  We extend quantum noise spectroscopy (QNS) of amplitude control noise to
settings where dephasing noise or detuning errors make significant
contributions to qubit dynamics. Previous approaches to characterize amplitude
noise are limited by their vulnerability to low-frequency dephasing noise and
static detuning errors, which can overwhelm the target control noise signal and
introduce bias into estimates of the amplitude noise spectrum. To overcome this
problem, we leverage optimal control to identify a family of amplitude control
waveforms that optimally suppress low-frequency dephasing noise and detuning
errors, while maintaining the spectral concentration in the amplitude filter
essential for spectral estimation. The waveforms found via numerical
optimization have surprisingly simple analytic forms, consisting of oscillating
sine waves obeying particular amplitude and frequency constraints. In
numerically simulated QNS experiments, these waveforms demonstrate superior
robustness, enabling accurate estimation of the amplitude noise spectrum in
regimes where existing approaches are biased by low-frequency dephasing noise
and detuning errors.
