Symmetry-protected dissipative preparation of matrix product states

Abstract

We propose and analyze a method for efficient dissipative preparation of matrix product states that exploits their symmetry properties. Specifically, we construct an explicit protocol that makes use of driven-dissipative dynamics to prepare the Affleck-Kennedy-Lieb-Tasaki (AKLT) states, which features symmetry-protected topological order and non-trivial edge excitations. We show that the use of symmetry allows for robust experimental implementation without fine-tuned control parameters. Numerical simulations show that the preparation time scales polynomially in system size $n$. Furthermore, we demonstrate that this scaling can be improved to $\mathcal{O}(\log^2n)$ by using parallel preparation of AKLT segments and fusing them via quantum feedback. A concrete scheme using excitation of trapped neutral atoms into Rydberg state via Electromagnetically Induced Transparency is proposed, and generalizations to a broader class of matrix product states are discussed