Certifying bipartite entanglement on a superconducting processor from a corrected QAOA cost layer

RESUMO

The Quantum Approximate Optimisation Algorithm is the canonical near-term heuristic, yet on real superconducting hardware its behaviour is set by device physics, not by the algorithm. Hardware demonstrations rarely prove the intended coupling is realised, that genuine entanglement is prepared, or what controls it. We report a pre-registered single-device study on the nine-qubit superconducting processor Red at the Barcelona Supercomputing Center, using its five-qubit component. Across six calibrations we certify bipartite entanglement of a corrected QAOA cost layer on the good coupler at depth one by two-qubit tomographic negativity: 0.077, BCa 95% CI [0.065, 0.091], excluding zero every day, while the coupling-off twin stays separable and the degraded coupler equals zero. We then measure the device physics directly: in a pre-registered manipulation on a fixed Bell preparation (not the QAOA layer), reducing the CZ pulse amplitude causally reduces the certified negativity along a positive, well-fit slope (R^2 = 0.83-0.96), every rung-level interval excluding zero and surviving Holm and Benjamini-Hochberg correction. This is a local linearisation of a peaked response, not a global monotone law: the negativity peaks at conditional phase |zeta| = pi, which the nominal amplitude overshoots. The J=0 twin is a separate off-state control and the fringe visibility is constant, so the effect is coherent. The average gate fidelity is non-monotone in the drive and is reported only as a diagnostic. A per-circuit statevector guardrail excludes a diagonal compilation fault we disclose and repair. A randomized-measurement witness is consistent with entanglement but underpowered. The certificate collapses by depth three, and a pre-registered sixteen-instance depth-three ensemble shows no optimisation signal (one-sided Wilcoxon p = 0.15). We claim no advantage; the instances are classically trivial.