  In experimental control of quantum systems, the precision is often hindered
by imperfect applied electronics that distort control pulses delivered to
target quantum devices. To mitigate such error, the deconvolution method is
commonly used for compensating the distortion via an identified convolutional
model. However, its effectiveness is limited by model inaccuracies (e.g.,
imprecise parameters or unmodeled distortion dynamics). In this paper, we
propose a learning-based scheme to eliminate the residual calibration error by
repeatedly applying the deconvolution operations. The resulting iterative
deconvolution method is shown to be able to correct both linear and nonlinear
model errors to the highest precision allowed by available finite sampling
rates. The calibration error induced by finite sampling rates is also analyzed,
from which we propose that the inter-sampling error can be suppressed by
actively introducing nonlinear components in the control electronics.
