Fourier Fingerprints

Quantum Fourier models provide an exciting way of studying quantum machine learning. To facilitate an easy entry into this field of reasearch, we're actively developing the QML-Essentials toolbox. Now, when trying to train such models on some dataset and evaluating different Ansätze (a community term describing the structure of a model), one quickly notice that not all Ansätze perform equal, although in theory they should all have the same spectrum (determined by the number of data encodings).

In our paper Fourier Fingerprints of Ansatzes in Quantum Machine Learning, we introduce a metric to predict the performance of various Ansätze without having to train them. This works by evaluating the correlation between the coefficients, i.e. the terms in the partial Fourier series, the model represents. Doing this for each possible combination of coefficients, we can then build sth. which we refer to as "Fourier Fingerprints", in the following depicted for several different Ansätze.

Based on these fingerprints, one can derive a single-value metric to rank the Ansätze based on their intrinsic correlations. In our work (which is currently under review, but hopefully get's published soon), we successfully showed that this metric is capable of predicting the performance of various Ansätze, both on synthetic Fourier series datasets and an application specific dataset from the domain of high-energy physics.