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We present a numerical study of a model of quantum walk in a periodic potential on a line. We take the simple view that different potentials have different affects on the way in which the coin state of the walker is changed. For simplicity and definiteness, we assume that the walker's coin state is unaffected at sites without the potential, and rotated in an unbiased way according to the Hadamard matrix at sites with the potential. This is the simplest and most natural model of a quantum walk in a periodic potential with two coins. Six generic cases of such quantum walks are studied numerically. It is found that, of the six cases, four cases display significant localization effect where the walker is confined in the neighborhood of the origin for a sufficiently long time. Associated with such a localization effect is the recurrence of the probability of the walker returning to the neighborhood of the origin. 相似文献
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Change-over switch for quantum states transfer with topological channels in a circuit-QED lattice 下载免费PDF全文
We propose schemes to realize robust quantum states transfer between distant resonators using the topological edge states of a one-dimensional circuit quantum electrodynamics(QED)lattice.Analyses show that the distribution of edge states can be regulated accordingly with the on-site defects added on the resonators.And we can achieve different types of quantum state transfer without adjusting the number of lattices.Numerical simulations demonstrate that the on-site defects can be used as a change-over switch for high-fidelity single-qubit and two-qubit quantum states transfer.This work provides a viable prospect for flexible quantum state transfer in solid-state topological quantum system. 相似文献
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在一维分立时间量子行走中,通过静态和动态两种方式随机地断开连接边引入无序效应,研究了静态逾渗和动态逾渗对量子行走传输特性以及位置自由度和硬币自由之间纠缠的影响.随着演化时间的增加,静态逾渗会使得量子行走从弹道传输转变为安德森局域化,而动态逾渗则会使之转变为经典扩散.理想情况下,量子纠缠在较短的时间内就达到一个常数值E_0.静态逾渗量子行走的纠缠减小,并随着时间做无规振荡,而动态逾渗量子行走的纠缠则会随着时间光滑地增加,并在某一时间超过理想情况下的常数值,表现出动态逾渗增强量子纠缠的特性. 相似文献
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完全图KN 上某个顶点连接到图G将破坏其对称性. 为加速定位这类结构异常, 基于散射量子行走模型设计搜索算法, 首先给出了算法酉算子的定义, 在此基础上利用完全图的对称性, 将算法的搜索空间限定为一个低维的坍缩图空间. 以G为一个顶点的情况为例, 利用硬币量子行走模型上的研究结论简化了坍缩图空间中酉算子的计算, 并借助矩阵扰动理论分析算法演化过程. 针对星图SN 上结构异常的研究表明, 以星图中心节点为界将整个图分为左右两个部分, 当且仅当两部分在N→∞时具有相同的特征值, 搜索算法可以获得量子加速. 本文说明星图上的分析方法和结论可以推广至完全图的坍缩图上. 基于此, 本文证明无论完全图连接的图G结构如何, 搜索算法均可在O(√N) 时间内定位到目标顶点, 成功概率为1-O(1√N), 即量子行走搜索该类异常与经典搜索相比有二次加速. 相似文献
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The stopping time of a one-dimensional bounded classical random walk(RW) is defined as the number of steps taken by a random walker to arrive at a fixed boundary for the first time.A quantum walk(QW) is a non-trivial generalization of RW,and has attracted a great deal of interest from researchers working in quantum physics and quantum information.In this paper,we develop a method to calculate the stopping time for a one-dimensional QW.Using our method,we further compare the properties of stopping time for QW and RW.We find that the mean value of the stopping time is the same for both of these problems.However,for short times,the probability for a walker performing a QW to arrive at the boundary is larger than that for a RW.This means that,although the mean stopping time of a quantum and classical walker are the same,the quantum walker has a greater probability of arriving at the boundary earlier than the classical walker. 相似文献
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We implement a quantum walk in phase space with a new mechanism based on the superconducting resonator-assisted double quantum dots.By analyzing the hybrid system,we obtain the necessary factors implementing a quantum walk in phase space:the walker,coin,coin flipping and conditional phase shift.The coin flipping is implemented by adding a driving field to the resonator.The interaction between the quantum dots and resonator is used to implement conditional phase shift.Furthermore,we show that with different driving fields the quantum walk in phase space exhibits a ballistic behavior over 25 steps and numerically analyze the factors influencing the spreading of the walker in phase space. 相似文献
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《Physics letters. A》2020,384(32):126828
We simulate various topological phenomena in condense matter, such as formation of different topological phases, boundary and edge states, through two types of quantum walk with step-dependent coins. Particularly, we show that one-dimensional quantum walk with step-dependent coin simulates all types of topological phases in BDI family, as well as all types of boundary and edge states. In addition, we show that step-dependent coins provide the number of steps as a controlling factor over the simulations. In fact, with tuning number of steps, we can determine the occurrences of boundary, edge states and topological phases, their types and where they should be located. These two features make quantum walks versatile and highly controllable simulators of topological phases, boundary, edge states, and topological phase transitions. We also report on emergences of cell-like structures for simulated topological phenomena. Each cell contains all types of boundary (edge) states and topological phases of BDI family. 相似文献
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Quantum walks have been investigated as they have remarkably different features in contrast to classical random walks. We present a quantum walk in a one-dimensional architecture, consisting of two coins and a walker whose evolution is in both position and phase spaces alternately controlled by the two coins respectively. By analyzing the dynamics evolution of the walker in both the position and phase spaces, we observe an influence on the quantum walk in one space from that in the other space, which behaves like decoherence. We propose an implementation of the two-coin quantum walk in both position and phase spaces via cavity quantum electrodynamics(QED). 相似文献
