Native 2D pairwise hardware-efficient ansatz on a 4-qubit 2x2 grid, referencing arXiv:2607.12996

Primitive: hardware-efficient parameterized quantum circuit (PQC) ansatz with a native 2D pairwise entanglement pattern.

About the referenced work (as stated in its abstract): The authors note that PQCs are a central building block of variational quantum algorithms and quantum machine learning, and that existing ansatz designs often adopt hardware-agnostic or simplified 1D chain/ring entanglement patterns. Motivated by native 2D connectivity in planar superconducting-qubit architectures, they construct a native 2D pairwise ansatz and compare its expressibility and trainability against representative 1D ansatze at identical layer depths. For a fixed 16-qubit system, the abstract reports that the 2D ansatz has the smallest KL divergence at layer counts L=1 and L=2 and that its second-order frame potential approaches the theoretical lower bound more rapidly at shallow depth; it also examines the gradient variance of a Pauli-Z-string expectation value, with the differences narrowing at larger L.

What this card shows: a deterministic simulator instantiation of a small, textbook-style 2D pairwise ansatz on a 4-qubit 2x2 grid: three layers of single-qubit Ry rotations at fixed illustrative angles, interleaved with pairwise CZ entanglers along the horizontal pairs (0,1),(2,3) and vertical pairs (0,2),(1,3). This is a deterministic run on the Provenova simulator, not a reproduction of the paper's numerical experiments, and it uses a single fixed parameter setting rather than any trained or optimized values. It is inspired by, and references, the cited paper; it does not reproduce that paper's results and implies no endorsement by its authors.