Fighting dephasing noise with robust optimal control

We address the experimentally relevant problem of robust mitigation of dephasing noise acting on a qubit. We first present an extension of a method for representing $1/\omega^{\alpha}$ noise developed by Kuopanportti et al. to the efficient representation of arbitrary Markovian noise. We then add qubit control pulses to enable the design of numerically optimized, two-dimensional control functions with bounded amplitude, that are capable of decoupling the qubit from the dephasing effects of a broad variety of Markovian noise spectral densities during arbitrary one qubit quantum operations. We illustrate the method with development of numerically optimized control pulse sequences that minimize decoherence due to a combination of $1/\omega$ and constant offset noise sources. Comparison with the performance of standard dynamical decoupling protocols shows that the numerically optimized pulse sequences are considerably more robust with respect to the noise offset, rendering them attractive for application to situations where homogeneous dephasing noise sources are accompanied by some extent of heterogeneous dephasing. Application to the mitigation of dephasing noise on spin qubits in silicon indicates that high fidelity single qubit gates are possible with current pulse generation technology.