  We introduce fermionic machine learning (FermiML), a machine learning
framework based on fermionic quantum computation. FermiML models are expressed
in terms of parameterized matchgate circuits, a restricted class of quantum
circuits that map exactly to systems of free Majorana fermions. The FermiML
framework allows for building fermionic counterparts of any quantum machine
learning (QML) model based on parameterized quantum circuits, including models
that produce highly entangled quantum states. Importantly, matchgate circuits
are efficiently simulable classically, thus rendering FermiML a flexible
framework for utility benchmarks of QML methods on large real-world datasets.
We initiate the exploration of FermiML by benchmarking it against unrestricted
PQCs in the context of classification with random quantum kernels. Through
experiments on standard datasets (Digits and Wisconsin Breast Cancer), we
demonstrate that FermiML kernels are on-par with unrestricted PQC kernels in
classification tasks using support-vector machines. Furthermore, we find that
FermiML kernels outperform their unrestricted candidates on multi-class
classification, including on datasets with several tens of relevant features.
We thus show how FermiML enables us to explore regimes previously inaccessible
to QML methods.
