Direct sampling of projected entangled-pair states

Abstract

Variational Monte Carlo studies employing projected entangled-pair states (PEPS) have recently shown that they can provide answers on long-standing questions such as the nature of the phases in the two-dimensional $J_1-J_2$ model. The sampling in these Monte Carlo algorithms is typically performed with Markov Chain Monte Carlo algorithms employing local update rules, which often suffer from long autocorrelation times and interdependent samples. We propose a sampling algorithm that generates independent samples from a PEPS, bypassing all problems related to finite autocorrelation times. This algorithm is a generalization of an existing direct sampling algorithm for unitary tensor networks. We introduce an auxiliary probability distribution from which independent samples can be drawn, and combine it with importance sampling in order to evaluate expectation values accurately. We benchmark our algorithm on the classical Ising model and on variational optimization of two-dimensional quantum spin models.

References in corpus (53)

• The density-matrix renormalization group in the age of matrix product states
• Quantum trajectories and open many-body quantum systems
• Time-dependent variational principle for quantum lattices
• Unifying time evolution and optimization with matrix product states
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Criticality, the area law, and the computational power of PEPS
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Competing states in the t-J model: uniform d-wave state versus stripe state
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• The computational complexity of PEPS
• Green Function Monte Carlo with Stochastic Reconfiguration
• Recurrent Neural Network Wave Functions
• Deep autoregressive models for the efficient variational simulation of many-body quantum systems
• Unsupervised Generative Modeling Using Matrix Product States
• Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States
• Differentiable Programming Tensor Networks
• Variational optimization with infinite projected entangled-pair states
• The iPEPS algorithm, improved: fast full update and gauge fixing
• Solving Statistical Mechanics Using Variational Autoregressive Networks
• Flow-based generative models for Markov chain Monte Carlo in lattice field theory
• Algorithms for finite Projected Entangled Pair States
• Gradient methods for variational optimization of projected entangled-pair states
• Tangent-space methods for uniform matrix product states
• Tensor network study of the Shastry-Sutherland model in zero magnetic field
• Variational quantum Monte Carlo simulations with tensor-network states
• Isometric Tensor Network States in Two Dimensions
• Perfect Sampling with Unitary Tensor Networks
• Neural Quantum States of frustrated magnets: generalization and sign structure
• Strings, Projected Entangled Pair States, and variational Monte Carlo methods
• A simple tensor network algorithm for two-dimensional steady states
• Time Evolution of an Infinite Projected Entangled Pair State: an Efficient Algorithm
• Unifying Projected Entangled Pair States contractions
• Tree Tensor Networks for Generative Modeling
• Optimizing large parameter sets in variational quantum Monte Carlo
• Excitations and the tangent space of projected entangled-pair states
• Projected Entangled Pair States at Finite Temperature: Imaginary Time Evolution with Ancillas
• Monte Carlo simulation with Tensor Network States
• Variational Approach to Projected Entangled Pair States at Finite Temperature
• Neural network wave functions and the sign problem
• Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
• Simulating excitation spectra with projected entangled-pair states
• Riemannian optimization of isometric tensor networks
• Gradient optimization of finite projected entangled pair states
• Excitations with projected entangled pair states using the corner transfer matrix method
• Time-dependent study of disordered models with infinite projected entangled pair states
• Accurate simulation for finite projected entangled pair states in two dimensions
• Dynamical large deviations of two-dimensional kinetically constrained models using a neural-network state ansatz
• Time Evolution of an Infinite Projected Entangled Pair State: an Algorithm from First Principles
• Variational Monte Carlo simulations using tensor-product projected states
• Matrix-Product based Projected Wave Functions Ansatz for Quantum Many-Body Ground States
• Scale-renormalized matrix-product states for correlated quantum systems
• Nontrivial maturation metastate-average state in a one-dimensional long-range Ising spin glass: above and below the upper critical range

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• Autoregressive neural Slater-Jastrow ansatz for variational Monte Carlo simulation
• Entanglement entropy scaling of noisy random quantum circuits in two dimensions
• Two Dimensional Isometric Tensor Networks on an Infinite Strip
• All-mode Renormalization for Tensor Network with Stochastic Noise