  We explore the protection of quantum gates from arbitrary single- and
two-qubit noises with properly designed dynamical decoupling pulses. The
proposed dynamical decoupling method is a concatenation of a sequence of pulses
formed by $\sigma_x$, $\sigma_x\sigma_x$ with another sequence constructed by
$\sigma_z$, $\sigma_z\sigma_z$. The concatenation of the two sequences results
in desired pulses to fight agianst any single- and two-qubit errors. The
success of our method relies on the ability to adjust system parameters or
interaction terms, which can be achieved in different physical systems,
including trapped ions and superconducting qubits. We finally explore the
performance of our method numerically with the above-mentioned errors that are
changing at any moment and show the preferred protection offered by the method.
Therefore, our method is a timely step forward in preserving quantum gates at
the level of physical qubits.
