Fermionic Gaussian Testing and Non-Gaussian Measures via Convolution

2024/09/12 by Xintong Lyu, Lyu, Xingjian, Kaifeng Bu +1 · 6 citations
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Computational Complexity (cs.CC) #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2409.08180

openalex publication_date 2024/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Growth and spreading of quantum resources under random circuit dynamics
• DMFT data supporting [arXiv:2512.03689]
• Is it Gaussian? Testing bosonic quantum states
• Quantum Higher Order Fourier Analysis and the Clifford Hierarchy
• Measuring non-Gaussianity with Correlation
• Graphical Calculus for Fermionic Tensors

Related

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• Computable fermionic non-Gaussianity from the covariance matrix
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• Displaced Fermionic Gaussian States and their Classical Simulation