Fermionic Kernel Methods For Regression and Classification

We extend fermionic machine learning (FermiML) — a machine-learning (ML) framework based on fermionic quantum computation — to tackle both regression and classifications tasks on complex datasets. FermiML models are built using parameterized matchgate circuits, a restricted class of quantum circuits that map exactly to systems of free Majorana fermions. These circuits remain efficiently simulable classically, making FermiML a powerful benchmark for quantum machine learning (QML). Building on our prior work [arXiv:2404.19032], we improve the framework and demonstrate its scalability to large datasets and its robustness across a variety of classification benchmarks, including imbalanced datasets. In addition, we extend FermiML to kernel regression and demonstrate its efficiency in various benchmarks. We systematically study angle encoding schemes for FermiML and find encodings that improve performance for both tasks. Finally, we benchmark our fermionic models against fully-quantum counterparts and provide open-source code, inviting the community to surpass our results on a practical machine learning task of their choice.