AI Insight
This paper presents two new algorithms for sampling probability distributions from two-dimensional isometric tensor network states, extending existing one-dimensional methods to higher dimensions. The first algorithm generates individual configurations with their probabilities through independent sampling, while the second uses a greedy search approach to identify multiple high-probability configurations simultaneously. Numerical testing shows both algorithms work effectively across quantum states with different levels of entanglement and system sizes.
Why it matters
These algorithms could improve computational efficiency for quantum advantage experiments and quantum Monte Carlo simulations by enabling better sampling of two-dimensional quantum systems. The methods provide practical tools for analyzing larger and more complex quantum systems that were previously difficult to handle with existing one-dimensional approaches.
arXiv:2602.02245v2 Announce Type: replace-cross
Abstract: Sampling a quantum system’s 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 generalize existing 1D tensor networks sampling algorithms. Our first proposed algorithm 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.
Source: Sampling two-dimensional isometric tensor network states