On validity of quantum partial adiabatic search

Abstract

In this paper, we further verify the validity of the quantum partial adiabatic search algorithm which was initialized in the previous related works by revisiting its quantum circuit model. The main results got here are as follows. When considering implementing quantum partial adiabatic evolution on a quantum circuit, a correction is given for the time slice estimation for the first stage during this approximation in the previous related works, new evidence is provided for a time complexity cost \(O(\sqrt{N}/M)\) of quantum partial adiabatic algorithm is impossible, and the correct time complexity \(O(\sqrt{N/M})\) of it is emphasized once more according to its circuit correspondence, in which N is the total number of elements in the search problem of which M of them are the marked ones. The findings exposed are hopeful for revisiting quantum partial adiabatic evolution and its connection with the quantum circuit model.