  Achieving high-fidelity control of quantum systems is essential for
realization of a practical quantum computer. Composite pulse sequences which
suppress different types of errors can be nested to suppress a wide variety of
errors but the result is often not optimal, especially in the presence of
constraints such as bandwidth limitations. Robust smooth pulse shaping provides
flexibility, but obtaining such analytical pulse shapes is a non-trivial
problem, and choosing the appropriate parameters typically requires a numerical
search in a high-dimensional space. In this work, we extend a previous
analytical treatment of robust smooth pulses to allow the determination of
pulse parameters without numerical search. We also show that the problem can be
reduced to a set of coupled ordinary differential equations which allows for a
more streamlined numerical treatment.
