Factorization of numbers with physical systems
FacultiesFakultät für Naturwissenschaften
LicenseStandard (Fassung vom 03.05.2003)
In the present thesis we approach the factorization problem with a combination of quantum physics and aspects of number theory. The key to our approach is based on Gauss sums which are central to number theory. We take advantage of the cyclic properties of Gauss sums. The main idea consists in regarding a Gauss sum to arise from the superposition of quantum paths which are weighted by quadratic phase factors. Thus our schemes solely base on interference. We present three quantum optical realizations which we discuss in the context of experimental requirements and limitations. All systems allow for direct access to Gauss sums via fluorescence measurements from the excited state. We develop methods for gaining information on the divisors of N from different types of Gauss sums. We also discuss a recent factorization experiment. By means of nuclear magnetic resonance Prof. Michael Mehring (University of Stuttgart) has demonstrated the factorization of a six-digit number using sequences of radio frequency-pulses.
Subject HeadingsFaktorisierung [GND]
Quantum optics [LCSH]