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Abstract: We formulate a framework for discrete-time quantum walks, motivated by classical random walks with memory. We present a specific representation of the classical walk with memory 2 on which t...
Abstract: In this paper we address the problem of understanding the success of algorithms that organize patches according to graph-based metrics. Algorithms that analyze patches extracted from images ...
Quantum walk represents one of the most promising resources for the simulation of physical quantum systems [1], and has also emerged as an alternative to the standard circuit model for quantum computi...
A formalism in terms of Hertz potentials is presented describing sum-frequency generation in a uniaxial non-linear crystal. A scheme is proposed consisting in aligning the side-walk propagation of ext...
We show that all the time-dependent statistical properties of the rightmost points of a branching Brownian motion can be extracted from the traveling wave solutions of the Fisher-KPP equation. We show...
We study the quantum walk search algorithm of Shenvi, Kempe and Whaley [PRA 67 052307 (2003)] on data structures of one to two spatial dimensions, on which the algorithm is thought to be less efficie...
We consider 2-state time-inhomogeneous quantum walks defined by two matrices on the line. For the time-homogeneous walks determined by a unitary matrix, the limit distribution is expressed by a simple...
Multi-dimensional quantum walks usually require large coin spaces. Here we show that the non-localized case of the spatial density probability of the two-dimensional Grover walk can be obtained using ...
We study the discrete-time quantum walk-based search for a marked vertex on a graph. By considering various structures in which not all vertices are equivalent, we investigate the relationship between...
A new optical chip that allows pairs of photons to take a quantum walk has been unveiled by an international team of physicists. The tiny device contains an array of 21 coupled optical waveguides and ...
We study the single particle dynamics of a mobile non-Abelian anyon hopping around many pinned anyons on a surface. The dynamics is modelled by a discrete time quantum walk and the spatial degree of f...
We consider a discrete-time quantum walk Wt, at time t on a graph with joined half lines J, which is composed of  half lines with the same origin. Our analysis is based on a reduction of the walk o...
Physicists in Austria have demonstrated a "quantum walk" in detail for the first time, using trapped ions. Such experiments could allow us to better understand the transition between the quantum and c...
Random walks describe diffusion processes, where movement at every time step is restricted to only the neighbouring locations. We construct a quantum random walk algorithm, based on discretisation of ...

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