Spectral and asymptotic properties of Grover walks on crystal lattice

[1]  R. Feynman,et al.  Quantum Mechanics and Path Integrals , 1965 .

[2]  Stanley Gudder,et al.  Realistic quantum probability , 1988 .

[3]  Timothy S. Murphy,et al.  Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals , 1993 .

[4]  Motoko Kotani,et al.  Asymptotic behavior of the transition probability of a random walk on an infinite graph , 1998 .

[5]  Motoko Kotani,et al.  Albanese Maps and Off Diagonal Long Time Asymptotics for the Heat Kernel , 2000 .

[6]  John Watrous Quantum Simulations of Classical Random Walks and Undirected Graph Connectivity , 2001, J. Comput. Syst. Sci..

[7]  Norio Konno,et al.  A new type of limit theorems for the one-dimensional quantum random walk , 2002, quant-ph/0206103.

[8]  Norio Konno,et al.  Quantum Random Walks in One Dimension , 2002, Quantum Inf. Process..

[9]  Andris Ambainis,et al.  QUANTUM WALKS AND THEIR ALGORITHMIC APPLICATIONS , 2003, quant-ph/0403120.

[10]  A. ADoefaa,et al.  ? ? ? ? f ? ? ? ? ? , 2003 .

[11]  Mark Hillery,et al.  Quantum walks on graphs and quantum scattering theory , 2004 .

[12]  M. Szegedy,et al.  Quantum Walk Based Search Algorithms , 2008, TAMC.

[13]  Igor Jex,et al.  Recurrence properties of unbiased coined quantum walks on infinite d -dimensional lattices , 2008, 0805.1322.

[14]  Norio Konno,et al.  Limit distributions of two-dimensional quantum walks , 2008, 0802.2749.

[15]  Mark C. Wilson,et al.  Asymptotic expansions of oscillatory integrals with complex phase , 2009, 0903.3585.

[16]  I. Jex,et al.  Recurrences in three-state quantum walks on a plane , 2010, 1005.0688.

[17]  Etsuo Segawa,et al.  Localization of quantum walks induced by recurrence properties of random walks , 2011, 1112.4982.

[18]  Iwao Sato,et al.  Quantum graph walks I: mapping to quantum walks , 2012, 1211.0803.

[19]  Iwao Sato,et al.  Quantum graph walks II: Quantum walks on graph coverings , 2012, 1211.4719.

[20]  F. M. Andrade,et al.  Unveiling and exemplifying the unitary equivalence of discrete time quantum walk models , 2013, 1304.3690.

[21]  Etsuo Segawa,et al.  Limit measures of inhomogeneous discrete-time quantum walks in one dimension , 2011, Quantum Inf. Process..

[22]  Etsuo Segawa,et al.  The spreading behavior of quantum walks induced by drifted random walks on some magnifier graph , 2015 .