Note (September 2026): This preprint is superseded by a new manuscript and dataset (doi:10.5281/zenodo.22803589); several of its claims are withdrawn there. [Update note, April 2026]A more comprehensive version of this work, with substantially increasedstatistics (12 phase points, 1000 shots/point, additional supplementaryexperiments including isenergetic and gap-insertion tests), has beenposted: "Phase-Resolved Observation of Amplitude-Phase Coupling in aStrongly Driven Superconducting Qubit" (DOI: [10.5281/zenodo.19816115]). The Berryconnection interpretation discussed in the present record has beenrevised in the subsequent work; readers interested in the mechanismanalysis should consult the accompanying mechanism paper(DOI: [10.5281/zenodo.19816695]).[End of update note] We report a differential measurement comparing the phase response of a superconducting transmonqubit under two control trajectories: a closed-loop Figure-8 pulse (non-zero area in the IQcontrol plane) and a constant-amplitude Rectangular pulse (zero area). Measurements were performedat five drive amplitudes on a Rigetti Ankaa-3 processor (qubit #25) via AWS Braket. Threetrajectory-dependent features are observed that are not trivially explained by Kerr nonlinearityalone: (1) progressive divergence of optimal control phase between trajectories, (2) trajectorydependentmodulation visibility with a crossover between low and high amplitudes, and (3) apparentsuppression of phase modulation for the Figure-8 trajectory at amplitude A = 0.8 whilethe Rectangular trajectory retains clear sinusoidal modulation. Observations 1 and 2 are robustand statistically clear. Observation 3 is suggestive but requires further statistical validation withincreased shot counts. These results are interpreted in the context of amplitude-phase coupling(APC) with measured coupling strength κ ≈ 0.9 rad/a u , previously reported in Ref. [1]. We proposefour follow-up experiments—including an isenergetic control test—to discriminate geometriccontributions from dynamic nonlinearities.
We report phase-resolved measurements of amplitude-phase coupling (APC) in strongly driven superconducting transmon qubits, a symmetry-based mechanism analysis, and follow-up experiments on a second device. On a Rigetti Ankaa-3 transmon (1000 shots per point, five drive amplitudes, matched root-mean-square drive), the fitted optimal control phase
ϕ∗(A) drifts by more than 3 rad across the explored amplitude range for both a rectangular reference pulse and a self-intersecting Figure-8 trajectory, and the phase contrast of the two waveform families exhibits a reproducible low-/high-amplitude crossover. Theoretically, we prove that in the resonant rotating frame of the three-level Duffing model a constant-phase rectangular drive cannot produce any phase-dependent population response:
CRect=0 exactly. Any measured rectangular phase contrast is therefore a probe of physics outside this model (beyond-rotating-wave carrier-phase dependence, control-chain distortion, readout imperfections). The Figure-8 waveform breaks the symmetry intrinsically through its 2:1 Fourier content; a third-order resonance
ω+ω−2ω=0 mediated by the anharmonic level
∣2⟩ predicts
CF8∝A6N2 at weak drive, confirmed by direct numerical propagation (fitted log-log slope
5.97±0.02; loop-number ratio 2434 vs. predicted 2500). On the successor device Cepheus-1-108Q, the predicted phase contrast lies below the binomial shot-noise floor at the accessible amplitudes, but the same dataset reveals a stronger signature of the underlying first-order average-Hamiltonian cancellation: the phase-averaged survival probability of the Figure-8 train remains pinned at
⟨P(∣0⟩)⟩ϕ≈0.985 across all tested conditions, while the isenergetic rectangular reference sweeps the full range 0.24-0.93—an approximately 70-fold suppression of the Rabi-drive response. Together these results identify APC as a measurable control-landscape feature with distinct intrinsic and extrinsic components, and demonstrate a calibration-free, amplitude-insensitive idling property of Figure-8 pulse trains.
We report phase-resolved measurements revealingamplitude–phase coupling (APC) in a strongly drivensuperconducting qubit. Using 1000 shots per point acrossfive drive amplitudes on a Rigetti Ankaa-3 transmonqubit (Qubit 58; T1 = 36.7 μs, T2 = 22.2 μs), we comparea rectangular reference pulse and a self-intersectingFigure-8 trajectory under matched root-mean-squaredrive amplitude. From harmonic fits to the phasedependentsurvival probability, we extract the optimalcontrol phase ϕ∗(A) and show that it shifts by more than3 rad across the explored amplitude range for both pulsefamilies. To quantify phase sensitivity, we define thephase contrast C(A) = maxϕ ˆ F −minϕ ˆ F and the contrastratio R(A) = CF8/CRect. At low amplitude (A ≤ 0.6),the Figure-8 trajectory reduces phase contrast relativeto the rectangular reference (R = 0.48–0.57), whereas athigh amplitude (A ≥ 0.8) it increases it (R = 1.22–1.45),revealing a crossover in trajectory-dependent phase sensitivity.An independent replication acquired in a separatecalibration session at 100 shots per point preserves thesame low- and high-amplitude sign structure. Additionalpulse-train continuity tests show that internal timinggaps reduce phase contrast without measurably shiftingthe optimal phase, and that a fixed 4 ns gap showsno statistically significant dependence on its placementwithin the train. These observations identify APC as anexperimentally accessible feature of the measured controllandscape and show that fixed-phase calibration canbecome systematically biased across drive amplitudes inthe strongly driven regime.
We present experimental validation of a software-defined geometric noise suppression protocol on a commercial superconducting quantum processor (Rigetti Ankaa-3 via AWS Braket). The protocol combines three elements: (1) time-reversal symmetric Figure-8 control pulses that create closed trajectories in parameter space, (2) node-synchronized stroboscopic readout that gates measurements at loop-closure times, and (3) adaptive phase tracking that compensates for environmental drift. Key experimental results include: break-even threshold exceeded with +10 percentage point improvement over baseline idle; phase-dependent noise suppression achieving +82 percentage point improvement through optimal phase selection; and discovery of amplitude-phase coupling (APC) where optimal phase shifts by ≈ 0.9 rad per unit amplitude change. This coupling, interpretable as an environmentally-induced Berry connection in control parameter space, explains why conventional fixed-parameter calibration fails at varying drive strengths. The adaptive protocol successfully tracks environmental drift, recovering from 13% to 85% fidelity autonomously. These results demonstrate that geometric structure in quantum control can be exploited for robust, hardware-agnostic noise suppression without physical device modification.
We present experimental validation of a software-defined geometric noise suppression protocol on a commercial superconducting quantum processor (Rigetti Ankaa-3 via AWS Braket). The protocol combines three elements: (1) time-reversal symmetric Figure-8 control pulses that create closed trajectories in parameter space, (2) node-synchronized stroboscopic readout that gates measurements at loop-closure times, and (3) adaptive phase tracking that compensates for environmental drift. Key experimental results include: break-even threshold exceeded with +10 percentage point improvement over baseline idle; phase-dependent noise suppression achieving +82 percentage point improvement through optimal phase selection; and discovery of amplitude-phase coupling (APC) where optimal phase shifts by ≈ 0.9 rad per unit amplitude change. This coupling, interpretable as an environmentally-induced Berry connection in control parameter space, explains why conventional fixed-parameter calibration fails at varying drive strengths. The adaptive protocol successfully tracks environmental drift, recovering from 13% to 85% fidelity autonomously. These results demonstrate that geometric structure in quantum control can be exploited for robust, hardware-agnostic noise suppression without physical device modification.