Role of coherence in adiabatic search algorithms

Abstract

We systematically investigate the role of coherence in adiabatic search algorithms by using the relative entropy measure of coherence. Both in the ideal case (adiabatic evolution) and the non-ideal case (nonadiabatic evolution), the success probability increases with the decreases of coherence. In addition, the coherence depletion in global adiabatic search algorithm, local adiabatic search algorithm and an adiabatic search algorithm with constant evolution time was discussed. The results show that the coherence decreases faster in more efficient algorithm and an exponential decaying of coherence is necessary to achieve fast search (constant evolution time) in the adiabatic search algorithm. More importantly, we demonstrate that the efficiency of adiabatic search algorithm can be improved by utilizing appropriate method to speed up the coherence depletion.