

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