Continuous time quantum walks and the quantum kicked rotor

Abstract

The quantum kicked rotor (QKR) is a quintessential model for quantum chaos in floquet systems, with potential applications in quantum computing and quantum sensor development. We investigate the relation between the evolution of the QKR at quantum resonance conditions and a continuous-time quantum walk in one dimension. We show that the dynamics of a quasi-periodic rotor at resonance can be realized by temporally varying the transition probabilities of a continuous-time quantum walk. This correspondence can be used to engineer the initial states of a QKR to realize experimentally relevant distributions for downstream quantum information processing. To probe the quantum advantage by using the QKR as a system for search algorithms, we use a projective measurement approach to investigate the statistics of first detection times (FDT) with the detector placed at desired target sites. Unlike the classical random walk, the probability of the first detection for the QKR-continuous-time quantum walk, decays like (time)^−3 with superimposed oscillations. We further show that this advantage can be suppressed in the presence of noisy kicks.