机器学习算法对量子多体态的逼近能力
Approximating power of machine-learning ansatz for quantum many-body states
摘要：
最近提出了一种具有限制玻尔兹曼机（RBM）结构的人工神经网络（ANN），作为一种通用的变分量子多体波函数。在这项工作中，我们提供了物理的见解，这ananomaly的性能。我们揭示了RBM结构与扰动序列之间的联系，这解释了文献中证明的RBM ansazt在某些简单模型中实现的出色精度。基于这种关系，我们改进了数值算法，以实现更好的性能RBM的情况下，局部极小值复杂的收敛到全局之一。我们引入其他类的变分波函数，这也是能够复制的微扰结构，并表明它们的性能是可比的RBM。此外，我们研究了一个少层RBM的性能近似基态的随机，一维几何不变的模型，以及随机矩阵乘积状态（MPS）。我们发现，在近似这样的状态的误差表现出广泛的分布，并在很大程度上取决于目标状态的纠缠特性。
英文摘要：
An artificial neural network (ANN) with the restricted Boltzmann machine (RBM) architecture was recently proposed as a versatile variational quantum many-body wave function. In this work we provide physical insights into the performance of this ansatz. We uncover the connection between the structure of RBM and perturbation series, which explains the excellent precision achieved by RBM ansazt in certain simple models, demonstrated in the literature. Based on this relation, we improve the numerical algorithm to achieve better performance of RBM in cases where local minima complicate the convergence to the global one. We introduce other classes of variational wave-functions, which are also capable of reproducing the perturbative structure, and show that their performance is comparable to that of RBM. Furthermore, we study the performance of a few-layer RBM for approximating ground states of random, translationally-invariant models in 1d, as well as random matrix-product states (MPS). We find that the error in approximating such states exhibits a broad distribution, and is largely determined by the entanglement properties of the targeted state.
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