We show that any matrix product state (MPS) can be exactly represented by a recurrent neural network (RNN) with a linear memory update. We generalize this RNN architecture to 2D lattices using a multilinear memory update. It supports perfect sampling and wave function evaluation in polynomial time, and can represent an area law of entanglement entropy. Numerical evidence shows that it can encode the wave function using a bond dimension lower by orders of magnitude when compared to MPS, with an accuracy that can be systematically improved by increasing the bond dimension.

翻译：我们证明，任何矩阵乘积态（MPS）都可以由具有线性记忆更新的递归神经网络（RNN）精确表示。我们将此RNN架构推广到二维晶格，采用多线性记忆更新。该架构支持多项式时间内的完美采样和波函数评估，并能表示纠缠熵的面积律。数值证据表明，与MPS相比，该架构能够以低数个数量级的键维度编码波函数，且其精度可通过增加键维度系统地提高。