Factorization of numbers with Gauss sums: I. Mathematical background

Abstract

We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples. This algorithm relies solely on interference and scales exponentially.

21 pages, 8 figures

References in corpus (11)

• Experimental demonstration of Shor's algorithm with quantum entanglement
• Factorization of Numbers with the temporal Talbot effect: Optical implementation by a sequence of shaped ultrashort pulses
• Gauss sum factorization with cold atoms
• Factorizing Numbers with the Gauss Sum Technique: NMR Implementations
• Efficient Quantum Algorithms for Estimating Gauss Sums
• Factoring numbers with a single interferogram
• NMR implementation of Factoring Large Numbers with GaußSums: Suppression of Ghost Factors
• NMR implementations of Gauss sums
• Factorization of numbers with Gauss sums: II. Suggestions for implementations with chirped laser pulses
• Chirping a two-photon transition in a multi-state ladder
• Factorization of numbers with truncated Gauss sums at rational arguments

Cited by in corpus (4)

• Quantum Information Processing by Weaving Quantum Talbot Carpets
• Factorization of numbers with Gauss sums: II. Suggestions for implementations with chirped laser pulses
• The physics of thermal light second-order interference beyond coherence
• Factorization of numbers with Gauss sums: III. Algorithms with Entanglement