相关论文: Quantum Walks On Graphs

Quantum walks are well-known for their ballistic dispersion, traveling $\Theta(t)$ away in $t$ steps, which is quadratically faster than a classical random walk's diffusive spreading. In physical implementations of the walk, however, the…

In this dissertation we demonstrate that the continuous-time quantum walk models remain powerful for nontrivial graph structures. We consider two aspects of this problem. First, it is known that the standard Continuous-Time Quantum Walk…

In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the nowadays widespread discrete-time quantum walk on a line. Here the walker at each time step can either remain in…

We propose a phenomenon of discrete-time quantum walks on graphs called the pulsation, which is a generalization of a phenomenon in the quantum searches. This phenomenon is discussed on a composite graph formed by two connected graphs…

Quantum random walks represent a powerful tool for the implementation of various quantum algorithms. We consider a convolution problem for the graphs which provide quantum and classical random walks. We suggest a new method for lattices and…

The quantum walk was originally proposed as a quantum mechanical analogue of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete time quantum walks provide a…

Quantum versions of random walks on the line and cycle show a quadratic improvement in their spreading rate and mixing times respectively. The addition of decoherence to the quantum walk produces a more uniform distribution on the line, and…

In this paper we extend the concept of persistence, well defined for classical stochastic dynamics, to the context of quantum dynamics. We demonstrate the idea via quantum random walk and a successive measurement scheme, where persistence…

We analyze the solution of the coined quantum walk on a line. First, we derive the full solution, for arbitrary unitary transformations, by using a new approach based on the four "walk fields" which we show determine the dynamics. The…

A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. For a long time, these models have interested the community for their nice properties such as locality or translation invariance. This…

We consider quantum random walks on congested lattices and contrast them to classical random walks. Congestion is modelled with lattices that contain static defects which reverse the walker's direction. We implement a dephasing process…

We introduce quantum walks with a time-dependent coin, and show how they include, as a particular case, the generalized quantum walk recently studied by Wojcik et al. {[}Phys. Rev. Lett. \textbf{93}, 180601(2004){]} which exhibits…

We introduce a fidelity-based measure $\text{D}_{\text{CQ}}(t)$ to quantify the differences between the dynamics of classical (CW) and quantum (QW) walks over a graph. We provide universal, graph-independent, analytic expressions of this…

Quantum walks play an important role in the area of quantum algorithms. Many interesting problems can be reduced to searching marked states in a quantum Markov chain. In this context, the notion of quantum hitting time is very important,…

We give new observations on the mixing dynamics of a continuous-time quantum walk on circulants and their bunkbed extensions. These bunkbeds are defined through two standard graph operators: the join G + H and the Cartesian product of…

Quantum walks, being the quantum analogue of classical random walks, are expected to provide a fruitful source of quantum algorithms. A few such algorithms have already been developed, including the `glued trees' algorithm, which provides…

Quantum walks function as essential means to implement quantum simulators, allowing one to study complex and often directly inaccessible quantum processes in controllable systems. In this contribution, the notion of a driven Gaussian…

It is well-known that classical random walks on regular graphs converge to the uniform distribution. Quantum walks, in their various forms, are quantizations of their corresponding classical random walk processes. Gerhardt and Watrous…

It is demonstrated that in contrast to the well-known case with a quantum particle moving freely in a real line, the wave packets corresponding to the coherent states for a free quantum particle on a circle do not spread but develop…

The quantum walk differs fundamentally from the classical random walk in a number of ways, including its linear spreading and initial condition dependent asymmetries. Using stationary phase approximations, precise asymptotics have been…