Generalized quantum search Hamiltonian
Joonwoo Bae, Younghun Kwon · Physical Review A · 2002
There are Hamiltonians that solve the search problem of finding one of N items in $O(\sqrt{N})$ steps. These are Hamiltonians describing an oscillation between two states. In this paper we propose a generalized search Hamiltonian ${H}_{g}.$ Then the known search Hamiltonians become special cases of ${H}_{g}.$ For the generalized search Hamiltonian, we present the remarkable result that searching with 100% success is subject only to the phase factor in ${H}_{g}$ and independent of the number of states or initialization.