2009/02/28 by M. Štefaňák, Martin Stefanak, T. Kiss +2 · 1 citation
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum and electron transport phenomena #Quantum-Dot Cellular Automata #quant-ph
paper · pdf · doi:10.1088/1367-2630/11/4/043027
published as New J. Phys. 11 (2009) 043027 · Journal reference added, minor corrections in the text
openalex publication_date 2009/04/23 · arxiv created 2009/04/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Abstract. The Pólya number of a classical random walk on a regular lattice is known to depend solely on the dimension of the lattice. For one and two dimensions it equals one, meaning unit probability to return to the origin. This result is extremely sensitive to the directional symmetry, any deviation from the equal probability to travel in each direction results in a change of the character of the walk from recurrent to transient. Applying our definition of the Pólya number to quantum walks on a line we show that the recurrence character of quantum walks is more stable against bias. We determine the range of parameters for which biased quantum walks remain recurrent. We find that there exist genuine biased quantum walks which are recurrent. Recurrence of biased quantum walks on a line 2 1.