Verified measurement-based quantum computing with hypergraph states

Understand

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.