  We study dynamical error suppression from the perspective of reducing
sequencing complexity, in order to facilitate efficient semi-autonomous
quantum-coherent systems. With this aim, we focus on digital sequences where
all interpulse time periods are integer multiples of a minimum clock period and
compatibility with simple digital classical control circuitry is intrinsic,
using so-called em Walsh functions as a general mathematical framework. The
Walsh functions are an orthonormal set of basis functions which may be
associated directly with the control propagator for a digital modulation
scheme, and dynamical decoupling (DD) sequences can be derived from the
locations of digital transitions therein. We characterize the suite of the
resulting Walsh dynamical decoupling (WDD) sequences, and identify the number
of periodic square-wave (Rademacher) functions required to generate a Walsh
function as the key determinant of the error-suppressing features of the
relevant WDD sequence. WDD forms a unifying theoretical framework as it
includes a large variety of well-known and novel DD sequences, providing
significant flexibility and performance benefits relative to basic
quasi-periodic design. We also show how Walsh modulation may be employed for
the protection of certain nontrivial logic gates, providing an implementation
of a dynamically corrected gate. Based on these insights we identify Walsh
modulation as a digital-efficient approach for physical-layer error
suppression.
