Citation: Cian, Ze-Pei, Mohammad Hafezi, and Maissam Barkeshli. "Extracting Wilson loop operators and fractional statistics from a single bulk ground state." arXiv preprint arXiv:2209.14302 (2022).
Web: https://arxiv.org/abs/2209.14302
Tags: MTC-reconstruction, Abelian-anyons, Tensor-networks
This paper gives a method for extracting Wilson loop operators for abelian anyons from a single bulk ground state which is NOT based on the entanglement bootstrap programme. In fact, this paper takes a very different approach to the papers I normally read. Instead of coming up with a clean formula or conceptual picture for how to reconstruct some piece of data, they just do it. They search over all possible local operators until they find the Wilson loops. That is, they search for operators supported on loops which leave the ground state invariant (1-form symmetries) and call then Wilson loops.
Their procedure works by first assuming an ansatz - the Wilson loops will be representable by MPOs. Then, they do a computational search over the parameters with respect to a well-chosen cost function. It's gradient descent! They use this method to extract Wilson loops on perturbed toric code and semion models.
This paper is a nice datapoint for answering the question "to what extent has AI impacted research in topological quantum information?". Lots of problems can be reinterpreted in terms of searching for solutions in high-dimensional spaces. Gradient descent and machine learning approaches are the accepted computer-scientific ways to do such things!