Related papers: Quantum search with a continuous-time quantum walk…
A kicking sequence of the atom optics kicked rotor at quantum resonance can be interpreted as a quantum random walk in momentum space. We show how to steer such a random walk by applying a random sequence of intensities and phases of the…
We analytically investigate the recently proposed and implemented discrete-time quantum walk based on kicked ultra-cold atoms. We show how the internal level structure of the kicked atoms leads to the emergence of a relative light-shift…
We consider a new model of quantum walk on a one-dimensional momentum space that includes both discrete jumps and continuous drift. Its time evolution has two stages; a Markov diffusion followed by localized dynamics. As in the well known…
In quantum computing, the quantum walk search algorithm is designed for locating fixed marked nodes within a graph. However, when multiple marked nodes exist, the conventional search algorithm lacks the capacity to simultaneously amplify…
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 report the experimental implementation of discrete-time topological quantum walks of a Bose-Einstein condensate in momentum space. Introducing stroboscopic driving sequences to the generation of a momentum lattice, we show that the…
We introduce the driven discrete time quantum walk, where walkers are added during the walk instead of only at the beginning. This leads to interference in walker number and very different dynamics when compared to the original quantum…
Quantum walks are standard tools for searching graphs for marked vertices, and they often yield quadratic speedups over a classical random walk's hitting time. In some exceptional cases, however, the system only evolves by sign flips,…
One approach to the development of quantum search algorithms is the quantum walk. A spatial search can be effected by the continuous-time evolution of a single quantum particle on a graph containing a marked site. In many physical…
We discuss the use of high-order quantum accelerator modes to achieve an atom optical realization of a biased quantum random walk. We first discuss how one can create co-existent quantum accelerator modes, and hence how momentum transfer…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. Searching in this mathematical framework has interested the community since a long time. However, most results consider spatial search…
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…
Each step in a quantum random walk is typically understood to have two basic components; a `coin-toss' which produces a random superposition of two states, and a displacement which moves each component of the superposition by different…
We have realized a quantum walk in momentum space with a rubidium spinor Bose-Einstein condensate by applying a periodic kicking potential as a walk operator and a resonant microwave pulse as a coin toss operator. The generated quantum…
Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the…
Quantum walks have been very successful in the development of search algorithms in quantum information, in particular in the development of spatial search algorithms. However, the construction of continuous-time quantum search algorithms in…
The quantum walk is the quantum analogue of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to…
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…
In this letter we introduce the concept of a driven quantum walk. This work is motivated by recent theoretical and experimental progress that combines quantum walks and parametric down- conversion, leading to fundamentally different…
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…