Randomized Dynamically Corrected Gates with Bounded Controls

Dynamically corrected gates (DCGs) implement a target unitary while canceling specified error terms, enabling high-fidelity quantum operations in practice. Although many constructions exist, most provide only low-order error suppression because higher-order DCGs are often costly and difficult to construct under realistic bounded controls. We introduce a randomized DCG construction that raises the robustness order by randomizing over low-order gate designs. Specifically, we show that randomizing over non-robust control functions yields first-order robustness, and that randomizing over first-order-robust DCGs substantially suppresses the leading error, approaching second-order robustness. This approach enables more robust gate implementations with shorter sequences, while remaining compatible with realistic bounded-control constraints.