摘要
In this paper, we study a kind of nonlinear model of adiabatic evolution in quantum search problem. As will be seen here, for this problem, there always exists a possibility that this nonlinear model can successfully solve the problem, while the linear model can not. Also in the same setting, when the overlap between the initial state and the final stare is sufficiently large, a simple linear adiabatic evolution can achieve O(1) time efficiency, but infinite time complexity for the nonlinear model of adiabatic evolution is needed. This tells us, it is not always a wise choice to use nonlinear interpolations in adiabatic algorithms. Sometimes, simple linear adiabatic evolutions may be sufficient for using.
作者
孙杰
路松峰
孙杰;路松峰(School of Computer Science and Technology,Huazhong University of Science and Technology;College of Educational Information and Technology,Hubei Normal University)
基金
Supported by the National Natural Science Foundation of China under Grant Nos.61402188 and 61173050
the support from the China Postdoctoral Science Foundation under Grant No.2014M552041
