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The limit theorems of discrete- and continuous-time quantum walks on the line have been intensively studied.
Quantum integrable systems related to lie algebras
Olshanetsky, M., Perelomov, A.M.: · 1983
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Quantum computation and decision trees
Farhi, E., Gatmann, S.: · 1998
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Quantum Computation and Quantum Information
Nielsen, M.A., Chuang, I.L.: · 2000
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One-dimensional quantum walks
Ambainis, A., Bach, E., Nayak, A., Vishwanath, A., Watrous, J.: · 2001
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Quantum random walks in one dimension
Konno, N.: · 2002
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Quantum walks and their algolismic applications
Ambainis, A.: · 2003
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Quantum random walks – an introductory overview
Kempe, J.: · 2003
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Quantum random-walk search algorithm
Shenvi, N., Kempe, J., Whaley, K.B.: · 2003
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Heun equation and Inozemtsev models
Takemura, K.: · 2003
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The Heun equation and the Calogero-Moser-Sutherland system I: the bethe ansatz method
Takemura, K.: · 2003
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The Heun equation and the Calogero-Moser-Sutherland system II: perturbation and algebraic solution
Takemura, K.: · 2004
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The Heun equation and the Calogero-Moser-Sutherland system III: the finite gap property and the monodromy
Takemura, K.: · 2004
Cited alongside, same era.
Convergence of continuous-time quantum walks on the line
Gottlieb, A.D.: · 2005
Cited alongside, same era.
One-dimensional three-state quantum walk
Inui, N., Konno, N., Segawa, E.: · 2005
Cited alongside, same era.
Limit theorem for continuous-time quantum walk on the line
Konno, N.: · 2005
Cited alongside, same era.
A new type of limit theorems for the one-dimensional quantum random walk
Konno, N.: · 2005
Cited alongside, same era.
The Heun equation and the Calogero-Moser-Sutherland system IV: The hermite-krichever ansatz
Takemura, K.: · 2005
Cited alongside, same era.
Quantum Walks. Volume 1954 of Lecture Notes in Mathematics. Springer-Verlag, (Heidelberg) (2008) 309–452
Konno, N.: · 2008
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Limit theorems for quantum walks driven by many coins
Segawa, E., Konno, N.: · 2008
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Quantum Walks for Computer Scientists
Venegas-Andreca, S.E.: · 2008
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Continuous-time quantum walks on Erdős-Rényi networks
Xu, X.P., Liu, F.: · 2008
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Limit theorems for discrete-time quantum walks on trees
Chisaki, K., Hamada, M., Konno, N., Segawa, E.: · 2009
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D’Alessandro, D.: · 2009
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Connecting the discrete- and continuous-time quantum walks
Strauch, F.W.: · 2006
Cited alongside, same era.
The Heun equation and the Calogero-Moser-Sutherland system V: generalized darboux transformations
Takemura, K.: · 2006
Cited alongside, same era.
Decoherence in quantum walks – a review
Kendon, V.: · 2007
Cited alongside, same era.
Quantum transport on small-world networks: A continuous-time quantum walk approach
Mülken, O., Pernice, V., Blumen, A.: · 2007
Cited alongside, same era.
Zur theorie der riemann’schen functionen zweiter ordnung mit vier verzweigungspunkten
Heun, K.:
Cited in the paper.
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Continuous-time quantum walks on the threshold network model
Ide, Y., Konno, N.: · 2010
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Limit theorems for quantum walks with memory
Konno, N., Machida, T.: · 2010
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Limit theorem for a time-dependent coined quantum walk on the line
Machida, T., Konno, N.: · 2010
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Limit theorems for a localization model of 2-state quantum walks
Machida, T.: · 2011
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