Sampling two-dimensional isometric tensor network states

TL;DR

This paper introduces two new algorithms for sampling from two-dimensional isometric tensor network states, extending well-known 1D methods to 2D, with demonstrated effectiveness across different quantum states.

Contribution

The paper presents the first two algorithms for sampling 2D isometric tensor network states, including independent sampling and a greedy search for high-probability configurations.

Findings

Algorithms effectively sample diverse quantum states

High-probability configurations identified efficiently

Applicable to states with varying entanglement levels

Abstract

Sampling a quantum systems underlying probability distributions is an important computational task, e.g., for quantum advantage experiments and quantum Monte Carlo algorithms. Tensor networks are an invaluable tool for efficiently representing states of large quantum systems with limited entanglement. Algorithms for sampling one-dimensional (1D) tensor networks are well-established and utilized in several 1D tensor network methods. In this paper we introduce two novel sampling algorithms for two-dimensional (2D) isometric tensor network states (isoTNS) that can be viewed as extensions of algorithms for 1D tensor networks. The first algorithm we propose performs independent sampling and yields a single configuration together with its associated probability. The second algorithm employs a greedy search strategy to identify K high-probability configurations and their corresponding probabilities. Numerical results demonstrate the effectiveness of these algorithms across quantum states with varying entanglement and system size.