Segmented composite design of robust single-qubit quantum gates

Over the past few decades, quantum information processing research has focused heavily on error-mitigation schemes and error-correcting codes. However, while many proposed schemes have been successful in mitigating errors, most of them are perturbative and assume deterministic systematic errors, leaving studies of the problem considering the full noise and errors distribution scarce. In this work we introduce an error-mitigation scheme for robust single-qubit unitary gates based on a composite segmented design that accounts for the full distribution of the physical noise and errors in the system. We provide two optimization approaches to construct these robust segmented gates, perturbative and nonperturbative, which address all orders of errors. We demonstrate the effectiveness of our scheme in the photonics realm for the realization of dual-rail directional couplers. Specifically, we show that the three-segment composite design for the fundamental single-qubit unitary operations reduces the error by an order of magnitude for a realistic distribution of errors. Moreover, we demonstrate that the two approaches are compatible for small errors and significantly reduce the overhead of modern error-correction codes. Our methods are rather general and can be applied to other realizations of quantum information processing units.