Physical Review A - Atomic, Molecular, and Optical Physics
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.
Hayes, David; Khodjasteh, Kaveh; Viola, Lorenza; and Biercuk, Michael J., "Reducing Sequencing Complexity in Dynamical Quantum Error Suppression by Walsh Modulation" (2011). Open Dartmouth: Faculty Open Access Scholarship. 3152.