Year: 2005
Type: article
Abstract: We present a mathematical formalism for the description of un- restricted quantum walks with entangled coins and one walker. The numerical behaviour of such walks is examined when using a Bell state as the initial coin state, with two different coin operators, two different shift operators, and one walker. We compare and contrast the performance of these quantum walks with that of a classical random walk consisting of one walker and two maximally correlated coins as well as quantum walks with coins sharing different degrees of entanglement. We illustrate that the behaviour of our walk with entangled coins can be very different in comparison to the usual quantum walk with a single coin. We also demonstrate that simply by changing the shift operator, we can generate widely different distributions. We also compare the behaviour of quantum walks with maximally entangled coins with that of quantum walks with non-entangled coins. Finally, we show that the use of different shift operators on two and three qubit coins leads to different position probability distributions in one- and two-dimensional graphs.
Source: New Journal of Physics
Authors: S E Venegas-Andraca, J L Ball, K Burnett, S Bose
Institutions: University of Oxford, University College London
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,610
OpenAlex ID: W2015416844