Wu, DianRossi, RiccardoVicentini, FilippoCarleo, Giuseppe2023-08-282023-08-282023-08-282023-07-0510.1103/PhysRevResearch.5.L032001https://infoscience.epfl.ch/handle/20.500.14299/200080WOS:001050226900002We 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 two-dimensional 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.Physics, MultidisciplinaryPhysicstext::journal::journal article::research article