Efficient preparation of non-Abelian topological orders in the doubled Hilbert space
Shang Liu · Physical review. B./Physical review. B · 2024
Realizing non-Abelian 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 non-Abelian, can be realized in the doubled Hilbert space, although the intrinsic nature of density matrices restricts possible excitations.