论文标题
从张量网络量子状态到紧张的复发神经网络
From Tensor Network Quantum States to Tensorial Recurrent Neural Networks
论文作者
论文摘要
我们表明，任何矩阵乘积状态（MPS）都可以通过线性内存更新的复发性神经网络（RNN）准确表示。我们使用多线性内存更新将此RNN体系结构推广到2D晶格。它支持多项式时间的完美采样和波功能评估，并且可以代表纠缠熵的区域定律。数值证据表明，与MPS相比，它可以使用键尺寸较低的键尺寸编码波函数，其精度可以通过增加键尺寸来系统地改善。
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.
