Optimizing the quantum adiabatic algorithm

In the quantum adiabatic algorithm, as the adiabatic parameter s(t) changes slowly from zero to one with finite rate, a transition to excited states inevitably occurs and this induces an intrinsic computational error. We show that this computational error depends not only on the total computation time T but also on the time derivatives of the adiabatic parameter s(t) at the beginning and the end of evolution. Previous work [A. T. Rezakhani, A. K. Pimachev, and D. A. Lidar, Phys. Rev. A 82, 052305 (2010)] also suggested this result. With six typical paths, we systematically demonstrate how to optimally design an adiabatic path to reduce the computational errors. Our method has a clear physical picture and also explains the pattern of computational error. In this paper we focus on the quantum adiabatic search algorithm although our results are general.National Basic Research Program of China [2013CB921903, 2012CB921300]; National Natural Science Foundation of China [11274024, 11334001, 11429402]SCI(E)EIARTICLEwubiao@pku.edu.cn19