Fermionic Machine Learning

We introduce fermionic machine learning (Fer-miML), a machine learning framework based on fermionic quan-tum 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” coun-terparts of any quantum machine learning (QML) model based on parameterized quantum circuits, including models that pro-duce highly entangled quantum states. Importantly, matchgate circuits are efficiently simulable classically, thus rendering Fer-miML 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.