Optimal sampling of tensor networks targeting wave function's fast decaying tails

Understand

We introduce an optimal strategy to sample quantum outcomes of local measurement strings for isometric tensor network states.

• Our method generates samples based on an exact cumulative bounding function, without prior knowledge, in the minimal amount of tensor network contractions.
• The algorithm avoids sample repetition and, thus, is efficient at sampling distribution with exponentially decaying tails.
• We illustrate the computational advantage provided by our optimal sampling method through various numerical examples, involving condensed matter, optimization problems, and quantum circuit scenarios.