Two-qubit Grover search (N=4, single iteration) referencing arXiv:2607.24658

Primitive: Grover's search (2-qubit, single-iteration). This card builds the textbook Grover circuit on a 4-element search space (N=4). Two Hadamards prepare the uniform superposition; a controlled-Z acts as the oracle that phase-flips the marked basis state |11⟩; and a Hadamard–X–CZ–X–Hadamard block implements the Grover diffusion (inversion about the mean). For N=4 with a single marked item, one Grover iteration is the canonical exact case, and in the ideal noiseless setting the amplitude concentrates on the marked state.

About the referenced paper. This circuit is inspired by and references “Exact and Fixed-Point Grover Search with Qudits” (Tanay Roy, arXiv:2607.24658). Per its abstract, the paper presents a unified framework for qudit-based Grover search—constructing oracles and diffusion operators with and without ancillas, generalizing deterministic (exact) and fixed-point variants that guarantee exact or bounded success probabilities, analyzing phase-matching techniques, giving explicit circuit decompositions for diverse hardware, and comparing Bloch-sphere trajectories to visualize how phase choices amplify the target. The abstract frames this as a hardware-oriented toolkit for multilevel systems, potentially reducing circuit depth.

What this run is—and is not. The circuit above is a plain qubit Grover on N=4, not the paper's qudit construction, and this is a deterministic simulator run on Provenova, not a reproduction of any experiment or hardware result from the paper. The measured shot distribution below comes solely from our simulator and reflects only this small qubit circuit. Nothing here implies validation, endorsement, or involvement by the author. We link the arXiv abstract so readers can consult the primary source; the exact and fixed-point qudit variants it describes are the paper's contribution, not ours.