相关论文: The quantum to classical transition for random wal…
In this paper for the first time, we construct quantum analogs starting from classical stochastic processes, by replacing random which path decisions with superpositions of all paths. This procedure typically leads to non-unitary quantum…
The quantum walk is a quantum counterpart of the classical random walk that exhibits nonclassical behaviors and outperforms the classical random walk in various aspects. It has been known that a single particle can be propagated by a…
We generalize the quantum random walk protocol for a particle in a one-dimensional chain, by using several types of biased quantum coins, arranged in aperiodic sequences, in a manner that leads to a rich variety of possible wave function…
We introduce the quantum stochastic walk (QSW), which determines the evolution of generalized quantum mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all…
Discrete time quantum walks are known to be universal for quantum computation. This has been proven by showing that they can simulate a universal quantum gate set. In this paper, we examine computation by quantum walks in terms of language…
We advance the previous studies of quantum walks on the line with two coins. Such four-state quantum walks driven by a three-direction shift operator may have nonzero stationary distributions (localization), thus distinguishing themselves…
The decoherence of quantum states defines the transition between the quantum world and classical physics. Decoherence or, analogously, quantum mechanical collapse events pose fundamental questions regarding the interpretation of quantum…
Exploring the quantum walk as a tool of generating various probability distributions and quantum entanglements is a topic of current interest. In the present work, we use extensive numerical simulations to investigate the influence of…
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of classical…
We study the quatum to classical transition process in the context of quantum field theory. Extending the influence functional formalism of Feynman and Vernon, we study the decoherence process for self-interacting quantum fields in flat…
Accurate modeling of the temporal evolution of asset prices is crucial for understanding financial markets. We explore the potential of discrete-time quantum walks to model the evolution of asset prices. Return distributions obtained from a…
We extract the information of a quantum motion and decode it into a certain orbit via a single measurable quantity. Such that a quantum chaotic system can be reconstructed as a chaotic attractor. Two configurations for reconstructing this…
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 effect of decoherence on the continuous-time quantum walk on the hypercube is revisited. Previously, an exact solution was found for a decoherence model that preserved the effective tensor-product form of the dynamics. Here a new model…
We analyze the long time behavior of a discrete time quantum walk subject to decoherence with a strong spatial dependence, acting on one half of the lattice. We show that, except for limiting cases on the decoherence parameter, the quantum…
We address the performance of a coin-biased quantum walk as a generator for non-classical position states of the walker. We exploit a phenomenon of coherent localisation in the position space --- resulting from the choice of small values of…
The dimensionality of the internal coin space of discrete-time quantum walks has a strong impact on the complexity and richness of the dynamics of quantum walkers. While two-dimensional coin operators are sufficient to define a certain…
We present analytical treatment of quantum walks on multidimensional hyper-cycle graphs. We derive the analytical expression of the probability distribution for strong and weak decoherence regimes. Upper bound to mixing time is obtained.
Quantum walks with long-range steps $R^{-\gamma}$ ($R$ being the distance between sites) on a discrete line behave in similar ways for all $\gamma\geq2$. This is in contrast to classical random walks, which for $\gamma >3$ belong to a…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…