From Tensor Network Quantum States to Tensorial Recurrent Neural Networks

Abstract

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.

14 pages, 10 figures

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• Enhancing variational Monte Carlo using a programmable quantum simulator
• Impact of conditional modelling for a universal autoregressive quantum state
• Sparse Autoregressive Neural Networks for Classical Spin Systems
• Non-stabilizerness of Neural Quantum States
• Time-dependent Neural Galerkin Method for Quantum Dynamics
• Quantum-assisted variational Monte Carlo
• Optimisation of ultrafast singlet fission in 1D rings towards unit efficiency
• Simple Fermionic backflow states via a systematically improvable tensor decomposition
• Efficiency of the hidden fermion determinant states Ansatz in the light of different complexity measures
• Seeding neural network quantum states with tensor network states
• Neuralized Fermionic Tensor Networks for Quantum Many-Body Systems
• Gaussian Processes for Finite Size Extrapolation of Many-Body Simulations
• Group Convolutional Neural Network for the Low-Energy Spectrum in the Quantum Dimer Model
• Hybrid between biologically and quantum-inspired many-body states
• High-precision ground state parameters of the two-dimensional spin-1/2 Heisenberg model on the square lattice