Efficient Preparation of Nonabelian Topological Orders in the Doubled Hilbert Space

Abstract

Realizing nonabelian topological orders and their anyon excitations is an esteemed objective. In this work, we propose a novel approach towards this goal: quantum simulating topological orders in the doubled Hilbert space - the space of density matrices. We show that ground states of all quantum double models (toric code being the simplest example) can be efficiently prepared in the doubled Hilbert space; only finite-depth local operations are needed. In contrast, this is not the case in the conventional Hilbert space: Ground states of only some of these models are known to be efficiently preparable. Additionally, we find that nontrivial anyon braiding effects, both abelian and nonabelian, can be realized in the doubled Hilbert space, although the intrinsic nature of density matrices restricts possible excitations.