Universal quantum control with dynamical correction

Error correction is generally demanded in large-scale quantum information processing and quantum computation. We provide here a universal and real-time control strategy to dynamically correct the arbitrary type of errors in the system Hamiltonian. It yields multiple error-resilient paths for the interested system which are activated by the von Neumann equation for ancillary projection operators. With no extra control fields and precise designs, the path-dependent global phase alone suffices to mitigate the error-induced transitions among distinct paths as long as it varies faster than the other parameters. The corrected paths can also be regarded as the approximate solutions to the time-dependent Schr\"odinger equation perturbed by errors. Our dynamical-correction strategy is practiced with the cyclic transfer of populations in a three-level system, showing a superior error resilience to the parallel-transport condition. It provides a promising idea for advancing control methodologies in imprecise quantum systems.