Computing Solution Space Properties of Combinatorial Optimization Problems Via Generic Tensor Networks

We introduce a unified framework to compute the solution space properties of broad class combinatorial optimization problems. These include finding one optimum solutions, counting number solutions given size, and enumeration sampling size. Using independent set problem as an example, we show how all these can be computed in approach generic tensor networks. demonstrate versatility this computational tool by applying it several examples, including computing entropy constant for hardcore lattice gases, studying overlap gap properties, analyzing performance quantum classical algorithms maximum sets.