Let Quantum Neural Networks Choose Their Own Frequencies
Ben Jaderberg Antonio A. Gentile Youssef Achari Berrada Elvira Shishenina Vincent E. Elfving
Parameterized quantum circuits as machine learning models are typically well
described by their representation as a partial Fourier series of the input
features, with frequencies uniquely determined by the feature map's generator
Hamiltonians. Ordinarily, these data-encoding generators are chosen in advance,
fixing the space of functions that can be represented. In this work we consider
a generalization of quantum models to include a set of trainable parameters in
the generator, leading to a trainable frequency (TF) quantum model. We
numerically demonstrate how TF models can learn generators with desirable
properties for solving the task at hand, including non-regularly spaced
frequencies in their spectra and flexible spectral richness. Finally, we
showcase the real-world effectiveness of our approach, demonstrating an
improved accuracy in solving the Navier-Stokes equations using a TF model with
only a single parameter added to each encoding operation. Since TF models
encompass conventional fixed frequency models, they may offer a sensible
default choice for variational quantum machine learning.