Faster quantum concentration via Grover's search

ABSTRACT One of the most important challenges in information networks is to gather data from a larger set of nodes to a smaller set of nodes. This can be done via the use of a concentrator architecture in the connection topology. This paper is a proof-of-concept that demonstrates a quantum-based controller in large interconnection networks can asymptotically perform this task faster. We specifically present quantum algorithms for routing concentration assignments on full capacity fat-and-slim concentrators, bounded fat-and-slim concentrators, and regular fat-and-slim concentrators. Classically, the concentration assignment takes time on all these concentrators, where n is the number of inputs. Powered by Grover's quantum search algorithm, our algorithms take time, where c is the capacity of the concentrator. Thus, our quantum algorithms are asymptotically faster than their classical counterparts, when . In general, satisfies implying a time complexity of for any .