Representing Arbitrary Ground States of Toric Code by Restricted Boltzmann Machine

Penghua Chen, Bowen Yan, Shawn X. Cui

Published 2024-07-01, updated 2024-07-15Version 2

We systematically analyze the representability of toric code ground states by Restricted Boltzmann Machine with only local connections between hidden and visible neurons. This analysis is pivotal for evaluating the model's capability to represent diverse ground states, thus enhancing our understanding of its strengths and weaknesses. Subsequently, we modify the Restricted Boltzmann Machine to accommodate arbitrary ground states by introducing essential non-local connections efficiently. The new model is not only analytically solvable but also demonstrates efficient and accurate performance when solved using machine learning techniques. Then we generalize our the model from $Z_2$ to $Z_n$ toric code and discuss future directions.