Certifying topological states of matter

Topological phases of matter are paradegmatic materials with important applications in material science and quantum computing.

The characterization and classification of topological states of matter is not yet fully understood as such states fall outside the paradigm of standard Landau theory. Hitherto, such a characterization has focused mainly on the difficulty of preparing topological states via quantum circuits, or required knowledge of the ground space of the parent Hamiltonian.  
In this talk, the speaker proposes an alternative method for certifying the presence of topological order from the quantum state itself, by exploiting the connection between topological quantum states and quantum error correction. He provides evidence that the coherent information of a quantum error correcting code can be used to answer affirmatively whether a given multi-partite quantum state possesses topological properties or not.

This work is in collaboration with Alonso Viladomat (TU Munich), and Ricardo Costa de Almeida and Philipp Hauke (University of Trento).