RydbergPhaseDepthQA: A Finite-Size Hardware Witness of a Multi-Controlled-Phase Depth-Hierarchy Mechanism on IonQ Forte-1

Abstract

RydbergPhaseDepthQA investigates whether a finite-size witness of the recently established quantum circuit-depth hierarchy mechanism remains experimentally distinguishable after provider compilation and noisy execution on a real quantum processor. The experiment compares a frozen exact (C^7Z) phase-witness circuit with a matched ablation obtained by removing exactly one pre-provider QIS two-qubit layer. The exact circuit has 36 CX gates and two-qubit depth 27, while the ablated circuit has 35 CX gates and depth 26. Hardware execution was performed on IonQ Forte-1 through the Open Quantum platform. An independent confirmatory campaign comprised three exact runs, three matched depth-minus-one runs, and one identity control, with 499 shots per job. The exact implementation achieved a success probability of 0.995992 (95% CI [0.992652, 0.998664]), compared with 0.000668 (95% CI [0, 0.002004]) for the depth-minus-one ablation. The exact-minus-ablation separation was 0.995324, with a 95% lower confidence bound of 0.991316. The identity false-positive probability was 0.002004 (95% CI [0, 0.006012]). All four frozen confirmatory statistical criteria passed, yielding RPDQA_FULL_PASS = True. These results provide a positive finite-size hardware witness of the multi-controlled-phase depth-hierarchy mechanism: for the tested (C^7Z) construction, the experimentally observed separation survives the full path from frozen QIS circuits through provider compilation to noisy QPU execution. The result does not constitute an experimental proof of the complete theoretical (d >= 12) hierarchy, nor does it claim that the final provider-native or pulse-level schedules preserve an exactly one-layer depth difference. The repository includes the frozen circuits, raw hardware results, analysis code, integrity hashes, and reproducibility tools: https://github.com/malikberrada/RydbergPhaseDepthQA