General error estimate for adiabatic quantum computing

Most investigations devoted to the conditions for adiabatic quantum computing are based on the first-order correction /Delta E-2(t)<< 1. However, it is demonstrated that this first-order correction does not yield a good estimate for the computational error. Therefore, a more general criterion is proposed, which includes higher-order corrections as well, and shows that the computational error can be made exponentially small-which facilitates significantly shorter evolution times than the above first-order estimate in certain situations. Based on this criterion and rather general arguments and assumptions, it can be demonstrated that a run-time T of order of the inverse minimum energy gap Delta E-min is sufficient and necessary, i.e., T=O(Delta E-min(-1)). For some examples, these analytical investigations are confirmed by numerical simulations.