Controlled quantum search on structured databases

Abstract

By proposing two schemes (namely, a multistage and a single-stage one) based on the continuous-time quantum walk (CTQW), we study the quantum search on balanced trees of height r with N vertices. For the multistage scheme, we achieve the search for a marked leaf vertex with a runtime Θ(N(2r-1)/2r) and a success probability close to 100% when the branching factor is large. For the single-stage scheme with adjustable edge weights, we achieve the search with an optimal runtime Θ(N) and a success probability close to 100% as well. Furthermore, we show that our search algorithms also work for real trees with unbalanced structures and are quite robust against various kinds of small perturbations.