In the quantum adiabatic algorithm, as the adiabatic parameter $s\left(t\right)$ 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 $s\left(t\right)$ 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.

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• Quantum algorithms
• Quantum error correction