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Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation.
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Quantum walks on graphs
D. Aharonov, A. Ambainis, J. Kempe, and U. Vazirani · 2001
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One-dimensional quantum walks
A. Ambainis, E. Bach, A. Nayak, A. Vishwanath, and J. Watrous · 2001
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The Physics of Quantum Information
D. Bouwmeester, A. Ekert, and A. Zeilinger (Eds.) · 2001
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PhD thesis: Calcul Quantique - Marches Aléatoires Quantiques et Etude d’Enchevêtrement
J. Kempe · 2001
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Probabilistic quantum memories
C. Trugenberger · 2001
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Quantum simulations of classical random walks and undirected graph connectivity
J. Watrous · 2001
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P.A. Benioff · 2002
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An example of the difference between quantum and classical random walks
A. Childs, E. Farhi, and S. Gutmann · 2002
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Krawtchouk matrices from classical and quantum walks
P. Feinsilver and J. Kocik · 2002
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Information and Computation: Classical and quantum aspects
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Creating superpositions that correspond to efficiently integrable probability distributions
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Diffusion of epicenters of earthquake aftershocks, omori’s law, and generalized continuous-time random walk models
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Algorithm for data clustering in pattern recognition problems based on quantum mechanics
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A comparison of quantum oracles
E. Kashefi, A. Kent, V. Vedral, and K. Banaszek · 2002
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Decoherence in a quantum walk on the line
V. Kendon and B. Tregenna · 2002
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Limit theorems and absorption problems for quantum random walks in one dimension
N. Konno · 2002
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Quantum random walks in one dimension
N. Konno · 2002
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Quantum walks in higher dimensions
T.D. MacKay, S.D. Bartlett, L.T. Stephenson, and B.C. Sanders · 2002
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Global entanglement in multiparticle systems
D.A. Meyer and N.R. Wallach · 2002
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Quantum walks on the hypercube
C. Moore and A. Russell · 2002
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Implementing the quantum random walk
B.C. Travaglione and G.J. Milburn · 2002
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Phase transitions in quantum pattern recognition
C. Trugenberger · 2002
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Quantum pattern recognition
C. Trugenberger · 2002
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Quantum search of spatial regions
S. Aaronson and A. Ambainis · 2003
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Adiabatic quantum state generation and statistical zero knowledge
D. Aharonov and A. Ta-Shma · 2003
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Quantum walks and their algorithmic applications
A. Ambainis · 2003
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Quantum walks on cycles
M. Bednarska, A. Grudka, P. Kurzyński, T. Łuczak, and A. Wójcik · 2003
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Toward an architecture for quantum programming
S. Bettelli, T. Calarco, and L. Serafini · 2003
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Quantum random walks with decoherent coins
T.A. Brun, H.A. Carteret, and A. Ambainis · 2003
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Quantum to classical transition for random walks
T.A. Brun, H.A. Carteret, and A. Ambainis · 2003
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Quantum walks driven by many coins
T.A. Brun, H.A. Carteret, and A. Ambainis · 2003
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Three routes to the exact asympstotics for the one-dimensional quantum walk
H.A. Carteret, M.E.H. Ismail, and B. Richmond · 2003
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Exponential algorithmic speedup by quantum walk
A.M. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, and D. Spielman · 2003
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A note on the classical lower bound for a quantum walk algorithm
S.A. Fenner and Y. Zhang · 2003
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Quantum walks based on an interferometric analogy
M. Hillery, J. Bergou, and E. Feldman · 2003
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Discrete quantum walks hit exponentially faster
J. Kempe · 2003
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Quantum random walks - an introductory overview
J. Kempe · 2003
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Decoherence can be useful in quantum walks
V. Kendon and B. Tregenna · 2003
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Decoherence in discrete quantum walks
V. Kendon and B. Tregenna · 2003
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Optical cavity implementations of the quantum walk
P.L. Knight, E. Roldán, and J.E. Sipe · 2003
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Quantum walk on the line as an interference phenomenon
P.L. Knight, E. Roldán, and J.E. Sipe · 2003
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Absorption problems for quantum walks in one dimension
N. Konno, T. Namiki, T. Soshi, and A. Sudbury · 2003
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Two models of quantum random walk
J. Košík · 2003
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Looking at nature as a computer
N. Margolus · 2003
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From cbits to qbits: Teaching computer scientists quantum mechanics
N.D. Mermin · 2003
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Markovian behavior and constrained maximization of the entropy in chaotic quantum systems
A. Romanelli, A.C. Sicardi Schifino, G. Abal, R. Donangelo, and R. Siri · 2003
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A quantum random walk search algorithm
N. Shenvi, J. Kempe, and R.B. Whaley · 2003
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Controlling discrete quantum walks: coins and initial states
B. Tregenna, W. Flanagan, R. Maile, and V. Kendon · 2003
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Quantum computation and image processing: New trends in artificial intelligence
S.E. Venegas-Andraca and S. Bose · 2003
