Related papers: Driven Discrete Time Quantum Walks
The quantum walk was introduced as a quantum counterpart of the random walk and has been intensively studied since around 2000. Its applications include topological insulators, radioactive waste reduction, and quantum search. The first…
We analyze a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum-walk features such as localization that starkly distinguishes classical from quantum…
We study the evolution of initially extended distributions in the coined quantum walk on the line by analyzing the dispersion relation of the process and its associated wave equations. This allows us, in particular, to devise an initially…
Quantum walks exhibit many unique characteristics compared to classical random walks. In the classical setting, self-avoiding random walks have been studied as a variation on the usual classical random walk. Classical self-avoiding random…
The Hadamard walk is a typical model of the discrete-time quantum walk. We investigate sojourn times of the Hadamard walk on a line by a path counting method.
The staggered quantum walk is a type of discrete-time quantum walk model without a coin which can be generated on a graph using particular partitions of the graph nodes. We design Hamiltonians for potential realization of the staggered…
We study the effects of interparticle interactions and power-law tunneling couplings on quantum walks executed by both a single one and a pair of hard-core bosons moving in clean and disordered one-dimensional lattices. For this purpose, we…
We address the question of symmetries of an important type of quantum walks. We introduce all the necessary definitions and provide a rigorous formulation of the problem. Using a thorough analysis, we reach the complete answer by presenting…
This paper establishes a robust link between quantum dynamics and classical ones by deriving probabilistic representation for both continuous time and discrete time quantum walks. We first adapt Molchanov formula, originally employed in the…
We experimentally demonstrate a quantum walk on a line in phase space using one and two trapped ion. A walk with up to 23 steps is realized by subjecting an ion to state-dependent displacement operations interleaved with quantum coin…
We use simple deterministic dynamical systems as coins in studying quantum walks. These dynamical systems can be chosen to display, in the classical limit, a range of behaviors from the integrable to chaotic, or deterministically random. As…
We analyze final-time dependent discrete-time quantum walks in one dimension. We compute asymptotics of the return probability of the quantum walk by a path counting approach. Moreover, we discuss a relation between the quantum walk and the…
We give a quantum algorithm for finding a marked element on the grid when there are multiple marked elements. Our algorithm uses quadratically fewer steps than a random walk on the grid, ignoring logarithmic factors. This is the first known…
How self-loops on vertices affect quantum walks is an interesting issue, and self-loops play important roles in quantum walk based algorithms. However, the original model that adjusting the effect of self-loops by changing their number has…
We analyze the application of the history state formalism to quantum walks. The formalism allows one to describe the whole walk through a pure quantum history state, which can be derived from a timeless eigenvalue equation. It naturally…
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 show that a one-dimensional discrete time quantum walk can be used to implement a generalized measurement in terms of positive operator value measure (POVM) on a single qubit. More precisely, we show that for a single qubit any set of…
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…
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…
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.…