Fermionic Gaussian Testing and Non-Gaussian Measures via Convolution

TL;DR

This paper introduces a fermionic convolution framework to identify non-Gaussian features in fermionic states, proposing an efficient test for Gaussianity and a new measure for non-Gaussianity relevant to quantum computation.

Contribution

It presents a novel fermionic convolution method, an efficient Gaussianity testing protocol, and a new non-Gaussian entropy measure for fermionic systems.

Findings

Efficient three-copy protocol for fermionic Gaussianity testing

Introduction of Non-Gaussian Entropy as a resource measure

Enhanced understanding of fermionic non-Gaussianity in quantum computation

Abstract

We define fermionic convolution and demonstrate its utility in characterizing fermionic non-Gaussian components, which are essential to the computational advantage of fermionic systems. Using fermionic convolution, we propose an efficient protocol that tests the fermionic Gaussianity of pure states using three copies of the input state. We also introduce "Non-Gaussian Entropy," an experimentally accessible resource measure that quantifies fermionic non-Gaussianity. These results provide new insights into the study of fermionic quantum computation.