From tensor-network quantum states to tensorial recurrent neural networks
Dian Wu, Riccardo Rossi, Filippo Vicentini, Giuseppe Carleo
Abstract
A recurrent neural network with a linear memory update is proposed to exactly represent any matrix product state (MPS) and is further generalized to 2D lattices using a multilinear memory update. It supports perfect sampling and wave-function evaluation in polynomial time, provides exact representation of an area law of entanglement entropy, and outperforms MPS by orders of magnitude in parameter efficiency.
Topics & Concepts
Quantum entanglementRecurrent neural networkTensor productDimension (graph theory)Multilinear mapArtificial neural networkMatrix product stateEntropy (arrow of time)Quantum stateComputer scienceQuantumComputational complexity theoryAlgorithmMathematicsPure mathematicsQuantum mechanicsArtificial intelligencePhysicsQuantum many-body systemsMachine Learning in Materials ScienceQuantum and electron transport phenomena