Fermionic Gaussian Testing and Non-Gaussian Measures via Convolution

• URL: http://arxiv.org/abs/2409.08180v2
• Date: Tue, 8 Oct 2024 14:58:44 GMT
• Title: Fermionic Gaussian Testing and Non-Gaussian Measures via Convolution
• Authors: Xingjian Lyu, Kaifeng Bu,
• Abstract summary: We define fermionic convolution and demonstrate its utility in characterizing fermionic non-Gaussian components. We also introduce "Non-Gaussian Entropy," an experimentally accessible resource measure that quantifies fermionic non-Gaussianity.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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