All you have to do is to define what gate would correspond to each arity hyperedge, if it's just Z, CZ, CZZ, etc., then something like this works (assuming a simple hypergraph with only unique vertices in every hyperedge):
QuantumCircuitOperator[
Switch[Length[#],
0,Nothing,
1,QuantumOperator["1"]->#,
_,{"C",QuantumOperator["1"]->First[#],Rest[#]}
]&/@DeleteDuplicates/@ResourceFunction["RandomHypergraph"][{10,{{3,1},{5,2},{4,3}}}]
]
N.B. In WQF operator "1" is the same as Z, and "0" is -Z
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