We study dynamical error suppression from the perspective of reducingsequencing complexity, in order to facilitate efficient semi-autonomousquantum-coherent systems. With this aim, we focus on digital sequences whereall interpulse time periods are integer multiples of a minimum clock period andcompatibility with simple digital classical control circuitry is intrinsic,using so-called em Walsh functions as a general mathematical framework. TheWalsh functions are an orthonormal set of basis functions which may beassociated directly with the control propagator for a digital modulationscheme, and dynamical decoupling (DD) sequences can be derived from thelocations of digital transitions therein. We characterize the suite of theresulting Walsh dynamical decoupling (WDD) sequences, and identify the numberof periodic square-wave (Rademacher) functions required to generate a Walshfunction as the key determinant of the error-suppressing features of therelevant WDD sequence. WDD forms a unifying theoretical framework as itincludes a large variety of well-known and novel DD sequences, providingsignificant flexibility and performance benefits relative to basicquasi-periodic design. We also show how Walsh modulation may be employed forthe protection of certain nontrivial logic gates, providing an implementationof a dynamically corrected gate. Based on these insights we identify Walshmodulation as a digital-efficient approach for physical-layer errorsuppression.
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