Related papers: Quantum walk on a line for a trapped ion
Quantum walks can be used either as tools for quantum algorithm development or as entanglement generators, potentially useful to test quantum hardware. We present a novel algorithm based on a discrete Hadamard quantum walk on a line with…
The quantum random walk has drawn special interests because its remarkable features to the classical counterpart could lead to new quantum algorithms. In this paper, we propose a feasible scheme to implement quantum random walks on a line…
A new model that maps a quantum random walk described by a Hadamard operator to a particular case of a random walk is presented. The model is represented by a Markov chain with a stochastic matrix, i.e., all the transition rates are…
Inspired by the classical phenomenon of random walk, the concept of quantum walk has emerged recently as a powerful platform for the dynamical simulation of complex quantum systems, entanglement production and universal quantum computation.…
We present numerical study of a model of quantum walk in periodic potential on the line. We take the simple view that different potentials affect differently the way the coin state of the walker is changed. For simplicity and definiteness,…
Quantum walks have by now been realized in a large variety of different physical settings. In some of these, particularly with trapped ions, the walk is implemented in phase space, where the corresponding position states are not orthogonal.…
We propose a scheme to implement the one-dimensional coined quantum walk with electrons transported through a two-dimensional network of spintronic semiconductor quantum rings. The coin degree of freedom is represented by the spin of the…
We consider asymptotic behaviour of a Hadamard walk on a cycle. For a walk which starts with a state in which all the probability is concentrated on one node, we find the explicit formula for the limiting distribution and discuss its…
In this paper we investigate one dimensional quantum walks with two-step memory, which can be viewed as an extension of quantum walks with one-step memory. We develop a general formula for the amplitudes of the two-step-memory walk with…
Quantum walks can reconstruct quantum algorithms for quantum computation, where the precise controls of quantum state transfers between arbitrary distant sites are required. Here, we investigate quantum walks using a periodically…
Quantum state preparation in high-dimensional systems is an essential requirement for many quantum-technology applications. The engineering of an arbitrary quantum state is, however, typically strongly dependent on the experimental platform…
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…
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…
Quantum walks, whose dynamics is prescribed by alternating unitary coin and shift operators, possess topological phases akin to those of Floquet topological insulators, driven by a time-periodic field. While there is ample theoretical work…
We clarify that coined quantum walk is determined by only the choice of local quantum coins. To do so, we characterize coined quantum walks on graph by disjoint Euler circles with respect to symmetric arcs. In this paper, we introduce a new…
Quantum walks and random walks bear similarities and divergences. One of the most remarkable disparities affects the probability of finding the particle at a given location: typically, almost a flat function in the first case and a…
We present a discrete-time, one-dimensional quantum walk based on the entanglement between the momentum of ultracold rubidium atoms (the walk space) and two internal atomic states (the "coin" degree of freedom). Our scheme is highly…
We examine the physical implementation of a discrete time quantum walk with a four-dimensional coin. Our quantum walker is a photon moving repeatedly through a time delay loop, with time being our position space. The quantum coin is…
We propose a novel implementation of discrete time quantum walks for a neutral atom in an array of optical microtraps or an optical lattice. We analyze a one-dimensional walk in position space, with the coin, the additional qubit degree of…
We study the motion of M particles performing a quantum walk on the line. Under various conditions on the initial coin states for quantum walkers controlled by the Hadamard operator, we give theoretical criterion to observe the quantum…