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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...
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...
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...
Evolution of many particles on a one dimensional lattice subjected to quantum walk can cause spatial entanglement in the lattice position which can be exploited for quantum information/communication p...
The evolution operator of a discrete-time quantum walk involves a conditional shift in position space which entangles the coin and position degrees of freedom of the walker. After several steps, the c...
Single atoms have been spotted doing the quantum version of the random walk by physicists in Germany. This sighting of a quantum walk” could help in the design of quantum search algorithms, or in the...
Let p_j^(n) be the probability that a Hadamard quantum walk, started at site j on the integer lattice {0,...,n}, is absorbed at 0. We give an explicit formula for p_j^(n). Our formula proves a conject...
Quantum walks can be used either as tools for quantum algorithm development or as entanglement generators, potentially useful to test quantum hardware. We present a novel algorithm based on a discrete...
We give the first example of faster transport with a quantum walk on an inherently directed graph, on the directed line with a variable number of self-loops at each vertex. These self-loops can be tho...

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