I have some combinatorial optimization problems which I would like to analyze using QAOA. These problems are coming from various applications in scientific computing such as solving PDEs. Some of these problems can be phrased as combinatorial optimization problems - in particular graph traversal problems - based on recent results in the research literature. The idea is to find the optimal path with the least cost.
What's the cost? The classical loss function is continuous. For instance, the loss function could be a least-squares loss function. Or a loss function given by some integrals and derivatives if we have a variational formulation of a PDE.
How do I even convert this loss function to a cost function of Boolean variables so I can convert it to a cost function for QUBO like problems? I am stumped. Are there any resources in the literature?