Fermion Sampling Made More Efficient

TL;DR

This paper introduces a new fermion sampling algorithm with quadratic polynomial time complexity, doubling the efficiency of previous methods, and demonstrates its effectiveness in quantum physics simulations and machine learning tasks.

Contribution

The paper presents a novel fermion sampling algorithm with significantly improved computational efficiency, especially in marginal distribution sampling, applicable to physics and machine learning.

Findings

Algorithm is twice as fast as previous methods.

Achieves polynomial time complexity quadratic in fermion number.

Demonstrates improved efficiency in physics and machine learning applications.

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.