Recurrences in three-state quantum walks on a plane

Journal Article · Thu Jul 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.012303· OSTI ID:21440472

Kollar, B; Kiss, T ^[1]; Stefanak, M; Jex, I ^[2]

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1. Department of Quantum Optics and Quantum Information, Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences, Konkoly-Thege Miklos ut 29-33, H-1121 Budapest (Hungary)
2. Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Brehova 7, 115 19 Praha 1--Stare Mesto (Czech Republic)

We analyze the role of dimensionality in the time evolution of discrete-time quantum walks through the example of the three-state walk on a two-dimensional triangular lattice. We show that the three-state Grover walk does not lead to trapping (localization) or recurrence to the origin, in sharp contrast to the Grover walk on the two-dimensional square lattice. We determine the power-law scaling of the probability at the origin with the method of stationary phase. We prove that only a special subclass of coin operators can lead to recurrence, and there are no coins that lead to localization. The propagation for the recurrent subclass of coins is quasi-one dimensional.

• OSTI ID: 21440472
• Journal Information: Physical Review. A, Vol. 82, Issue 1; Other Information: DOI: 10.1103/PhysRevA.82.012303; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EVOLUTION
ONE-DIMENSIONAL CALCULATIONS
ORIGIN
PROBABILITY
QUANTUM MECHANICS
QUANTUM OPERATORS
QUANTUM STATES
TETRAGONAL LATTICES
TRAPPING
TWO-DIMENSIONAL CALCULATIONS
CRYSTAL LATTICES
CRYSTAL STRUCTURE
MATHEMATICAL OPERATORS
MECHANICS