Related papers: Quantum search with a continuous-time quantum walk…
We study the distributions of the continuous-time quantum walk on a one-dimensional lattice. In particular we will consider walks on unbounded lattices, walks with one and two boundaries and Dirichlet boundary conditions, and walks with…
An ideal quantum walk transitions from one vertex to another with perfect fidelity, but in physical systems, the particle may be hindered by potential energy barriers. Then the particle has some amplitude of tunneling through the barriers,…
When classically searching a database, having additional correct answers makes the search easier. For a discrete-time quantum walk searching a graph for a marked vertex, however, additional marked vertices can make the search harder by…
The discrete time quantum walk defined as a quantum-mechanical analogue of the discrete time random walk have recently been attracted from various and interdisciplinary fields. In this review, the weak limit theorem, that is, the asymptotic…
The quantum walk was originally proposed as a quantum mechanical analogue of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete time quantum walks provide a…
Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or…
Focusing on a continuous-time quantum walk on $\mathbb{Z}=\left\{0,\pm 1,\pm 2,\ldots\right\}$, we analyze a probability distribution with which the quantum walker is observed at a position. The walker launches off at a localized state and…
Continuous-time quantum walks provide an alternative method for quantum search problems. Most of the earlier studies confirmed that quadratic speedup exists in some synthetic Hamiltonians, but whether there is quadratic speedup in real…
A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal…
Quantum walks in atomic systems, owing to their continuous nature, are especially well-suited for the simulation of many-body physics and can potentially offer an exponential speedup in solving certain black box problems. Photonics offers…
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 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…
Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more…
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…
Describing a particle in an external electromagnetic field is a basic task of quantum mechanics. The standard scheme for this is known as "minimal coupling", and consists of replacing the momentum operators in the Hamiltonian by modified…
One-dimensional discrete-time quantum walks show a rich spectrum of topological phases that have so far been exclusively analysed in momentum space. In this work we introduce an alternative approach to topology which is based on the…
We show that a quantum walk process can be used to construct and secure quantum memory. More precisely, we show that a localized quantum walk with temporal disorder can be engineered to store the information of a single, unknown qubit on a…
The first general analytic solutions for the one-dimensional walk in position and momentum space are derived. These solutions reveal, among other things, new symmetry features of quantum walk probability densities and further insight into…
Quantum algorithms for searching one or more marked items on a d-dimensional lattice provide an extension of Grover's search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms…
Propagation and interference of quantum-mechanical particles comprise an important part of elementary processes in quantum physics, and their essence can be modeled using a quantum walk, a mathematical concept that describes the motion of a…