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 (14)

• The density-matrix renormalization group in the age of matrix product states
• Quantum trajectories and open many-body quantum systems
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Criticality, the area law, and the computational power of PEPS
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Algorithms for finite Projected Entangled Pair States
• Variational quantum Monte Carlo simulations with tensor-network states
• Strings, Projected Entangled Pair States, and variational Monte Carlo methods
• Tree Tensor Networks for Generative Modeling
• Projected Entangled Pair States at Finite Temperature: Imaginary Time Evolution with Ancillas
• Monte Carlo simulation with Tensor Network States
• Variational Monte Carlo simulations using tensor-product projected states
• Nontrivial maturation metastate-average state in a one-dimensional long-range Ising spin glass: above and below the upper critical range

Cited by in corpus (8)

• From Tensor Network Quantum States to Tensorial Recurrent Neural Networks
• Efficient Simulation of Dynamics in Two-Dimensional Quantum Spin Systems with Isometric Tensor Networks
• Snapshot based characterization of particle currents and the Hall response in synthetic flux lattices
• Optimal sampling of dynamical large deviations in two dimensions via tensor networks
• 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