Rrapaj Ermal, Roggero Alessandro
Department of Physics, University of California, Berkeley, California 94720, USA.
School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA.
Phys Rev E. 2021 Jan;103(1-1):013302. doi: 10.1103/PhysRevE.103.013302.
Restricted Boltzmann machines (RBMs) are simple statistical models defined on a bipartite graph which have been successfully used in studying more complicated many-body systems, both classical and quantum. In this work, we exploit the representation power of RBMs to provide an exact decomposition of many-body contact interactions into one-body operators coupled to discrete auxiliary fields. This construction generalizes the well known Hirsch's transform used for the Hubbard model to more complicated theories such as pionless effective field theory in nuclear physics, which we analyze in detail. We also discuss possible applications of our mapping for quantum annealing applications and conclude with some implications for RBM parameter optimization through machine learning.
受限玻尔兹曼机（RBMs）是定义在二分图上的简单统计模型，已成功用于研究更复杂的多体系统，包括经典和量子系统。在这项工作中，我们利用RBMs的表示能力，将多体接触相互作用精确分解为与离散辅助场耦合的单体算符。这种构造将用于哈伯德模型的著名的赫希变换推广到更复杂的理论，如核物理中的无π介子有效场论，我们对此进行了详细分析。我们还讨论了我们的映射在量子退火应用中的可能应用，并通过机器学习得出了对RBM参数优化的一些启示。
