共查询到20条相似文献,搜索用时 15 毫秒
1.
We investigate the evolution of a discrete-time one-dimensional quantum walk driven by a position-dependent coin. The rotation angle, which depends upon the position of a quantum particle, parameterizes the coin operator. For different values of the rotation angle, we observe that such a coin leads to a variety of probability distributions, e.g. localized, periodic, classicallike, semi-classical-like, and quantum-like. Further, we study the Shannon entropy associated with position and the coin space of a quantum particle, and compare them with the case of the position-independent coin. Our results show that the entropy is smaller for most values of the rotation angle as compared to the case of the position-independent coin. We also study the effect of entanglement on the behavior of probability distribution and Shannon entropy by considering a quantum walk with two identical position-dependent entangled coins. We observe that in general, a wave function becomes more localized as compared to the case of the positionindependent coin and hence the corresponding Shannon entropy is lower. Our results show that a position-dependent coin can be used as a controlling tool of quantum walks. 相似文献
2.
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
3.
《中国物理 B》2015,(5)
In this paper, we discuss the properties of lazy quantum walks. Our analysis shows that the lazy quantum walks have O(t n) order of the n-th moment of the corresponding probability distribution, which is the same as that for normal quantum walks. The lazy quantum walk with a discrete Fourier transform(DFT) coin operator has a similar probability distribution concentrated interval to that of the normal Hadamard quantum walk. Most importantly, we introduce the concepts of occupancy number and occupancy rate to measure the extent to which the walk has a(relatively) high probability at every position in its range. We conclude that the lazy quantum walks have a higher occupancy rate than other walks such as normal quantum walks, classical walks, and lazy classical walks. 相似文献
4.
In the continuous space and time limit, we show that the probability density to find the quantum random walk (QRW) driven by the Hadamard "coin" solves a hyperbolic evolution equation similar to the one obtained for a random two-velocity evolution with spatially inhomogeneous transition rates between the velocity states. In spite of the presence of a nonlinear drift term, it is remarkable that the QRW position can easily be described in simple analytical terms. This allows us to derive the quadratic time dependence of the variance typical for the QRW. 相似文献
5.
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
6.
We present a quantum protocol for the task of weak coin flipping. We find that, for one choice of parameters in the protocol, the maximum probability of a dishonest party winning the coin flip if the other party is honest is 1/sqrt[2]. We also show that if parties restrict themselves to strategies wherein they cannot be caught cheating, their maximum probability of winning can be even smaller. As such, the protocol offers additional security in the form of cheat sensitivity. 相似文献
7.
量子行走是经典随机行走在量子力学框架下的对应, 理论上可以用来解决一类无序数据库的搜索问题. 因为携带信息的量子态的扩散速度与经典相比有二次方式的增长, 所以量子行走优于经典随机行走, 量子行走的特性值得加以利用. 量子行走作为一种新发现的物理现象的数学描述, 引发了一种新的思维方式, 孕育了一种新的理论计算模型. 最新研究表明, 量子行走本身也是一种通用计算模型, 可被视为设计量子算法的高级工具, 因此受到部分计算机理论科学领域学者的关注和研究. 对于多数问题求解方案的量子算法的设计, 理论上可以只在量子行走模型下进行考虑. 基于Grover算法的相位匹配条件, 本文提出了一个新的基于量子行走的搜索算法. 理论演算表明: 一般情况下本算法的时间复杂度与Grover算法相同, 但是当搜索的目标数目多于总数的1/3时, 本算法搜索成功的概率要大于Grover算法. 本文不但利用Grover算法中相位匹配条件构造了一个新的量子行走搜索算法, 而且在本研究室原有的量子电路设计研究成果的基础上给出了该算法的量子电路表述. 相似文献
8.
In the literature, there are numerous studies of one-dimensional discrete-time quantum walks (DTQWs) using a moving shift operator. However, there is no exact solution for the limiting probability distributions of DTQWs on cycles using a general coin or swapping shift operator. In this paper, we derive exact solutions for the limiting probability distribution of quantum walks using a general coin and swapping shift operator on cycles for the first time. Based on the exact solutions, we show how to generate symmetric quantum walks and determine the condition under which a symmetric quantum walk appears. Our results suggest that choosing various coin and initial state parameters can achieve a symmetric quantum walk. By defining a quantity to measure the variation of symmetry, deviation and mixing time of symmetric quantum walks are also investigated. 相似文献
9.
Alain Joye 《Communications in Mathematical Physics》2011,307(1):65-100
We consider the discrete time unitary dynamics given by a quantum walk on the lattice
\mathbb Zd{\mathbb {Z}^d} performed by a quantum particle with internal degree of freedom, called coin state, according to the following iterated rule:
a unitary update of the coin state takes place, followed by a shift on the lattice, conditioned on the coin state of the particle.
We study the large time behavior of the quantum mechanical probability distribution of the position observable in
\mathbb Zd{\mathbb {Z}^d} when the sequence of unitary updates is given by an i.i.d. sequence of random matrices. When averaged over the randomness,
this distribution is shown to display a drift proportional to the time and its centered counterpart is shown to display a
diffusive behavior with a diffusion matrix we compute. A moderate deviation principle is also proven to hold for the averaged
distribution and the limit of the suitably rescaled corresponding characteristic function is shown to satisfy a diffusion
equation. A generalization to unitary updates distributed according to a Markov process is also provided. 相似文献
10.
