  Recently the continuous time algorithm based on the generalized quantum
search Hamiltonian was presented. In this letter, we consider the running time
of the generalized quantum search Hamiltonian. We provide the surprising result
that the maximum speedup of quantum search in the generalized Hamiltonian is
the O(1) running time regardless of the number of total states. It seems to
violate the proof of Zalka that the quadratic speedup is optimal in quantum
search. However the argurment of Giovannetti et al. that a quantum speedup
comes from the interaction between subsystems(or, equivalently entanglement)
(and is concerned with the Margolus and Levitin theorem) supports our result.
