Quantum HodgeRank: Topology-Based Rank Aggregation on Quantum Computers
Quantum Physics
2025-06-26 v3
Abstract
HodgeRank generalizes ranking algorithms, e.g. Google PageRank, to rank alternatives based on real-world (often incomplete) data using graphs and discrete exterior calculus. It analyzes multipartite interactions on high-dimensional networks with a complexity that scales exponentially with dimension. We develop a quantum algorithm that approximates the HodgeRank solution with complexity independent of dimension. Our algorithm extracts relevant information from the state such as the ranking consistency, which achieves a superpolynomial speedup over similar classical methods.
Cite
@article{arxiv.2407.20452,
title = {Quantum HodgeRank: Topology-Based Rank Aggregation on Quantum Computers},
author = {Caesnan M. G. Leditto and Angus Southwell and Behnam Tonekaboni and Muhammad Usman and Kavan Modi},
journal= {arXiv preprint arXiv:2407.20452},
year = {2025}
}