Fermionic Machine Learning

TL;DR

FermiML introduces a fermionic quantum machine learning framework using matchgate circuits, enabling efficient classical simulation and effective classification performance on real-world datasets, bridging quantum and classical ML.

Contribution

The paper presents FermiML, a novel fermionic quantum machine learning framework based on matchgate circuits, allowing efficient classical simulation and broad applicability.

Findings

FermiML kernels match unrestricted PQC kernels in binary classification.

FermiML outperforms unrestricted PQCs in multi-class classification.

FermiML enables exploration of regimes previously inaccessible to QML.

Abstract

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.