Open Access
2016 The Quantum Sieve of Eratosthenes
A. Sowa
Author Affiliations +
J. Phys. Math. 7(2): 1-6 (2016). DOI: 10.4172/2090-0902.1000180


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.


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A. Sowa. "The Quantum Sieve of Eratosthenes." J. Phys. Math. 7 (2) 1 - 6, 2016.


Published: 2016
First available in Project Euclid: 31 August 2017

Digital Object Identifier: 10.4172/2090-0902.1000180

Keywords: integer factorization , quantum algorithm for Dirichlet multiplication (convolution) , quantum sieve

Rights: Copyright © 2016 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.7 • No. 2 • 2016
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