Quantum walks driven by many coins
By Todd A. Brun, H. Carteret, Andris Ambainis. 2002
155 citations recorded by the source corpus.
Quantum random walks have been much studied recently, largely due to their highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum random walk on the line: the use of multiple quantum ``coins'' (or more generally, coins of higher dimension) in order to diminish the effects of interference between paths. We find solutions to this system in terms of the single-coin random walk, and compare the asymptotic limit of these solutions to numerical simulations. We find exact analytical expressions for the time dependence of the first two moments, and show that in the long-time limit the ``quantum-mechanical'' behavior of the one-coin walk persists, even if each coin is flipped only twice. We further show that this is generic for a very broad class of possible walks, and that this behavior disappears only in the limit of a new coin for every step of the walk.
Subfields: Artificial Intelligence, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/a2f171aea632d20adfd0822020f8c7543f9ee7d1
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Salvador Elías Venegas-Andraca
- Julia Kempe
- Andris Ambainis
- Miklos Santha
- Andrew M. Childs
- Dominik Janzing
In Computational Theory and Mathematics
Citations in the corpus
- Quantum walks: a comprehensive review (2012, methodology): “in [86,87], Segawa and Konno [403] have used the Wigner formula of rotation matrices for quantum walks published by Miyazaki et al.”
- Quantum random walks: An introductory overview (2003, background): “There is another interesting option to transition the coined walk between quantum and classical taken by Brun et al. [49, 51].”