# Symmetry-protected dissipative preparation of matrix product states

## TL;DR

This paper introduces a symmetry-protected dissipative protocol for efficiently preparing matrix product states with topological order, robust against certain errors, and scalable with system size.

## Contribution

It presents a novel dissipative method leveraging symmetry for preparing complex quantum states, with improved scalability and a concrete experimental scheme.

## Key findings

- Preparation time scales polynomially with system size
- Parallel preparation reduces scaling to logarithmic squared
- Protocol is robust against symmetry-respecting errors

## 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 a many-body quantum state that features symmetry-protected topological order and non-trivial edge excitations. The preparation protocol is protected from errors that respect the symmetry, allowing for robust experimental implementation without fine-tuned control. Numerical simulations show that the preparation time scales polynomially in system size $n$. Furthermore, we demonstrate that this scaling can be improved to $\mathcal{O}(\log^2 n)$ by using parallel preparation of individual segments and fusing them via quantum feedback. A concrete scheme using excitation of trapped neutral atoms into Rydberg states via electromagnetically induced transparency is proposed, and generalizations to a broader class of matrix product states are discussed.