TY - JOUR

T1 - Staggered quantum walk on hexagonal lattices

AU - Chagas, Bruno

AU - Portugal, Renato

AU - Boettcher, Stefan

AU - Segawa, Etsuo

N1 - Funding Information:
B.C. and R.P. acknowledge financial support from CNPq and CAPES. S.B. thanks LNCC for its hospitality and acknowledges financial support from CNPq through the Ciêencia sem Fronteiras program. E.S. acknowledges financial support from the Grant-in-Aid for Young Scientists (B) and of Scientific Research (B) Japan Society for the Promotion of Science (Grants No. 16K17637 and No. 16K03939).
Publisher Copyright:
© 2018 American Physical Society.

PY - 2018/11/9

Y1 - 2018/11/9

N2 - A discrete-time staggered quantum walk was recently introduced as a generalization that allows the unification of other versions, such as the coined and Szegedy's walk. However, it also produces forms of quantum walks not covered by previous versions. To explore their properties, we study here the staggered walk on a hexagonal lattice. Such a walk is defined using a set of overlapping tessellations that cover the graph edges, and each tessellation is a partition of the node set into cliques. The hexagonal lattice requires at least three tessellations. Each tessellation is associated with a local unitary operator and the product of the local operators defines the evolution operator of the staggered walk on the graph. After defining the evolution operator on the hexagonal lattice, we analyze the quantum walk dynamics with the focus on the position standard deviation and localization. We also obtain analytic results for the time complexity of spatial search algorithms with one marked node using cyclic boundary conditions.

AB - A discrete-time staggered quantum walk was recently introduced as a generalization that allows the unification of other versions, such as the coined and Szegedy's walk. However, it also produces forms of quantum walks not covered by previous versions. To explore their properties, we study here the staggered walk on a hexagonal lattice. Such a walk is defined using a set of overlapping tessellations that cover the graph edges, and each tessellation is a partition of the node set into cliques. The hexagonal lattice requires at least three tessellations. Each tessellation is associated with a local unitary operator and the product of the local operators defines the evolution operator of the staggered walk on the graph. After defining the evolution operator on the hexagonal lattice, we analyze the quantum walk dynamics with the focus on the position standard deviation and localization. We also obtain analytic results for the time complexity of spatial search algorithms with one marked node using cyclic boundary conditions.

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U2 - 10.1103/PhysRevA.98.052310

DO - 10.1103/PhysRevA.98.052310

M3 - Article

AN - SCOPUS:85056640468

SN - 1050-2947

VL - 98

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 5

M1 - 052310

ER -