Mixing times in quantum walks on two-dimensional grids

Journal Article · Fri Oct 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.042341· OSTI ID:21450759

Marquezino, F L; Portugal, R; Abal, G ^[1]

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1. Laboratorio Nacional de Computacao Cientifica-LNCC Avenida Getulio Vargas 333, Petropolis, Rio de Janeiro 25651-075 (Brazil)

Mixing properties of discrete-time quantum walks on two-dimensional grids with toruslike boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an exact expression for the stationary distribution of the coherent walk over odd-sided lattices is obtained after solving the eigenproblem for the evolution operator for this particular graph. The limiting distribution and mixing time of a quantum walk with a coin operator modified as in the abstract search algorithm are obtained numerically. On the basis of these results, the relation between the mixing time of the modified walk and the running time of the corresponding abstract search algorithm is discussed.

• OSTI ID: 21450759
• Journal Information: Physical Review. A, Vol. 82, Issue 4; Other Information: DOI: 10.1103/PhysRevA.82.042341; (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
ALGORITHMS
BOUNDARY CONDITIONS
DISTRIBUTION
GRAPH THEORY
MIXING
QUANTUM MECHANICS
QUANTUM OPERATORS
QUANTUM STATES
RANDOMNESS
TWO-DIMENSIONAL CALCULATIONS
MATHEMATICAL LOGIC
MATHEMATICAL OPERATORS
MATHEMATICS
MECHANICS