On the Circuit Model of Global Adiabatic Search Algorithm

Local adiabatic search has been implemented on the quantum circuit model, and the time steps necessary to guarantee the approximation precision are of the same order as the time complexity of the algorithm. However, it is easy to verify that this conclusion doesn't hold for global adiabatic search. But we know that adiabatic computing is equivalent to the circuit model of quantum computation. Therefore, there must exist a corresponding quantum circuit that correctly implements such a global adiabatic search. In this Letter, we show that this indeed could be true.