Perfect Sampling with Unitary Tensor Networks

TL;DR

This paper introduces a perfect sampling method for unitary tensor networks, enabling direct, efficient sampling of configurations without Markov chain autocorrelation issues, improving computational efficiency in quantum many-body simulations.

Contribution

It presents a novel perfect sampling scheme for unitary tensor networks, eliminating equilibration and autocorrelation times, and introduces a partial sampling method to reduce sampling errors.

Findings

Perfect sampling scheme with zero autocorrelation times.

Direct sampling according to wavefunction probabilities.

Partial sampling reduces basis-dependent errors.

Abstract

Tensor network states are powerful variational ans\"atze for many-body ground states of quantum lattice models. The use of Monte Carlo sampling techniques in tensor network approaches significantly reduces the cost of tensor contractions, potentially leading to a substantial increase in computational efficiency. Previous proposals are based on a Markov chain Monte Carlo scheme generated by locally updating configurations and, as such, must deal with equilibration and autocorrelation times, which result in a reduction of efficiency. Here we propose a perfect sampling scheme, with vanishing equilibration and autocorrelation times, for unitary tensor networks -- namely tensor networks based on efficiently contractible, unitary quantum circuits, such as unitary versions of the matrix product state (MPS) and tree tensor network (TTN), and the multi-scale entanglement renormalization ansatz (MERA). Configurations are directly sampled according to their probabilities in the wavefunction, without resorting to a Markov chain process. We also describe a partial sampling scheme that can result in a dramatic (basis-dependent) reduction of sampling error.