Symmetry, average-Hamiltonian cancellation, and Rabi-drive suppression in a Figure-8–driven transmon: theory and follow-up experiments on a second device

We previously reported amplitude–phase coupling (APC) in a strongly driven superconductingqubit on Rigetti Ankaa-3, quantified by the phase-contrast ratio R(A) = CF8(A)/CRect(A)between a self-intersecting Figure-8 trajectory and a rectangular reference pulse. Here wedevelop a symmetry-based theoretical framework and report a complementary follow-upcampaign on a second platform, Rigetti Cepheus-1-108Q, to test the predictions on a differentdevice. The theoretical analysis establishes that, in the rotating frame on resonanceand starting from the ground state, a constant-phase rectangular drive cannot produce anyphase-dependent population response in the three-level Duffing model. The Figure-8 waveformbreaks this symmetry intrinsically through its 2:1 Fourier content, and a third-orderresonance ω+ω−2ω = 0 mediated by anharmonic coupling to |2⟩ generates a phase contrastpredicted to scale as CF8 ∝ A6N2 in the weak-drive regime. Direct numerical propagationof the 50-loop pulse train confirms this scaling with a fitted log-log slope of 5.97 ± 0.02across N ∈ {1, 5, 10, 25, 50} and a loop-number ratio CF8(N=50)/CF8(N=1) ≈ 2434 (predictedN2 = 2500). The Cepheus follow-up dataset (96+72 executables under bare-circuitprotocol matching the Ankaa-3 main paper, 12 phase points, 500 shots/point) does notdirectly resolve the predicted A6 scaling because the predicted CF8 values across the accessibleamplitude range Ahw ∈ {0.01, 0.03, 0.05, 0.08} remain at or below the binomialshot-noise floor σ ∼ 0.022. A separate and stronger qualitative signature is, however, observed:the phase-averaged survival probability ⟨P(|0⟩)⟩ϕ remains pinned near 0.985 for theFigure-8 waveform across all eight (A,N) conditions tested, while the Rectangular referenceproduces strong amplitude-dependent and N-dependent Rabi-like oscillations sweeping⟨P(|0⟩)⟩ϕ across the full range 0.24–0.93. We interpret this as the experimental fingerprintof the average-Hamiltonian cancellation ¯H (1)F8 = 0 that lies upstream of the predicted A6N2scaling, and which is observable on real hardware at much smaller drive strengths than theunderlying A6 contrast itself.