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 author       = {J T Chalker and P D Coddington},
 year         = {1988},
 title        = {Percolation, quantum tunnelling and the integer {Hall} effect},
 journal      = {Journal of Physics C: Solid State Physics},
 volume       = {21},
 number       = {14},
 pages        = {2665--2679},
 doi          = {10.1088/0022-3719/21/14/008},
)
@inproceedings(Childs,
 author       = {Andrew M. Childs and Richard Cleve and Enrico Deotto and Edward Farhi and Sam Gutmann and Daniel A. Spielman},
 year         = {2003},
 title        = {Exponential Algorithmic Speedup by a Quantum Walk},
 booktitle    = {Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing},
 series       = {STOC '03},
 publisher    = {Association for Computing Machinery},
 address      = {New York, NY, USA},
 pages        = {59--68},
 doi          = {10.1145/780542.780552},
 url          = {https://arxiv.org/abs/quant-ph/0209131},
)
@article(Scattering,
 author       = {Edgar Feldman and Mark Hillery},
 year         = {2004},
 title        = {Scattering theory and discrete-time quantum walks},
 journal      = {Physics Letters A},
 volume       = {324},
 number       = {4},
 pages        = {277 -- 281},
 doi          = {10.1016/j.physleta.2004.03.005},
 url          = {https://arxiv.org/abs/quant-ph/0312062},
)
@article(Higuchi,
 author       = {Yusuke Higuchi and Norio Konno and Iwao Sato and Etsuo Segawa},
 year         = {2012},
 title        = {Quantum graph walks {I}: mapping to quantum walks},
 journal      = {arXiv:1211.0803 [math-ph, physics:quant-ph]},
 url          = {http://arxiv.org/abs/1211.0803},
)
@article(Inui,
 author       = {Norio Inui and Yoshinao Konishi and Norio Konno},
 year         = {2004},
 title        = {Localization of two-dimensional quantum walks},
 journal      = {Physical Review A},
 volume       = {69},
 number       = {5},
 pages        = {052323},
 doi          = {10.1103/PhysRevA.69.052323},
 url          = {https://arxiv.org/abs/quant-ph/0311118},
)
@article(Inui-lazy,
 author       = {Norio Inui and Norio Konno and Etsuo Segawa},
 year         = {2005},
 title        = {One-dimensional three-state quantum walk},
 journal      = {Physical Review E},
 volume       = {72},
 number       = {5},
 pages        = {056112},
 doi          = {10.1103/PhysRevE.72.056112},
 url          = {https://arxiv.org/abs/quant-ph/0507207},
)
@article(Konno,
 author       = {Norio Konno},
 year         = {2002},
 title        = {Quantum {Random} {Walks} in {One} {Dimension}},
 journal      = {Quantum Information Processing},
 volume       = {1},
 number       = {5},
 pages        = {345--354},
 doi          = {10.1023/A:1023413713008},
 url          = {https://arxiv.org/abs/quant-ph/0206053},
)
@article(Michelson,
 author       = {Lennart Lorz and Meyer-Scott, Evan and Thomas Nitsche and Poto\v{c}ek, V\'{a}clav and Aur\'{e}l G\'{a}bris and Sonja Barkhofen and Igor Jex and Christine Silberhorn},
 year         = {2019},
 title        = {Photonic quantum walks with four-dimensional coins},
 journal      = {Physical Review Research},
 volume       = {1},
 number       = {3},
 pages        = {033036},
 doi          = {10.1103/PhysRevResearch.1.033036},
 url          = {https://arxiv.org/abs/1809.00591},
)
@article(Staggered,
 author       = {R. Portugal and R. A. M. Santos and T. D. Fernandes and Gon\c{c}alves, D. N.},
 year         = {2016},
 title        = {The staggered quantum walk model},
 journal      = {Quantum Information Processing},
 volume       = {15},
 number       = {1},
 pages        = {85--101},
 doi          = {10.1007/s11128-015-1149-z},
 url          = {https://arxiv.org/abs/1505.04761},
)
@article(Nase-hypercube,
 author       = {Poto\v{c}ek, V\'{a}clav and Aur\'{e}l G\'{a}bris and Tam\'{a}s Kiss and Igor Jex},
 year         = {2009},
 title        = {Optimized quantum random-walk search algorithms on the hypercube},
 journal      = {Physical Review A},
 volume       = {79},
 number       = {1},
 pages        = {012325},
 doi          = {10.1103/PhysRevA.79.012325},
 url          = {https://arxiv.org/abs/0805.4347},
)
@article(SKW,
 author       = {Neil Shenvi and Julia Kempe and K. Birgitta Whaley},
 year         = {2003},
 title        = {Quantum random-walk search algorithm},
 journal      = {Physical Review A},
 volume       = {67},
 number       = {5},
 pages        = {052307},
 doi          = {10.1103/PhysRevA.67.052307},
 url          = {https://arxiv.org/abs/quant-ph/0210064},
)
@inproceedings(Szegedy,
 author       = {M. {Szegedy}},
 year         = {2004},
 title        = {Quantum speed-up of Markov chain based algorithms},
 booktitle    = {45th Annual IEEE Symposium on Foundations of Computer Science},
 pages        = {32--41},
 doi          = {10.1109/FOCS.2004.53},
)
@article(Martin,
 author       = {\v{S}tefa\v{n}\'{a}k, M. and B. Koll\'{a}r and T. Kiss and I. Jex},
 year         = {2010},
 title        = {Full revivals in 2D quantum walks},
 journal      = {Physica Scripta},
 volume       = {T140},
 pages        = {014035},
 doi          = {10.1088/0031-8949/2010/T140/014035},
 url          = {https://arxiv.org/abs/1011.2066},
)