Amplitude Amplification and Estimation using a Floquet system

TL;DR

This paper demonstrates how the quantum kicked rotor, a well-studied Floquet system, can implement amplitude amplification and estimation algorithms, leveraging its dynamical localization to improve performance and analyzing robustness and experimental feasibility.

Contribution

It introduces a novel use of the quantum kicked rotor for quantum algorithms like amplitude amplification and estimation, exploiting its localization properties.

Findings

QKR can implement amplitude amplification and estimation algorithms.

Dynamical localization enhances algorithm performance by reducing runtime.

The robustness of the QKR-based algorithms is confirmed under noise and detuning.

Abstract

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.