| Issue |
EPL
Volume 83, Number 3, August 2008
|
|
|---|---|---|
| Article Number | 34008 | |
| Number of page(s) | 4 | |
| Section | Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics | |
| DOI | https://doi.org/10.1209/0295-5075/83/34008 | |
| Published online | 29 July 2008 | |
Factoring numbers with interfering random waves
Laboratoire Collisions, Agrégats, Réactivité - IRSAMC-(CNRS, Université de Toulouse, UPS) - Toulouse, France, EU
Corresponding author: beatrice@irsamc.ups-tlse.fr
Received:
16
April
2008
Accepted:
20
June
2008
We report on a new implementation of the factorisation of
numbers using Gauss sums which improves tremendously the efficiency to eliminate all “ghost" factors. We show that by choosing randomly
the terms in the Gauss sum, the required number of terms varies as lnN instead of ![$\sqrt[4]{N} $](/articles/epl/abs/2008/15/epl11122/epl11122_tex_eq1.png)
. As an illustration, we present
experimental results obtained by interfering thirty ultrashort laser pulses where we factorise 1340333404807. This new approach is
totally general and can be implemented for all the experiments based on the Gauss sum.
PACS: 42.65.Re – Ultrafast processes; optical pulse generation and pulse compression / 02.10.De – Algebraic structures and number theory / 42.79.Kr – Display devices, liquid-crystal devices
© EPLA, 2008
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