Related papers: Full state revivals in higher dimensional quantum …
Discrete-time quantum walks are well-known for exhibiting localization, a quantum phenomenon where the walker remains at its initial location with high probability. In companion with a joint Letter, we introduce oscillatory localization,…
Quantum walks, the quantum counterpart of classical random walks, are extensively studied for their applications in mathematics, quantum physics, and quantum information science. This study explores the periods and absolute zeta functions…
In this paper we unveil some features of a discrete-time quantum walk on the line whose coin depends on the temporal variable. After considering the most general form of the unitary coin operator, we focus on the role played by the two…
We consider two independent quantum walks on separate lines augmented by partial or full swapping of coins after each step. For classical random walks, swapping or not swapping coins makes little difference to the random walk…
The subject of this paper is a kind of dynamical systems called quantum walks. We study one-dimensional homogeneous analytic quantum walks U. We explain how to identify the space of all the uniform intertwining operators between these…
We consider quantum walks on the cycle in the non-stationary case where the `coin' operation is allowed to change at each time step. We characterize, in algebraic terms, the set of possible state transfers and prove that, as opposed to the…
A quantum walk is a time-homogeneous quantum-mechanical process on a graph defined by analogy to classical random walk. The quantum walker is a particle that moves from a given vertex to adjacent vertices in quantum superposition. Here we…
Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. However, the main impetus behind this interest is their use in quantum algorithms, which have always…
In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step towards this objective, the following question is being…
Entanglement is a key resource in many quantum information applications and achieving high values independently of the initial conditions is an important task. Here we address the problem of generating highly entangled states in a discrete…
We propose a new quantum numerical scheme to control the dynamics of a quantum walker in a two dimensional space-time grid. More specifically, we show how, introducing a quantum memory for each of the spatial grid, this result can be…
A simple coined quantum walk in one dimension can be characterized by a $SU(2)$ operator with three parameters which represents the coin toss. However, different such coin toss operators lead to equivalent dynamics of the quantum walker. In…
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 propose a variation of the quantum walk on a circle in phase space by conjoining the Hadamard coin flip with simultaneous displacement of the walker's location in phase space and show that this generalization is a proper quantum walk…
We show that a quantum state transfer, previously studied as a continuous time process in networks of interacting spins, can be achieved within the model of discrete time quantum walks with position dependent coin. We argue that due to…
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…
Quantum walks are versatile simulators of topological phases and phase transitions as observed in condensed matter physics. Here, we utilize a step dependent coin in quantum walks and investigate what topological phases we can simulate with…
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…
The quantum walk (QW) is the term given to a family of algorithms governing the evolution of a discrete quantum system and as such has a founding role in the study of quantum computation. We contribute to the investigation of QW phenomena…
We show that a genuine Parrondo paradox can emerge in two-state quantum walks without resorting to experimentally intricate high-dimensional coins. To achieve such goal we employ a time-dependent coin operator without breaking the…