Quasienergy Spectrum,entropy And Temperature In Quantum Walks System

Quantum walks are analogs of classical random walks and they are also quantum versions of cellular automata model.Classical random walks often are used to design classical algorithms for complex problems.Quantum walk can provide speed-up in computational power for various algorithms such as spatial search and graph connectivity.Now quantum walks are used in a wide range of applications in mathematics,physics,biology,medicine,computer science and engineering.At the same time,quantum walks can simulate the dynamical behavior of many physical systems such as Anderson localization and topology transition.Based on the theory of quantum walks,we do three works:First,energy level statistics is an effective method to characterize Anderson localization.We apply it to reflect the Anderson localization properties in quantum walks.Using Floquet theory,the quasienergy spectrum of one-dimensional periodic,quasiperiodic and random quantum walks are calculated.The correlation dimension,energy level spacing ratio and inverse participation ratio are focused.We found they increase with spreading exponent and surviving exponent.Therefore,the dynamical properties of DTQWs can also be understood from the view of the statistics of quasienergy spectrum.Second,three-state quantum walks have richer dynamical properties with the addition of stopped and immobile states to traditional quantum walks.Under the amplitude damping channel and broken link noise,we focus on the entroy and temperature properties of the three-state quantum walk.Results show that both amplitude damping channel and broken link noise can enhance the entanglement in coin space and position space with relative small noise intensity.Entanglement is relatively large at high temperature,and it is relatively small at low temperature.At last,quasiperiodic sequences are extensively studied in condensed matter physics,quantum optics,and materials science.For Fibonacci quasiperiodic quantum walks,we focus on the entroy and temperature properties in the amplitude damping channel and broken link noise,respectively.As comparisons,we also study periodic and random quantum walks.We find that the entanglement of Fibonacci quasiperiodic quantum walks is the same as that of periodic quantum walks for amplitude damping channel;the entanglement of Fibonacci quasiperiodic quantum walks is almost the same as that of random quantum walks for broken link noise.