Simultaneous calibration of rotation and phase errors in a single experiment

In weakly anharmonic qubits, coherent control errors take two generic forms -- over/under-rotation and phase errors -- whose suppression normally requires iterated experiments. We show that, for any symmetric $\pi/2$ pulse in the weak-driving regime, both follow from a single parametrization, $\mathcal{X}(\pi/2)=Z(\delta)X(\pi/2+\epsilon)Z(\delta)$, that ties the rotation error $\epsilon$ and the phase error $\delta$ directly to the system parameters. The parametrization enables DRAPE, a Ramsey-type protocol in which sweeping the phase-error correction reveals a crossing point that fixes both corrections at once. The phase correction is estimated with Heisenberg scaling while the rotation error saturates the standard quantum limit. We experimentally demonstrate DRAPE by calibrating a $\pi/2$ gate on the $|1\rangle\leftrightarrow |2\rangle$ transition of an IBM transmon, reducing the over-rotation from $0.997^\circ$ to $-0.007^\circ$ and the phase error from $2.52^\circ$ to $0.0052^\circ$ per gate, validated independently by phase- and rotation-error amplification protocols.