Related papers: Realization of a quantum walk in phase space using…
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 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…
In the present paper, the first in a series of two, we propose a model of universal quantum computation using a fermionic/bosonic multi-particle continuous-time quantum walk with two internal states (e.g., the spin-up and down states of an…
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…
In this work we introduce discrete-time quantum walks in state space, more precisely on Fock-state lattices. Fock-state lattices provide a natural and clean setting for implementing lattice models, particularly in quantum optical systems.…
Quantum walk research has mainly focused on evolutions due to repeated applications of time-independent unitary coin operators. However, the idea of controlling the single particle evolution using time-dependent unitary coins has still been…
A unit evolution step of discrete-time quantum walks is determined by both a coin-flip operator and a position-shift operator. The behavior of quantum walkers after many steps delicately depends on the coin-flip operator and an initial…
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…
We present an approach using quantum walks (QWs) to redistribute ultracold atoms in an optical lattice. Different density profiles of atoms can be obtained by exploiting the controllable properties of QWs, such as the variance and the…
We introduce a variation of the discrete time quantum walk, the nonreversal quantum walk, which does not step back onto a position which it has just occupied. This allows us to simulate a dimer and we achieve it by introducing a new type of…
Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing…
Quantum walk is a synonym for multi-path interference and faster spread of a particle in a superposition of position space. We study the effects of a quantum mechanical interaction modeled to mimic quantum mechanical gravitational…
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 implement the proof of principle for the quantum walk of one ion in a linear ion trap. With a single-step fidelity exceeding 0.99, we perform three steps of an asymmetric walk on the line. We clearly reveal the differences to its…
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 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 present a full quantum treatment of a five-level atomic system coupled to two quantum and two classical light fields. The two quantum fields undergo a cross-phase modulation induced by electro-magnetically induced transparency. The…
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…
In this paper, we work on a quantum walk whose system is manipulated by a five-diagonal unitary matrix, and present long-time limit distributions. The quantum walk launches off a location and delocalizes in distribution as its system is…
The physics of quantum walks on graphs is formulated in Hamiltonian language, both for simple quantum walks and for composite walks, where extra discrete degrees of freedom live at each node of the graph. It is shown how to map between…