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：我们显示,任何矩阵产品状态(MPS)都可以完全由具有线性内存更新的经常性神经网络(RNN)来代表。 我们使用多线性内存更新将RNN结构推广为 2D 层。 它支持在多线性内存更新中进行完美的取样和波函数评估, 并且可以代表缠绕酶的定律。 数字证据表明, 与 MPS 相比, 它可以使用比 MPS 更低的量级的债券维度对波函数进行编码, 精确度可以通过增加债券维度来系统改进。</s>