On Hypergraph Representation of Multipartite Quantum Systems

Borrowing ideas from the link between Calabi-Yau singularities and toric geometry in string theory compactifications, a hypergraph framework for multipartite quantum systems, extending graph representations to higher-order quantum correlations, is investigated. By implementing hyperedges in many-body Hamiltonian interactions, an interplay between hypergraph states and quantum state dynamics is established. The corresponding Hamiltonian hypergraph reveals the hierarchy of all possible multipartite interactions. However, the decoherence effects impose constraints on the realization of large hypergraph states. The findings show the importance of long coherence times and strong many-body couplings for the realization of large hypergraph states.