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Storing, processing and retrieving an image using quantum mechanics
S.E. Venegas-Andraca and S. Bose · 2003
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Improving gate-level simulation of quantum circuits
G.F. Viamontes, I. Markov, and J.P. Hayes · 2003
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Analysis of absorbing times of quantum walks
T. Yamasaki, H. Kobayashi, and H. Imai · 2003
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Quantum search algorithms
A. Ambainis · 2004
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Quantum walk algorithm for element distinctness
A. Ambainis · 2004
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Quantum walk algorithm for element distinctness
A. Ambainis · 2004
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One-dimensional quantum walks with absorbing boundaries
E. Bach, S. Coppersmith, M. Paz Goldshen, R. Joynt, and J. Watrous · 2004
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Examples of nonuniform limiting distributions for the quantum walk on even cycles
M. Bednarska, A. Grudka, P. Kurzyński, T. Łuczak, and A. Wójcik · 2004
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Spatial search by quantum walk
A.M. Childs and J. Goldstone · 2004
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Scattering theory and discrete-time quantum walks
E. Feldman and M. Hillery · 2004
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Weak limits for quantum random walks
G. Grimmett, S. Janson, and P.F. Scudo · 2004
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Temporal fluctuations of continuous-time quantum random walks on circles
N. Inui, K. Kasahara, Y. Konishi, and N. Konno · 2004
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Localization of two-dimensional quantum walks
N. Inui, Y. Konishi, and N. Konno · 2004
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Simulation of quantum random walks using the interference of a classical field
H. Jeong, M. Paternostro, and M.S. Kim · 2004
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Propagating quantum walks: the origin of interference structures
P.L. Knight, E. Roldán, and J.E. Sipe · 2004
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Symmetry of distribution for the one-dimensional hadamard walk
N. Konno · 2004
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Quantum walks and reversible cellular automata
N. Konno, K. Mistuda, T. Soshi, and H.J. Yoo · 2004
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Asymptotics of multivariate sequences, ii. multiple points of the singular variety
R. Pemantle and M. Wilson · 2004
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Analyzing the random-walk algorithm for SAT
H. Rantanen · 2004
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QIST 2004. a quantum information science and technology roadmap
Advanced Research and Development Activity · 2004
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Aperiodic quantum random walks
P. Ribeiro, P. Milman, , and R. Mosseri · 2004
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Quantum random walk on the line as a markovian process
A. Romanelli, A.C. Sicardi Schifino, R. Siri, G. Abal, A. Auyuanet, and R. Donangelo · 2004
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Elements of the Random Walk
J. Rudnick and G. Gaspari · 2004
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A brief survey of quantum programming languages
P. Selinger · 2004
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Towards a quantum programming language
P. Selinger · 2004
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Quantum speed-up of markov chain algorithms
M. Szegedy · 2004
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Earthquake simulation by restricted random walks
S.N. Ward · 2004
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Quantum search of spatial regions
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A structural approach to reversible computation
S. Abramsky · 2005
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Decoherence in quantum walks on the hypercube
G. Alagić and A. Russell · 2005
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A functional quantum programming language
T. Altenkirch and J. Grattage · 2005
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Coins make quantum walks faster
A. Ambainis, J. Kempe, and A. Rivosh · 2005
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Simulated quantum computation of molecular energies
A. Aspuru-Guzik, A.D. Dutoi, P.J. Love, and M. Head-Gordon · 2005
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Entanglement in coined quantum walks on regular graphs
I. Carneiro, M. Loo, X. Xu, M. Girerd, V. Kendon, and P.L. Knight · 2005
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Evanescence in coined quantum walks
H.A. Carteret, B. Richmond, and N.M. Temme · 2005
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Quantum algorithms for subset finding
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Entanglement measurement with discrete multiple-coin quantum walks
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Convergence of coined quantum walks on ℝ d \mathbb{R}^{d}
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Relation between coined quantum walks and quantum cellular automata
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Options, Futures and Other Derivatives (Sixth edition)
J.C. Hull · 2005
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Quantum Computing and Communications: an engineering approach
S. Imre and F. Balázs · 2005
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Fluctuations of quantum random walks on circles
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Localization of multi-state quantum walk in one dimension
N. Inui and N. Konno · 2005
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Quantum walks and orbital states of a weyl particle
M. Katori, S. Fujino, and N. Konno · 2005
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Complementarity and quantum walks
V. Kendon and B.C. Sanders · 2005
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Limit theorem for continuous-time quantum walk on the line
N. Konno · 2005
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A new type of limit theorems for the one-dimensional quantum random walk
N. Konno · 2005
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A path integral approach for disordered quantum walks in one dimension
N. Konno · 2005
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Scattering model for quantum random walks on hypercube
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One-dimensional three-state quantum walk
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Classical concepts in quantum programming
B. Ömer · 2005
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Quantum random walks do not need a coin toss
