The Quantum Sieve of Eratosthenes
Department of Mathematics and Statistics, University of Saskatchewan, Canada.
- *Corresponding Author:
- Sowa A
Department of Mathematics and Statistics
University of Saskatchewan, Canada
E-mail: [email protected]
Received Date: April 08, 2016; Accepted Date: June 22, 2016; Published Date: June 27, 2016
Citation: Sowa A (2016) The Quantum Sieve of Eratosthenes. J Phys Math 7:180. doi:10.4172/2090-0902.1000180
Copyright: © 2016 Sowa A. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
We introduce and examine quantum states of a special kind, referred to as E-states, whose properties are both structurally and functionally analogous to the sieve of Eratosthenes. More broadly, the concept of an E-state is related to a certain noncommutative extension of the Dirichlet ring, also discussed here for the first time. Furthermore, we demonstrate that E-states can be implemented on a universal quantum computer and, as a particular application, we construct an algorithm which implements the Dirichlet multiplication of sequences on a quantum computer. We also discuss the potential applicability of E-states to the problem of integer factorization although, we haste to add, we are not aware at present of the possibility of using this approach to obtain algorithms of sub-exponential complexity