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The quantum properties of topological insulator magnetic quantum rings formed by inhomogeneous magnetic fields are investigated using a series expansion method for the modified Dirac equation. Cycloid-like and snake-like magnetic edge states are respectively found in the bulk gap for the normal and inverted magnetic field profiles. The energy spectra, current densities and classical trajectories of the magnetic edge states are discussed in detail. The bulk band inversion is found to manifest itself through the angular momentum transition in the ground state for the cycloid-like states and the resonance tunneling effect for the snake-like states. 相似文献
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Clement Ampadu 《中国物理 B》2014,(3):109-111
We study the average position and the symmetry of the distribution in the SU(2) open quantum random walk (OQRW). We show that the average position in the central limit theorem (CLT) is non-uniform compared with the average position in the non-CLT. The symmetry of distribution is shown to be even in the CLT. 相似文献
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Irreversibility of a quantum walk induced by controllable decoherence employing random unitary operations 下载免费PDF全文
Quantum walk is different from random walk in reversibility and interference. Observation of the reduced re- versibility in a realistic quantum walk is of scientific interest in understanding the unique quantum behavior. We propose an idea to experimentally investigate the decoherence-induced irreversibility of quantum walks with trapped ions in phase space via the average fidelity decay. By introducing two controllable decoherence sources, i.e., the phase damping channel (i.e., dephasing) and the high temperature amplitude reservoir (i.e., dissipation), in the intervals between the steps of quantum walk, we find that the high temperature amplitude reservoir shows more detrimental effects than the phase damping channel on quantum walks. Our study also shows that the average fidelity decay works better than the position variance for characterizing the transition from quantum walks to random walk. Experimental feasibility to monitor the irreversibility is justified using currently available techniques. 相似文献
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By using the Bloch eigenmode matching approach, we numerically study the evolution of individual quantum Hall edge states with respect to disorder. As demonstrated by the two-parameter renormalization group flow of the Hall and Thouless conductances, quantum Hall edge states with high Chern number n are completely different from that of the n = 1 case. Two categories of individual edge modes are evaluated in a quantum Hall system with high Chern number. Edge states from the lowest Landau level have similar eigenfunctions that are well localized at the system edge and independent of the Fermi energy. On the other hand, at fixed Fermi energy, the edge state from higher Landau levels exhibit larger expansion, which results in less stable quantum Hall states at high Fermi energies. By presenting the local current density distribution, the effect of disorder on eigenmode-resolved edge states is distinctly demonstrated. 相似文献
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High Chern number phase in topological insulator multilayer structures: A Dirac cone model study 下载免费PDF全文
Yi-Xiang Wang 《中国物理 B》2022,31(9):90501-090501
We employ the Dirac cone model to explore the high Chern number (C) phases that are realized in the magnetic-doped topological insulator (TI) multilayer structures by Zhao et al. [Nature 588 419 (2020)]. The Chern number is calculated by capturing the evolution of the phase boundaries with the parameters, then the Chern number phase diagrams of the TI multilayer structures are obtained. The high-C behavior is attributed to the band inversion of the renormalized Dirac cones, along with which the spin polarization at the $varGamma$ point will get increased. Moreover, another two TI multilayer structures as well as the TI superlattice structures are studied. 相似文献
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J. WanX.P. Xu 《Physica A》2012,391(5):1919-1927
The recurrence properties of random walks can be characterized by Pólya number, i.e., the probability that the walker has returned to the origin at least once. In this paper, we investigate Pólya number and first return for bursty random walk on a line, in which the walk has different step size and moving probabilities. Using the concept of the Catalan number, we obtain exact results for first return probability, the average first return time and Pólya number for the first time. We show that Pólya number displays two different functional behavior when the walk deviates from the recurrent point. By utilizing the Lagrange inversion formula, we interpret our findings by transferring Pólya number to the closed-form solutions of an inverse function. We also calculate Pólya number using another approach, which corroborates our results and conclusions. Finally, we consider the recurrence properties and Pólya number of two variations of the bursty random walk model. 相似文献
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利用有序算符内的积分技术,给出了三参数双模压缩算符,构建了三参数双模压缩粒子数态,并且研究了该量子态的压缩效应、反聚束效应和对Cauchy-Schwartze不等式的违背.给出了量子态产生压缩效应和反聚束效应的条件,以及三参数双模压缩粒子数态的Wigner函数的解析式.讨论了参数变化和光子数变化对压缩效应、反聚束效应和Cauchy-Schwartze不等式的违背的影响.研究结果表明:随光子数的增大,压缩效应、反聚束效应和光场两模间的非经典相关性减弱;另一方面,随参数模的增大,压缩效应增强,但反聚束效应和光场两模间的非经典相关性却减弱. 相似文献
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Symmetry protected topological states (SPTs) have the same symmetry and the phase transition between them are beyond Landau?s symmetry breaking formalism. In this paper we study (1) the critical theory of phase transition between trivial and non-trivial SPTs, and (2) the relation between such critical theory and the gapless boundary theory of SPTs. Based on examples of SO(3) and SU(2) SPTs, we propose that under appropriate boundary condition the critical theory contains the delocalized version of the boundary excitations. In addition, we prove that the boundary theory is the critical theory spatially confined between two SPTs. We expect these conclusions to hold in general and, in particular, for discrete symmetry groups as well. 相似文献