Amplitude amplification and estimation using the atom-optics kicked rotor

Abstract

The atom-optics realization of the quantum kicked rotor represents one of the most well-studied experimental platforms for the physics of Anderson localization. In this work, we show that the same platform can be used to implement a quantum algorithm to perform quantum amplitude amplification (AA), a generalization of Grover's search algorithm. This is done using the usual kick sequence in combination with the well established technique of Raman velocity selection. We argue that this platform is well suited to implement AA, as its characteristic property of localization can be exploited to enhance the performance of the amplitude amplification algorithm by reducing its average runtime. We also introduce a kick potential which asymptotically leads to the optimal quantum speedup, constituting a complementary approach. Finally, we demonstrate that the scheme is fairly robust to noise in the kicks and discuss the experimental feasibility of each component of our proposal