Diagrammatic approach to quantum search
We introduce a simple diagrammatic approach for estimating how a randomly walking quantum particle searches on a graph in continuous time, which involves sketching small weighted graphs with self-loops and considering degenerate perturbation theorys effects on them. Using this method, we give the first example of degenerate perturbation theory solving search on a graph whose evolution occurs in a subspace whose dimension grows with \(N\).
quantum search perturbation theory quantum walks quantum algorithms grovers algorithm