HodgeRank generalizes ranking algorithms, such as Google’s 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.

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• Complex systems
• Dynamics of networks
• Network structure
• Quantum algorithms & computation
• Topological tools
• Real world networks
• Many-body techniques
• Networks Analysis Tools