  This work develops measures for quantifying the effects of field noise upon
targeted unitary transformations. Robustness to noise is assessed in the
framework of the quantum control landscape, which is the mapping from the
control to the unitary transformation performance measure (quantum gate
fidelity). Within that framework, a new geometric interpretation of stochastic
noise effects naturally arises, where more robust optimal controls are
associated with regions of small overlap between landscape curvature and the
noise correlation function. Numerical simulations of this overlap in the
context of quantum information processing reveal distinct noise spectral
regimes that better support robust control solutions. This perspective shows
the dual importance of both noise statistics and the control form for
robustness, thereby opening up new avenues of investigation on how to mitigate
noise effects in quantum systems.
