Efficient reverse engineering of robust one-qubit control pulses for broadband noise

We derive an analytical expression for the filter-transfer function of an arbitrary one-qubit gate through the use of dynamical invariant theory and Hamiltonian reverse engineering. We use this result to define a cost functional that provides an efficient way to optimize the filter function for robustness against any specified frequency bands of the noise power spectral density. We demonstrate the utility of our result for the case of purely dephasing noise. We report a set of control parameters for which the normalized filter function can be supressed to ∼10^-4 for noise frequencies less than 4π times the inverse gate time.