From Tensor Network Quantum States to Tensorial Recurrent Neural Networks
This provides a novel bridge between tensor network methods and neural networks for quantum state representation, potentially enabling more efficient simulations in quantum physics.
The paper demonstrates that matrix product states (MPS) can be exactly represented by recurrent neural networks (RNNs) with linear memory updates, and generalizes this to 2D lattices with multilinear updates, achieving polynomial-time wave function evaluation and area law entanglement entropy. Numerical results show it encodes wave functions with bond dimensions orders of magnitude lower than MPS while maintaining accuracy that improves with bond dimension.
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.