Identification of symmetry-protected topological states on noisy quantum computers

Daniel Azses, Rafael Haenel, Yehuda Naveh, Robert Raussendorf, Eran Sela, Emanuele G. Dalla Torre

Published 2020-02-11Version 1

Identifying topological properties is a major challenge because, by definition, topological states do not have a local order parameter. While a generic solution to this challenge is not available yet, toplogical states that are protected by a symmetry can be identified by protected degeneracies in their entanglement spectrum. Here, we provide two complementary protocols to probe these degeneracies based on, respectively, symmetry-resolved entanglement entropies and measurement-based computational algorithms. The interchangeability of the two protocols illustrates a deep link between the topological classification of quantum phases of matter and the computational power of their ground states. Both protocols are implemented on an IBM quantum computer and used to identify the topological cluster state. The comparison between the experimental findings and noisy simulations allows us to study the stability of topological states to perturbations and noise.