相关论文: Connecting the discrete and continuous-time quantu…

We address the problem of the construction of quantum walks on Cayley graphs. Our main motivation is the relationship between quantum algorithms and quantum walks. In particular, we discuss the choice of the dimension of the local Hilbert…

Coin and scattering are the two major formulations for discrete quantum walks models, each believed to have its own advantages in different applications. Although they are related in some cases, it was an open question their equivalence in…

We study the entanglement dynamics of discrete time quantum walks acting on bounded finite sized graphs. We demonstrate that, depending on system parameters, the dynamics may be monotonic, oscillatory but highly regular, or quasi-periodic.…

For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus,…

A quantum walk is the quantum analogue of a random walk. While it is relatively well understood how quantum walks can speed up random walk hitting times, it is a long-standing open question to what extent quantum walks can speed up the…

This article aims to provide an introductory survey on quantum random walks. Starting from a physical effect to illustrate the main ideas we will introduce quantum random walks, review some of their properties and outline their striking…

Discrete-time quantum walks are considered a counterpart of random walks and the study for them has been getting attention since around 2000. In this paper, we focus on a quantum walk which generates a probability distribution splitting to…

In discrete time, coined quantum walks, the coin degrees of freedom offer the potential for a wider range of controls over the evolution of the walk than are available in the continuous time quantum walk. This paper explores some of the…

The development of quantum walks in the context of quantum computation, as generalisations of random walk techniques, led rapidly to several new quantum algorithms. These all follow unitary quantum evolution, apart from the final…

We present a discrete-time, one-dimensional quantum walk based on the entanglement between the momentum of ultracold rubidium atoms (the walk space) and two internal atomic states (the "coin" degree of freedom). Our scheme is highly…

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…

When confined to a topological environment consisting of a cycle coupled with a half-line, quantum walks exhibit long-term statistical tendencies which differ dramatically from the tendencies of classical random walks in the same…

Quantum walks (QWs) exhibit different properties compared with classical random walks (RWs), most notably by linear spreading and localization. In the meantime, random walks that replicate quantum walks, which we refer to as…

Quantum random walks are shown to have non-intuitive dynamics, which makes them an attractive area of study for devising quantum algorithms for well-known classical problems as well as those arising in the field of quantum computing. In…

We look at two possible routes to classical behavior for the discrete quantum random walk on the line: decoherence in the quantum ``coin'' which drives the walk, or the use of higher-dimensional coins to dilute the effects of interference.…

Quantum versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times respectively. Non-unitary quantum walks can provide a useful optimisation of these…

One-dimensional discrete-time quantum walk has played an important role in development of quantum algorithms and protocols for different quantum simulations. The speedup observed in quantum walk algorithms is attributed to quantum…

Propagation in quantum walks is revisited by showing that very general 1D discrete-time quantum walks with time- and space-dependent coefficients can be described, at the continuous limit, by Dirac fermions coupled to electromagnetic…

Classical randomized algorithms use a coin toss instruction to explore different evolutionary branches of a problem. Quantum algorithms, on the other hand, can explore multiple evolutionary branches by mere superposition of states. Discrete…

We use quantum walks to construct a new quantum algorithm for element distinctness and its generalization. For element distinctness (the problem of finding two equal items among N given items), we get an O(N^{2/3}) query quantum algorithm.…