Abstract
The protection of quantum gates from arbitrary single- and two-qubit noises with properly designed dynamical decoupling (DD) pulses is explored. The proposed dynamical decoupling method is a concatenation of a sequence of pulses formed by sigma j,kx$\sigma <^>{x}_{j,k}$, sigma jx sigma kx$\sigma _{j}<^>{x}\sigma _{k}<^>{x}$ with another sequence constructed by sigma j,kz$\sigma <^>{z}_{j,k}$, sigma jz sigma kz$\sigma <^>{z}_{j}\sigma <^>{z}_{k}$. The concatenation of the two sequences results in desired pulses to fight against any single- and two-qubit errors. The success of the 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. Finallythe performance of the method is explored numerically with the above-mentioned errors that are changing at any moment and show the preferred protection offered by the method. Therefore, the method is a timely step forward in preserving quantum gates at the level of physical qubits.