On the optimal schedule of adiabatic quantum computing

A closer look at the adiabatic theorem of quantum mechanics suggests conditions for an optimal schedule in adiabatic quantum computing. If these conditions are satisfied, the computation time is proportional to the inverse of the minimum energy gap. Analytical calculations show that the computation time T for the adiabatic quantum search algorithm is T = 2 N acosh ( ε - 1 ) , where N is the number of search items and 1 - ε 2 is the probability to measure the searched state. For small ε , the calculated time is significantly shorter than the proposed T ∼ π / 2 N ε - 1 . The results are confirmed by numerical simulations for both the search algorithm and a toy problem.