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arXiv · 2109.07358

Fermion Sampling Made More Efficient

Haoran Sun·Jie Zou·Xiaopeng Li
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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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Haoran Sun, Jie Zou, Xiaopeng Li. 2021-09-15. Fermion Sampling Made More Efficient. https://doi.org/10.1103/physrevb.107.035119

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