Would be cool to use quantum entanglement to do instant FindSets (seeing if two elements are contained in the same set) for Kruskal MST algorithm.

Say each vertex is a photon.  Whenever you do a union you entangle the photons.  Then all you have to do to compare if the photons belong to the same set is to see if they are entangled.

This FindSet operation is already really fast O(lg*n).  However, this would be a constant time lookup.

What would the rest of the quantum MST algorithm be?