How Quantum is the Speedup in Adiabatic Unstructured Search?

Abstract: In classical computing, analog approaches have sometimes appeared to be more powerful than they really are. This occurs when resources, particularly precision, are not appropriately taken into account. While the same should also hold for analog quantum computing, precision issues are often neglected from the analysis. In this work we present a classical analog algorithm for unstructured search that can be viewed as analogous to the quantum adiabatic unstructured search algorithm devised by Roland and Cerf [Phys. Rev. A 65, 042308 (2002)]. We show that similarly to its quantum counterpart, the classical construction may also provide a quadratic speedup over standard digital unstructured search. We discuss the meaning and the possible implications of this result in the context of adiabatic quantum computing.