Non-monotonic Fidelity Phase Diagram of GHZ States from N=2 to N=12 on IBM Quantum Hardware

Overview Systematic experimental characterization of Greenberger-Horne-Zeilinger (GHZ) states from N=2 to N=12 qubits on IBM Quantum's ibm_torino processor (133 qubits, Heron r2 architecture). Key Discovery The fidelity landscape exhibits unexpected non-monotonic behavior — contradicting the conventional expectation of monotonic decay with increasing qubit number. Five Distinct Regions Identified Region N Fidelity Characteristic Peak 3 0.951 Optimal qubit chain Valley 4, 5 ~0.14 Decoherence collapse Recovery 6–8 ~0.69 V-shaped recovery Cliff 9 0.40 Stabilization 10–12 ~0.33 Fidelity floor Principal Results V-shaped recovery: Fidelity increases from F=0.07 (N=5) to F=0.73 (N=6), demonstrating that qubit chain quality dominates over circuit depth Mermin violation: M₃ = 3.65 ± 0.01, exceeding the classical bound by 143 standard deviations Asymmetric decoherence: For N≥9, the |1⟩⊗N component vanishes entirely while |0⟩⊗N maintains ~30% probability Implications This 11-point dataset suggests that "fidelity phase diagrams" could serve as a new tool for quantum processor characterization, complementing existing benchmarks. Reproducibility All IBM Quantum Job IDs are provided for independent verification.