Quantum HodgeRank: Topology-Based Rank Aggregation on Quantum Computers

TL;DR

This paper introduces a quantum algorithm for HodgeRank that efficiently computes rankings from high-dimensional, incomplete data, achieving superpolynomial speedup over classical methods.

Contribution

It develops a quantum algorithm for HodgeRank that operates independently of data dimension, enabling faster ranking computations on complex networks.

Findings

Quantum algorithm approximates HodgeRank with dimension-independent complexity.

Achieves superpolynomial speedup over classical ranking algorithms.

Effectively extracts ranking consistency information from quantum states.

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.