@article(C-C,
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},
)