# Distributed finite-time stabilization of entangled quantum states on tree-like hypergraphs

## TL;DR

This paper demonstrates that certain pure quantum states on tree-like hypergraph networks can be uniquely stabilized in finite time using distributed dissipative dynamics, leveraging quasi-local Hamiltonians.

## Contribution

It introduces a class of quasi-locality called 'tree-like hypergraphs' and shows that states stabilizable in finite time are unique ground states of specific Hamiltonians.

## Key findings

- States are robustly stabilizable in finite time.
- Stabilizable states are ground states of frustration-free, commuting Hamiltonians.
- Provides a structural characterization of stabilizable states.

## Abstract

Preparation of pure states on networks of quantum systems by controlled dissipative dynamics offers important advantages with respect to circuit-based schemes. Unlike in continuous-time scenarios, when discrete-time dynamics are considered, dead-beat stabilization becomes possible in principle. Here, we focus on pure states that can be stabilized by distributed, unsupervised dynamics in finite time on a network of quantum systems subject to realistic quasi-locality constraints. In particular, we define a class of quasi-locality notions, that we name "tree-like hypergraphs," and show that the states that are robustly stabilizable in finite time are then unique ground states of a frustration-free, commuting quasi-local Hamiltonian. A structural characterization of such states is also provided, building on a simple yet relevant example.