Fermion Sampling Made More Efficient

• URL: http://arxiv.org/abs/2109.07358v1
• Date: Wed, 15 Sep 2021 15:11:33 GMT
• Title: Fermion Sampling Made More Efficient
• Authors: Haoran Sun, Jie Zou and Xiaopeng Li
• Abstract summary: We propose a fermion sampling algorithm, which has a time-complexity -- in the fermion number and linear in the system size. This algorithm is about 100% more efficient in time than the best known algorithms. We demonstrate its power on several test applications, including sampling fermions in a many-body system and a machine learning task of text summarization.
• Score: 19.50440110966488
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Fermion sampling is to generate probability distribution of a many-body Slater-determinant wavefunction, which is termed "determinantal point process" in statistical analysis. For its inherently-embedded Pauli exclusion principle, its application reaches beyond simulating fermionic quantum many-body physics to constructing machine learning models for diversified datasets. Here we propose a fermion sampling algorithm, which has a polynomial time-complexity -- quadratic in the fermion number and linear in the system size. This algorithm is about 100% more efficient in computation time than the best known algorithms. In sampling the corresponding marginal distribution, our algorithm has a more drastic improvement, achieving a scaling advantage. We demonstrate its power on several test applications, including sampling fermions in a many-body system and a machine learning task of text summarization, and confirm its improved computation efficiency over other methods by counting floating-point operations.

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