Duality via Sequential Quantum Circuit in the Topological Holography Formalism

TL;DR

This paper demonstrates that duality in topological holography can be implemented using sequential quantum circuits on the boundary, preserving spectral properties and entanglement structure in low-energy states.

Contribution

It introduces a novel method to realize duality through sequential quantum circuits within the topological holography framework.

Findings

Duality corresponds to changing boundary conditions in topological field theories.

Sequential quantum circuits can implement duality transformations.

Spectra of Hamiltonians remain identical after duality mapping.

Abstract

Two quantum theories which look different but are secretly describing the same low-energy physics are said to be dual to each other. When realized in the Topological Holography formalism, duality corresponds to changing the gapped boundary condition on the top boundary of a topological field theory, which determines the symmetry of the system, while not affecting the bottom boundary where all the dynamics take place. In this paper, we show that duality in the Topological Holography formalism can be realized with a Sequential Quantum Circuit applied to the top boundary. As a consequence, the Hamiltonians before and after the duality mapping have exactly the same spectrum in the corresponding symmetry sectors, and the entanglement in the corresponding low-energy eigenstates differs by at most an area law term.