Higher-order protection of quantum gates: Hamiltonian engineering coordinated with dynamical decoupling

Dynamical decoupling represents an active approach towards the protection of quantum memories and quantum gates. Because dynamical decoupling operations can interfere with a system's own time evolution, the protection of quantum gates is more challenging than that of quantum states. In this work, we put forward a simple but general approach towards the realization of higher-order protection of quantum gates and further execute the first cloud-based demonstration of dynamical-decoupling-protected quantum gates at the first order and the second order. The central idea of our approach is to engineer (hence regain the control of) the gate Hamiltonian in coordination with higher-order dynamical decoupling sequences originally proposed for the protection of quantum memories. The physical demonstration on an IBM quantum processor indicates the effectiveness and potential of our approach on noisy intermediate scale quantum computers.