Quantum random walks, Physical Review A, vol.48, issue.2, p.1687, 1993. ,
DOI : 10.1103/PhysRevA.48.1687
From quantum cellular automata to quantum lattice gases, Journal of Statistical Physics, vol.59, issue.5-6, p.551, 1996. ,
DOI : 10.1007/BF02199356
URL : http://arxiv.org/abs/quant-ph/9604003
Quantum walks: a comprehensive review, Quantum Information Processing, vol.81, issue.5, p.1015, 2012. ,
DOI : 10.1007/s11128-012-0432-5
URL : http://arxiv.org/abs/1201.4780
Exploring topological phases with quantum walks, Physical Review A, vol.82, issue.3, p.33429, 2010. ,
DOI : 10.1103/PhysRevA.82.033429
URL : http://arxiv.org/abs/1003.1729
Bulk-boundary correspondence for chiral symmetric quantum walks, Physical Review B, vol.88, issue.12, p.121406, 2013. ,
DOI : 10.1103/PhysRevB.88.121406
Decoherence and Disorder in Quantum Walks: From Ballistic Spread to Localization, Physical Review Letters, vol.106, issue.18, p.180403, 2011. ,
DOI : 10.1103/PhysRevLett.106.180403
URL : http://arxiv.org/abs/1101.2638
Implementation of a spatial two-dimensional quantum random walk with tunable decoherence, Physical Review A, vol.86, issue.5, p.52327, 2012. ,
DOI : 10.1103/PhysRevA.86.052327
Localized state in a two-dimensional quantum walk on a disordered lattice, Physical Review A, vol.92, issue.4, p.42316, 2015. ,
DOI : 10.1103/PhysRevA.92.042316
Localization, delocalization, and topological phase transitions in the one-dimensional split-step quantum walk, Physical Review A, vol.92, issue.5, p.52311, 2015. ,
DOI : 10.1103/PhysRevA.92.052311
Localization, delocalization, and topological transitions in disordered two-dimensional quantum walks, Physical Review B, vol.91, issue.10, p.104202, 2015. ,
DOI : 10.1103/PhysRevB.91.104202
Observation of topologically protected bound states in photonic quantum walks, Nature Communications, vol.12, p.882, 2012. ,
DOI : 10.1038/ncomms1872
The Quantum Hall Effect, Graduate Texts in Contemporary Physics, 1990. ,
: Topological insulators, Reviews of Modern Physics, vol.82, issue.4, p.3045, 2010. ,
DOI : 10.1103/RevModPhys.82.3045
Unveiling hidden topological phases of a one-dimensional Hadamard quantum walk, Physical Review B, vol.92, issue.4, p.45424, 2015. ,
DOI : 10.1103/PhysRevB.92.045424
Classification of topological insulators and superconductors in three spatial dimensions, Physical Review B, vol.78, issue.19, p.195125, 2008. ,
DOI : 10.1103/PhysRevB.78.195125
Quantum to Classical Transition for Random Walks, Physical Review Letters, vol.91, issue.13, p.130602, 2003. ,
DOI : 10.1103/PhysRevLett.91.130602
URL : http://arxiv.org/abs/quant-ph/0208195
Disordered quantum walks in one lattice dimension, Journal of Mathematical Physics, vol.120, issue.10, p.102201, 2011. ,
DOI : 10.1007/BF01212354
URL : http://arxiv.org/abs/1101.2298
Topological phases and delocalization of quantum walks in random environments, Physical Review B, vol.84, issue.19, p.195139, 2011. ,
DOI : 10.1103/PhysRevB.84.195139
Nonlinear optical Galton board, Physical Review A, vol.75, issue.6, p.62333, 2007. ,
DOI : 10.1103/PhysRevA.75.062333
URL : http://arxiv.org/abs/quant-ph/0604084
Quantum walk as a simulator of nonlinear dynamics: Nonlinear Dirac equation and solitons, Physical Review A, vol.92, issue.5, p.52336, 2015. ,
DOI : 10.1103/PhysRevA.92.052336
Attractor-repeller pair of topological zero modes in a nonlinear quantum walk, Physical Review A, vol.93, issue.2, p.22329, 2016. ,
DOI : 10.1103/PhysRevA.93.022329
Fractional charge and zero modes for planar systems in a magnetic field, Physical Review D, vol.29, issue.10, p.2375, 1984. ,
DOI : 10.1103/PhysRevD.29.2375