Three-qubit CCZ hypergraph state, referencing arXiv:2607.21288

This card prepares the three-qubit CCZ hypergraph state, the primitive at the center of the referenced paper. It is a deterministic state-vector simulation run on Provenova and is not a reproduction of any experimental or device-independent result from the paper.

What the abstract states. The referenced work by Han, Kuang, Bu, and Wang describes the three-qubit CCZ state as "the smallest rank-three hypergraph state and an elementary entangled magic resource," whose cubic phase is governed by generalized stabilizers that are not Pauli strings. The authors report that twenty correlators drawn from five of the eight global input triples in a tripartite two-input, two-output scenario determine the state and the action of the Pauli X/Z measurements up to local isometries, and that the proof recovers the minus sign of the 111 amplitude. They further construct an explicit Bell inequality whose maximal quantum violation self-tests the state, proved via a sum-of-squares decomposition. These are claims from the abstract; nothing here reproduces or endorses them.

The circuit we run. The CCZ hypergraph state is CCZ|+++⟩. We prepare |+⟩ on qubits 0 and 1, apply a Toffoli (CCX) targeting qubit 2, and finish with a Hadamard on qubit 2. This realizes the standard identity CCZ = H₂·CCX·H₂ composed with |+⟩ preparation: the pre-Toffoli Hadamard on the target merges with the state-preparation Hadamard to the identity, leaving the four gates shown.

What our run shows. In exact simulation the output is an equal superposition over all eight computational basis states with a single relative minus sign on |111⟩ — the cubic phase that distinguishes a hypergraph state from an ordinary graph state. Sampling this state in the computational basis yields a near-uniform distribution over the eight outcomes, since the CCZ phase is not visible without a basis change. This card is inspired by and references the arXiv preprint linked above; it does not imply endorsement by its authors.