Discrete optimization in the MPS-MPO language

In discrete optimization problems, one usually asks for an optimal object from a finite set. Such problems appear in many fields ranging from transportation and logistics to computational biology and quantum error correction. Many of these are NP-complete, making exact solutions too hard to find and thus leaving a battle field for different approximate algorithms. In the current study, we show how to marry the formulation of such problems with tensor networks and show relevant examples including decoding of quantum error correcting codes by virtue of approximate MPS-MPO contraction and DMRG-like algorithm. The code for the study is publicly available as a Python package.