CZ conditional-phase calibration

Control-qubit response to a final analysis phase, swept alongside the coupler pulse amplitude that sets a CZ gate’s conditional phase – the calibration that follows locating the |1,1>-|0,2> avoided crossing itself (CZ gate calibration: the 11-02 avoided crossing chevron). With the target qubit prepared in |1>, the control qubit picks up a phase phi(A) set by the coupler pulse amplitude A; scanning the final pi/2 pulse’s analysis phase traces out that value directly, as the phase offset of the resulting fringe. The conditional phase grows smoothly with amplitude, so a tilted fringe pattern is the raw signature of a calibration that is working – the operating amplitude is simply wherever that tilt crosses phi = pi, read straight off the map rather than fitted from a stack of separate 1-D traces.

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import numpy as np
import polars as pl
import plotpress

A_CZ = 0.62                  # coupler pulse amplitude (a.u.) giving phi = pi
PHASE_SLOPE = 5.4              # radians of conditional phase per unit amplitude
CONTRAST = 0.85
rng = np.random.default_rng(414)

amplitude = np.linspace(0.30, 0.90, 320)      # coupler pulse amplitude, a.u.
phase = np.linspace(0.0, 4.0 * np.pi, 300)     # analysis phase, radians
A, PHI = np.meshgrid(amplitude, phase)

conditional_phase = PHASE_SLOPE * (A - A_CZ) + np.pi
p_excited = 0.5 + 0.5 * CONTRAST * np.cos(PHI - conditional_phase)
p_excited += rng.normal(0.0, 0.015, p_excited.shape)

# One row per swept (amplitude, phase) shot -- sorted before the reshape
# below so the pivot back to a grid is correct regardless of row order.
sweep = pl.DataFrame({
    "amplitude": A.ravel(),
    "phase_rad": PHI.ravel(),
    "p_excited": p_excited.ravel(),
}).sort(["phase_rad", "amplitude"])

amplitude_axis = sweep["amplitude"].unique().sort().to_numpy()
phase_axis = sweep["phase_rad"].unique().sort().to_numpy()
p_excited = sweep["p_excited"].to_numpy().reshape(phase_axis.size, amplitude_axis.size)

fig, ax = plotpress.subplots(figsize=(7.6, 5.4))
mesh = ax.pcolormesh(amplitude_axis, phase_axis, p_excited, cmap="viridis", vmin=0.0, vmax=1.0)
bar = fig.colorbar(mesh, ax=ax)
bar.set_title("P(e)")
ax.axvline(A_CZ, color="white", linestyle=":", linewidth=1.0)
ax.set_xlabel("coupler pulse amplitude (a.u.)")
ax.set_ylabel("analysis phase (rad)")
ax.set_title("Conditional phase reaches pi where the fringe tilt crosses the dotted line")
fig.tight_layout()