Related papers: Quantum reflections, random walks and cut-off
In the present paper, we consider a class of Markov processes on the discrete circle which has been introduced by K\"onig, O'Connell and Roch. These processes describe movements of exchangeable interacting particles and are discrete…
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…
Discrete-time quantum walks, quantum generalizations of classical random walks, provide a framework for quantum information processing, quantum algorithms and quantum simulation of condensed matter systems. The key property of quantum…
A quantum master equation of the Lindblad form is obtained in this paper by considering the spontaneous wave-packet reduction. Different classical equations can be derived after exactly mapping such a quantum master equation to a continuous…
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 survey the equations of continuous-time quantum walks on simple one-dimensional lattices, which include the finite and infinite lines and the finite cycle, and compare them with the classical continuous-time Markov chains. The focus of…
We investigate the statistics of the first detected passage time of a quantum walk. The postulates of quantum theory, in particular the collapse of the wave function upon measurement, reveal an intimate connection between the wave function…
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,…
The continuous limit of quantum walks (QWs) on the line is revisited through a recently developed method. In all cases but one, the limit coincides with the dynamics of a Dirac fermion coupled to an artificial electric and/or relativistic…
We study the motion of two non-interacting quantum particles performing a random walk on a line and analyze the probability that the two particles are detected at a particular position after a certain number of steps (meeting problem). The…
We investigate continuous-time quantum walks of two indistinguishable particles (bosons, fermions or hard-core bosons) in one-dimensional lattices with nearest-neighbour interactions. The two interacting particles can undergo independent-…
Discrete-time quantum walks (DTQWs) in random artificial electric and gravitational fields are studied analytically and numerically. The analytical computations are carried by a new method which allows a direct exact analytical…
Quantum recurrence theorem holds for quantum systems with discrete energy eigenvalues and fails to hold in general for systems with continuous energy. We show that during quantum walk process dominated by interference of amplitude…
We consider a network model, embedded on the Manhattan lattice, of a quantum localisation problem belonging to symmetry class C. This arises in the context of quasiparticle dynamics in disordered spin-singlet superconductors which are…
We define and analyze random quantum walks on homogeneous trees of degree $q\geq 3$. Such walks describe the discrete time evolution of a quantum particle with internal degree of freedom in $\C^q$ hopping on the neighboring sites of the…
Quantum walks are counterparts of classical random walks. They spread faster, which can be exploited in information processing tasks, and constitute a versatile simulation platform for many quantum systems. Yet, some of their properties can…
A particular example is produced to prove that quantum walks can be used to simulate full-fledged discrete gauge theories. A new family of $2D$ walks is introduced and its continuous limit is shown to coincide with the dynamics of a Dirac…
This note introduces some examples of quantum random walks in d-dimensional Eucilidean space and proves the weak convergence of their rescaled n-step densities. One of the examples is called the Plancherel quantum walk because the "quantum…
We consider a variant of the configuration model with an embedded community structure and study the mixing properties of a simple random walk on it. Every vertex has an internal $\mathrm{deg}^{\text{int}}\geq 3$ and an outgoing…
The cutoff phenomenon describes a sharp transition in the convergence of a family of ergodic finite Markov chains to equilibrium. Many natural families of chains are believed to exhibit cutoff, and yet establishing this fact is often…