Three-qubit CCZ hypergraph state referencing arXiv:2607.27094

Primitive: three-qubit hypergraph state via a controlled-controlled-Z (CCZ) gate.

This card is inspired by and references arXiv:2607.27094, "Native CCZ Gate with Fluxonium Qubits and a Microwave-Driven Coupler." As stated in the paper's abstract, the authors experimentally realize a 65-ns native controlled-controlled-phase operation, locally equivalent to the Toffoli gate, with a reported fidelity of 99.39(5)% in a three-qubit processor unit based on fluxonium qubits coupled via a microwave-driven transmon coupler. The abstract further notes that realizing the same operation through a conventional decomposition would require CZ fidelities of approximately 99.94%, that the gate is implemented with a single control pulse relying on a simple calibration procedure, and that the processor unit extends naturally to scalable two-dimensional layouts with low parasitic interactions.

The attached circuit is a small, textbook-class construction that exercises the same CCZ primitive the paper studies. It prepares each of three qubits in the |+> state and then applies a CCZ — expressed within the allowed gate set as a Hadamard-conjugated Toffoli (ccx) — yielding the canonical three-qubit hypergraph state on the single hyperedge {0,1,2}: the state that differs from a uniform superposition of all eight computational-basis strings only by a sign on the |111> amplitude.

Important: this is a deterministic run on the Provenova simulator, not a reproduction of the paper's experimental hardware results. No fidelity, calibration, or device-level claim from the paper is reproduced or verified here, and nothing in this card implies endorsement by the paper's authors. The card simply lets you inspect and re-run a faithful small circuit for the CCZ-based hypergraph-state primitive that the referenced work realizes natively in hardware.