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

Constructing k-local parent Lindbladians for matrix product density operators