Related papers: Mimicking the probability distribution of a two-di…
We have recently proposed a two-dimensional quantum walk where the requirement of a higher dimensionality of the coin space is substituted with the alternance of the directions in which the walker can move [C. Di Franco, M. Mc Gettrick, and…
We present a new scheme for a discrete-time quantum walk on two- and three-dimensional lattices using a two-state particle. We use different Pauli basis as translational eigestates for different axis and show that the coin operation, which…
Localization phenomena of quantum walks makes the propagation dynamics of a walker strikingly different from that corresponding to classical random walks. In this paper, we study the localization phenomena of four-state discrete-time…
One of the proposals for the exploitation of two-dimensional quantum walks has been the efficient generation of entanglement. Unfortunately, the technological effort required for the experimental realization of standard two-dimensional…
Exploiting multi-dimensional quantum walks as feasible platforms for quantum computation and quantum simulation is attracting constantly growing attention from a broad experimental physics community. Here, we propose a two-dimensional…
Quantum walks, both discrete (coined) and continuous time, form the basis of several recent quantum algorithms. Here we use numerical simulations to study the properties of discrete, coined quantum walks. We investigate the variation in the…
One-parameter family of discrete-time quantum-walk models on the square lattice, which includes the Grover-walk model as a special case, is analytically studied. Convergence in the long-time limit $t \to \infty$ of all joint moments of two…
While completely self-avoiding quantum walks have the distinct property of leading to a trivial unidirectional transport of a quantum state, an interesting and non-trivial dynamics can be constructed by restricting the self-avoidance to a…
In typical discrete-time quantum walk algorithms, one measures the position of the walker while ignoring its internal spin/coin state. Rather than neglecting the information in this internal state, we show that additionally measuring it…
We introduce the Peierls substitution to a two-dimensional discrete-time quantum walk on a square lattice to examine the spreading dynamics and the coin-position entanglement in the presence of an artificial gauge field. We use the ratio of…
We report on the possibility of controlling quantum random walks with a step-dependent coin. The coin is characterized by a (single) rotation angle. Considering different rotation angles, one can find diverse probability distributions for…
We analyze the role of dimensionality in the time evolution of discrete time quantum walks through the example of the three-state walk on a two-dimensional, triangular lattice. We show that the three-state Grover walk does not lead to…
We study one-dimensional quantum walk with four internal degrees of freedom resulted from two entangled qubits. We will demonstrate that the entanglement between the qubits and its corresponding coin operator enable one to steer the…
We present a mathematical formalism for the description of unrestricted quantum walks with entangled coins and one walker. The numerical behaviour of such walks is examined when using a Bell state as the initial coin state, two different…
The Grover walk, which is related to the Grover's search algorithm on a quantum computer, is one of the typical discrete time quantum walks. However, a localization of the two-dimensional Grover walk starting from a fixed point is striking…
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…
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…
We put forward a new, versatile and highly-scalable experimental setup for the realization of discrete two-dimensional quantum random walks with a single-qubit coin and tunable degree of decoherence. The proposed scheme makes use of a small…
We offer theoretical explanations for some recent observations in numerical simulations of quantum random walks (QRW). Specifically, in the case of a QRW on the line with one particle (walker) and two entangled coins, we explain the…
The three-state Grover walk on a line exhibits the localization effect characterized by a non-vanishing probability of the particle to stay at the origin. We present two continuous deformations of the Grover walk which preserve its…