Reducing sequencing complexity in dynamical quantum error suppression by Walsh modulation

We study dynamical error suppression from the perspective of reducing sequencing complexity, with an eye toward facilitating the development of efficient semiautonomous quantum-coherent systems. To this end, we focus on digital sequences where all interpulse time periods are integer multiples of a minimum clock period and compatibility with digital classical control circuitry is intrinsic. We use so-called Walsh functions as a unifying 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. Using this insight, we characterize the suite of resulting Walsh dynamical decoupling sequences-including both familiar and novel control sequences-and identify the number of periodic square-wave (Rademacher) functions required to generate the associated Walsh function as the key determinant of the error-suppressing features. We also show how Walsh modulation may be employed for the protection of certain nontrivial logic gates. Based on these insights, we identify Walsh modulation as a digital-efficient approach for physical-layer error suppression.