Amplitude Amplification and Estimation using a Floquet system

The quantum kicked rotor (QKR) is a fundamental model of time-dependent quantum chaos and the physics of Anderson localization. It is one of the most well-studied Floquet systems. In this work, it is shown that QKR can be used to implement a quantum algorithm to perform unstructured search; namely Amplitude Amplification, a generalization of Grover's search algorithm. Further, the QKR is employed for amplitude estimation when the amplitude of the marked states is unknown. It is also shown that the characteristic property of dynamical localization of the QKR can be exploited to enhance the performance of the amplitude amplification algorithm by reducing its average runtime. The sensitivity of the success probability of unstructured search to detuning from resonance and the effects of noisy kick strengths are analyzed and the robustness of the QKR based algorithm is demonstrated. The experimental feasibility of every component of the algorithm is discussed.