Constructing k-local parent Lindbladians for matrix product density operators

TL;DR

This paper develops an algorithm to determine if a small subspace of matrix product density operators can be the stable space of a local, frustration-free Lindbladian, aiding in the experimental preparation of these states.

Contribution

It introduces a method to construct k-local parent Lindbladians for specific MPDO subspaces, advancing the understanding of open system dynamics for state preparation.

Findings

Algorithm can identify if MPDO subspaces are stable under local Lindbladians

Constructs explicit Lindbladians for compatible MPDO subspaces

Facilitates experimental realization of MPDO states

Abstract

Matrix product density operators (MPDOs) are an important class of states with interesting properties. Consequently, it is important to understand how to prepare these states experimentally. One possible way to do this is to design an open system that evolves only towards desired states. A Markovian evolution of a quantum mechanical system can be generally described by a Lindbladian. In this work we develop an algorithm that for a given (small) linear subspace of MPDOs determines if this subspace can be the stable space for some frustration free Lindbladian consisting of only local terms and, if so, outputs a suitable Lindbladian.