Can quantum computer perform better than classical?

Abstract

A theoretical model of a quantum device which can factorize any number N in two steps i.e. by preparing an input state and performing a measurement is discussed. The analysis reveals that the duration of state preparation and measurement is proportional to N while the energy consumption grows like log N. These results suggest the existence of Heisenberg-type relation putting limits on the efficiency of a quantum computer in terms of a total computation time, a total energy consumption and a classical complexity of the problem.