Related papers: An index theorem for split-step quantum walks

The discrete-time quantum walk is a quantum counterpart of the random walk. It is expected that the model plays important roles in the quantum field. In the quantum information theory, entanglement is a key resource. We use the von Neumann…

Quantum walks behave differently from what we expect and their probability distributions have unique structures. They have localization, singularities, a gap, and so on. Those features have been discovered from the view point of mathematics…

This paper gives the quantum walks determined by graph zeta functions. The result enables us to obtain the characteristic polynomial of the transition matrix of the quantum walk, and it determines the behavior of the quantum walk. We treat…

We propose an alternative definition of an N-dimensional coined quantum walk by generalizing a recent proposal [Di Franco et al., Phys. Rev. Lett. 106, 080502 (2011)]. This N-dimensional alternate quantum walk, AQW_N, in contrast with the…

We consider crossovers with respect to the weak convergence theorems from a discrete-time quantum walk (DTQW). We show that a continuous-time quantum walk (CTQW) and discrete- and continuous-time random walks can be expressed as DTQWs in…

We propose an implementation of a quantum walk on a circle on an optomechanical system by encoding the walker on the phase space of a radiation field and the coin on a two-level state of a mechanical resonator. The dynamics of the system is…

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…

Quantum walks are standard tools for searching graphs for marked vertices, and they often yield quadratic speedups over a classical random walk's hitting time. In some exceptional cases, however, the system only evolves by sign flips,…

This work describes a new algorithm for creating a superposition over the edge set of a graph, encoding a quantum sample of the random walk stationary distribution. The algorithm requires a number of quantum walk steps scaling as…

We introduce and analyze a one-dimensional quantum walk with two time-independent rotations on the coin. We study the influence on the property of quantum walk due to the second rotation on the coin. Based on the asymptotic solution in the…

This note introduces some examples of quantum random walks in d-dimensional Eucilidean space and proves the weak convergence of their rescaled n-step densities. One of the examples is called the Plancherel quantum walk because the "quantum…

In this paper, we introduce a multidimensional generalization of Kitagawa's split-step discrete-time quantum walk, study the spectrum of its evolution operator for the case of one defect coins, and prove localization of the walk. Using a…

Quantum walk has been regarded as a primitive to universal quantum computation. By using the operations required to describe the single particle discrete-time quantum walk on a position space we demonstrate the realization of the universal…

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 set the ground for a theory of quantum walks on graphs- the generalization of random walks on finite graphs to the quantum world. Such quantum walks do not converge to any stationary distribution, as they are unitary and reversible.…

We propose a quantum circuit design for implementing coined quantum walks on complex networks. In complex networks, the coin and shift operators depend on the varying degrees of the nodes, which makes circuit construction more challenging…

We demonstrate a quantum walk with time-dependent coin bias. With this technique we realize an experimental single-photon one-dimensional quantum walk with a linearly-ramped time-dependent coin flip operation and thereby demonstrate two…

We show that a multi-step quantum walk can be realized for a single trapped ion with interpolation between quantum and random walk achieved by randomizing the generalized Hadamard coin flip phase. The signature of the quantum walk is…

We study the model of quantum walks on cycles enriched by the addition of 1-step memory. We provide a formula for the probability distribution and the time-averaged limiting probability distribution of the introduced quantum walk. Using the…

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 lattice, we derive an explicit expression for the…