Observing Floquet topological order by symmetry resolution

TL;DR

This paper investigates Floquet topological phases protected by symmetry in one-dimensional systems, demonstrating their detection via symmetry block cycling, phase transition signatures, and potential for quantum information teleportation, using both theory and quantum computers.

Contribution

It introduces a novel method to observe Floquet topological order through symmetry resolution and demonstrates its breaking at phase transitions with quantum computational evidence.

Findings

Symmetry block cycling indicates Floquet topological phases.

Topological phase transitions break the cycling periodicity.

Quantum teleportation is enabled by the Floquet topological phase.

Abstract

Symmetry protected topological order in one dimension leads to protected degeneracies between symmetry blocks of the reduced density matrix. In the presence of periodic driving, topological Floquet phases can be identified in terms of a cycling of these symmetry blocks between different charge quantum numbers. We discuss an example of this phenomenon with an Ising $\mathbb{Z}_2$ symmetry, using both analytic methods and real quantum computers. By adiabatically moving along the phase diagram, we demonstrate that the cycling periodicity is broken in Floquet topological phase transitions. An equivalent signature of the topological Floquet phase is identified as a computational power allowing to teleport quantum information.