The difficulty of training variational quantum algorithms and quantum machine learning models is well established. In particular, quantum loss landscapes are often highly nonconvex and dominated by poor local minima. While this renders their training NP hard in general, efficient heuristics that work well for typical instances may still exist. Here we propose a protocol that uses a targeted noise injection to smooth and regularize quantum loss landscapes. It works by exponentially suppressing the high-frequency components in the Fourier expansion of the quantum loss function. The protocol can be efficiently implemented in both hardware and simulations. We observe significant and robust improvements of solution quality across various problem types. Our method can be combined with existing techniques mitigating the local minima, such as the quantum natural gradient optimizer, and adds to the toolbox of methods for optimizing quantum loss functions.
Bagaev et al. (2025) studied this question.