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Optical implementability of the two-dimensional quantum walk
E. Roldán and J.C. Soriano · 2005
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Decoherence in the quantum walk on the line
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Introduction to the Theory of Computation
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Quantum programming languages: survey and bibliography
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Continuous-time quantum walks on the threshold network model
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Dynamical localization of Quantum Walks in Random Environments
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Continuous-time quantum walk on integer lattices and homogeneous trees
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Quantum walks and elliptic integrals
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Coined quantum walks on percolation graphs
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Limit distribution with a combination of density functions for a 2-state quantum walk
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Trapping of continuous-time quantum walks on Erdős-Rényi graphs
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M-particle quantum walks with δ \delta interaction
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von Neumann entanglement and decoherence in two dimensional quantum walks
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Convergence of quantum random walks with decoherence
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Localization of quantum walks induced by recurrence properties of random walks
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Dagger categories of tame relations
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Random Time-Dependent Quantum Walks
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A note on itô’s formula for discrete-time quantum walk
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Localization of discrete-time quantum walks on a half line via the CGMV method
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Quantum walk of two interacting bosons
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Quantum Radar
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Quantum walks with non-abelian anyons
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Models of quantum computation and quantum programming languages
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Topological phases and delocalization of quantum walks in random environments
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Two-photon quantum walks in an elliptical direct-write waveguide array
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Quantumness of noisy quantum walks: A comparison between measurement-induced disturbance and quantum discord
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Zitterbewegung, bloch oscillations and landau-zener tunneling in a quantum walk
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Are quantum walks the saviour of optical quantum computing?
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Quantum snake walk on graphs
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Cellular algebras and graph invariants based on quantum walks
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A multi-channel representation for images on quantum computers using the RGB α \alpha color space
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Quantum walks on complex networks with connection instabilities and community structure
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Explorations in Quantum Computing
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Controllability of quantum walks on graphs
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Brun-type formalism for decoherence in two-dimensional quantum walks
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Enhancing the spreading of quantum walks on star graphs by additional bonds
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Open quantum random walks on graphs
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Perfect state transfer on quotient graphs
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One-dimensional quantum walks with one defect
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Entanglement separation in spatially separated systems using quantum walk
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Hitting time of quantum walks with perturbation
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Limit theorems for the discrete-time quantum walk on a graph with joined half lines
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Index theory of one-dimensional quantum walks and cellular automata
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Recurrence for discrete time unitary evolutions
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Time averaged distribution of a discrete-time quantum walk on the path
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Watermarking and authentication of quantum images based on restricted geometric transformations
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Personal communication, 2012
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Dynamical localization for d d -Dimensional Random Quantum Walks
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Quantum walks on necklaces and mixing
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Sojourn times of the hadamard walk in one dimension
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Limit measures of inhomogeneous discrete-time quantum walks in one dimension
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On the relationship between quantum walks and zeta functions
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Asymptotic distribution of quantum walks on the line with two entangled coins
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On the hitting times of quantum versus random walks
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Experimental simulation and limitations of quantum walks with trapped ions
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Google in a quantum network
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Entanglement dynamics and quasi-periodicity in discrete quantum walks
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Thermodynamic behavior of the quantum walk
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Two-particle bosonic-fermionic quantum walk via 3d integrated photonics
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Spontaneous parametric down-conversion and quantum walks in arrays of quadratic nonlinear waveguides
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Two quantum walkers sharing coins
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