  We describe how the transient behavior of a tuned and matched resonator
circuit and a ringdown suppression pulse may be integrated into an optimal
control theory (OCT) pulse-design algorithm to derive control sequences with
limited ringdown that perform a desired quantum operation in the presence of
resonator distortions of the ideal waveform. Inclusion of ringdown suppression
in numerical pulse optimizations significantly reduces spectrometer deadtime
when using high quality factor (high-Q) resonators, leading to increased
signal-to-noise ratio (SNR) and sensitivity of inductive measurements. To
demonstrate the method, we experimentally measure the free-induction decay of
an inhomogeneously broadened solid-state free radical spin system at high Q.
The measurement is enabled by using a numerically optimized bandwidth-limited
OCT pulse, including ringdown suppression, robust to variations in static and
microwave field strengths. We also discuss the applications of pulse design in
high-Q resonators to universal control of anisotropic-hyperfine coupled
electron-nuclear spin systems via electron-only modulation even when the
bandwidth of the resonator is significantly smaller than the hyperfine coupling
strength. These results demonstrate how limitations imposed by linear response
theory may be vastly exceeded when using a sufficiently accurate system model
to optimize pulses of high complexity.
