Hypergraph states are generalizations of graph states where controlled-$Z$
gates on edges are replaced with generalized controlled-$Z$ gates on
hyperedges. Hypergraph states have several advantages over graph states. For
example, certain hypergraph states, such as the Union Jack states, are
universal resource states for measurement-based quantum computing with only
Pauli measurements, while graph state measurement-based quantum computing needs
non-Clifford basis measurements. Furthermore, it is impossible to classically
efficiently sample measurement results on hypergraph states with a constant
$L$1-norm error unless the polynomial hierarchy collapses to the third level.
Although several protocols have been proposed to verify graph states with only
sequential single-qubit Pauli measurements, there was no verification method
for hypergraph states. In this paper, we propose a method for verifying
hypergraph states with only sequential single-qubit Pauli measurements. As
applications, we consider verified blind quantum computing with hypergraph
states, and quantum supremacy demonstrations with hypergraph states.