Related papers: Momentum switches
We show how a quantum walk can be used to find a marked edge or a marked complete subgraph of a complete graph. We employ a version of a quantum walk, the scattering walk, which lends itself to experimental implementation. The edges are…
Quantum walks have been shown to be fruitful tools in analysing the dynamic properties of quantum systems. This article proposes to use quantum walks as an approach to Quantum Neural Networks (QNNs). QNNs replace binary McCulloch-Pitts…
We study transport properties of discrete quantum dynamical systems on the lattice, in particular Coined Quantum Walks and the Chalker--Coddington model. We prove existence of a non trivial charge transport and that the absolutely…
We examine the mixing time for random walks on graphs. In particular we are interested on investigating graphs with bottlenecks. Furthermore, the cutoff phenomenon is examined.
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…
In this paper we extend the concept of persistence, well defined for classical stochastic dynamics, to the context of quantum dynamics. We demonstrate the idea via quantum random walk and a successive measurement scheme, where persistence…
Inspired by recent breakthroughs with topological quantum materials, which pave the way to novel, high-efficiency, low-energy magnetoelectric devices and fault-tolerant quantum information processing, inter alia, topological quantum walks…
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…
This paper introduces the Attracting Random Walks model, which describes the dynamics of a system of particles on a graph with $n$ vertices. At each step, a single particle moves to an adjacent vertex (or stays at the current one) with…
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…
In this note, we discuss a general definition of quantum random walks on graphs and illustrate with a simple graph the possibility of very different behavior between a classical random walk and its quantum analogue. In this graph,…
In this paper, we consider discrete time quantum walks on graphs with coin focusing on the decentralized model, where the coin operation is allowed to change with the vertex of the graph. When the coin operations can be modified at every…
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…
In this paper, we analyze the potential for new types of searches using the formalism of scattering random walks on Quantum Computers. Given a particular type of graph consisting of nodes and connections, a "Tree Maze", we would like to…
By adding generalizations involving translations, the machinery of the quantum theory of free fields leads to the semiclassical equations of motion for a charged massive particle in electromagnetic and gravitational fields. With the…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
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 walks on graphs have shown prioritized benefits and applications in wide areas. In some scenarios, however, it may be more natural and accurate to mandate high-order relationships for hypergraphs, due to the density of information…
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…
The quantum random walk has been much studied recently, largely due to its highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum walk on the line: the presence of decoherence…