Quantum walk (QW), which is considered as the quantum counterpart of the classical random walk (CRW), is actually the quantum extension of CRW from the single-coin interpretation. The sequential unitary evolution engenders correlation between different steps in QW and leads to a non-binomial position distribution. In this paper, we propose an alternative quantum extension of CRW from the ensemble interpretation, named quantum random walk (QRW), where the walker has many unrelated coins, modeled as two-level systems, initially prepared in the same state. We calculate the walker's position distribution in QRW for different initial coin states with the coin operator chosen as Hadamard matrix. In one-dimensional case, the walker's position is the asymmetric binomial distribution. We further demonstrate that in QRW, coherence leads the walker to perform directional movement. For an initially decoherenced coin state, the walker's position distribution is exactly the same as that of CRW. Moreover, we study QRW in 2D lattice, where the coherence plays a more diversified role in the walker's position distribution. 相似文献
11.
The spatial distribution and transport of defect species in a mixed ionic-electronic conductor (MIEC) depend on the activity
of the external gas phase at either side of the MIEC, the defect equilibria and mobility of the species within the MIEC. Previous
researchers [1, 2] developed models for defect distribution and transport based on various assumptions, the most prevalent
of which is that the concentration of the ionic defect species is constant through the range of activities of the external
gas phase in which the MIEC finds application. However, the defect equilibria for many MIECs do not support this assumption.
It is desirable, therefore, to have explicit, analytical expressions for the spatial distribution of the defects as a function
of position and the flux as a function of the activity gradient of the defect species and the gas phase. Towards the development
of such a model, the defect concentration-oxygen partial pressure dependence in an oxide MIEC, such as Ce0.8Sm0.2O2−δ, is considered. From the defect equilibria, equations are developed for the dependence of the defect species on the oxygen
activity in the oxide MIEC. Then, to relate the defect equilibria to the spatial parameters of the MIEC, an analytic expression
for the variation of oxygen activity as a function of position in an electrolyte is derived. Equations relating oxygen activity
to position and defect concentration to oxygen activity are then combined to obtain a defect concentration-position relation.
All the relations are derived without the assumption of constant vacancy concentration. Finally, the results are compared
with those of previous models. 相似文献
12.
CLEMENT AMPADU 《理论物理通讯》2012,58(2):220-224
In this paper the return probability of the one-dimensional discrete-time quantum walk is studied. We derive probabilistic formulas for the return probability related to the quantum walk governed by the Fibonacci coin. 相似文献
13.
CLEMENT AMPADU 《理论物理通讯》2012,(8)
In this paper the return probability of the one-dimensional discrete-time quantum walk is studied. We derive probabilistic formulas for the return probability related to the quantum walk governed by the Fibonacci coin. 相似文献
14.
15.
In this paper, we study discrete-time quantum walks on
one-dimensional lattices. We find that the coherent dynamics
depends on the initial states and coin parameters. For infinite
size of lattices, we derive an explicit expression for the return
probability, which shows scaling behavior P(0, t) ~ t
-1 and
does not depends on the initial states of the walk. In the
long-time limit, the probability distribution shows various
patterns, depending on the initial states, coin parameters and the
lattice size. The time-averaged probability mixes to the limiting
probability distribution in linear time, i.e., the mixing time
M
ε
is a linear function of N (size of the lattices)
for large values of thresholds ϵ. Finally, we introduce
another kind of quantum walk on infinite or even-numbered size of
lattices, and show that by the method of mathematical induction,
the walk is equivalent to the traditional quantum walk with
symmetrical initial state and coin parameter. 相似文献
16.
A simple and accurate algorithm (phase scanning method) is proposed for 3D surface contouring and dynamic response determination of a vibrating object. A sinusoidal fringe pattern is projected onto a low-frequency vibrating object by a programmable liquid crystal display projector. The fringe patterns are captured by a high-speed CCD camera with a telecentric gauging lens. Phase values are evaluated point by point using phase scanning method. From the phase values of each point on the object, the contour of the specimen at different instants of vibration can be retrieved. In this paper, a small vibrating coin is used to demonstrate the validity of the method and the experimental results are compared with test results on a stationary coin using four-step phase shifting and fast Fourier transform methods. The technique is especially useful in applications where the vibrating object has a complicated shape. 相似文献
17.
We study the behaviour of the glued trees algorithm described by Childs et al. in [1] under decoherence. We consider a discrete time reformulation of the continuous time quantum walk protocol and apply a phase damping channel to the coin state, investigating the effect of such a mechanism on the probability of the walker appearing on the target vertex of the graph. We pay particular attention to any potential advantage coming from the use of weak decoherence for the spreading of the walk across the glued trees graph. 相似文献
18.
A way to synthesize three-dimensional phase-diffraction images of nanoobjects is proposed based on the numerical method of backward propagation of a field from the best focusing plane. The obtained phase images are used for solving the applied problem of object defect finding by methods of pattern recognition. The probability of defect detection by phase images is shown to be higher than for amplitude images. 相似文献
19.
The properties of the two-dimensional quantum walk with point,line,and circle disorders in phase are reported.Localization is observed in the two-dimensional quantum walk with certain phase disorder and specific initial coin states.We give an explanation of the localization behavior via the localized stationary states of the unitary operator of the walker+coin system and the overlap between the initial state of the whole system and the localized stationary states. 相似文献
20.
We consider the effect of different unitary noise mechanisms on the evolution of a quantum walk (QW) on a linear chain with a generic coin operation: (i) bit-flip channel noise, restricted to the coin subspace of the QW and (ii) topological noise caused by randomly broken links in the linear chain. Similarities and differences in the respective decoherent dynamics of the walker as a function of the probability per unit time of a decoherent event taking place are discussed. 相似文献