Phase-Resolved Observation of Amplitude–Phase Coupling in a Strongly Driven Superconducting Qubit

We report phase-resolved measurements revealing
amplitude–phase coupling (APC) in a strongly driven
superconducting qubit. Using 1000 shots per point across
five drive amplitudes on a Rigetti Ankaa-3 transmon
qubit (Qubit 58; T1 = 36.7 μs, T2 = 22.2 μs), we compare
a rectangular reference pulse and a self-intersecting
Figure-8 trajectory under matched root-mean-square
drive amplitude. From harmonic fits to the phasedependent
survival probability, we extract the optimal
control phase ϕ∗(A) and show that it shifts by more than
3 rad across the explored amplitude range for both pulse
families. To quantify phase sensitivity, we define the
phase contrast C(A) = maxϕ ˆ F −minϕ ˆ F and the contrast
ratio R(A) = CF8/CRect. At low amplitude (A ≤ 0.6),
the Figure-8 trajectory reduces phase contrast relative
to the rectangular reference (R = 0.48–0.57), whereas at
high 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 separate
calibration session at 100 shots per point preserves the
same low- and high-amplitude sign structure. Additional
pulse-train continuity tests show that internal timing
gaps reduce phase contrast without measurably shifting
the optimal phase, and that a fixed 4 ns gap shows
no statistically significant dependence on its placement
within the train. Because the comparison is made under
matched root-mean-square drive, the residual waveform
dependence of the phase landscape is not reducible to
a common amplitude-dependent offset alone. These
observations identify APC as an experimentally accessible
feature of the measured control landscape and show that
fixed-phase calibration can become systematically biased
across drive amplitudes in the strongly driven regime.