Nokia Bell Labs Publishes Analysis of Quantum Random Walks
Nokia Bell Labs has published an analysis of two-dimensional quantum random walks and their feasible regions. The research details the mathematical properties of these quantum phenomena.
Nokia Oyj's research arm, Nokia Bell Labs, has released a scientific publication detailing an analysis of two-dimensional quantum random walks. The paper, originally published in January 2011, examines the feasible regions where probabilities do not decay exponentially over time.
The study found that these feasible regions grow linearly with time, mirroring the behavior observed in one-dimensional quantum random walks. However, the limiting shape of the feasible region in the two-dimensional case differs significantly. It is characterized as an algebraic set, specifically the rational image of a compact algebraic variety.
Furthermore, the researchers computed the probability profile within this limit region. This profile is described as being related to the inverse power of the Gaussian curvature of the same algebraic variety. The methods employed are based on the analysis of the space-time generating function, following established mathematical approaches.
This publication contributes to the theoretical understanding of quantum walks and their mathematical properties, which is foundational for advancements in quantum computing and quantum information science.