An Efficient Exact Quantum Algorithm for the Integer Squarefree Decomposition Problem
Abstract
Quantum computers are known to be qualitatively more powerful than classical computers, but so far only a small number of different algorithms have been discovered that actually use this potential. It would therefore be highly desirable to develop other types of quantum algorithms that widen the range of possible applications. Here we propose an efficient and exact quantum algorithm for finding the squarefree part of a large integer  a problem for which no efficient classical algorithm exists. The algorithm relies on properties of Gauss sums and uses the quantum Fourier transform. We give an explicit quantum network for the algorithm. Our algorithm introduces new concepts and methods that have not been used in quantum information processing so far and may be applicable to a wider class of problems.
 Publication:

Scientific Reports
 Pub Date:
 February 2012
 DOI:
 10.1038/srep00260
 arXiv:
 arXiv:1108.5848
 Bibcode:
 2012NatSR...2E.260L
 Keywords:

 Quantum Physics
 EPrint:
 19 pages, 9 figures