Factorization of numbers with Gauss sums: II. Suggestions for implementations with chirped laser pulses

TL;DR

This paper explores three quantum implementation methods using chirped laser pulses to perform Gauss sum-based number factorization, providing practical encoding and detection strategies for the factors.

Contribution

It introduces three novel quantum schemes employing chirped laser pulses for Gauss sum factorization, expanding practical approaches for quantum number factoring.

Findings

Excitation probabilities correspond to Gauss sums in all schemes

Encoding of the number N is achieved through laser pulse parameters

Factors are identified via fluorescence signals

Abstract

We propose three implementations of the Gauss sum factorization schemes discussed in part I of this series: (i) a two-photon transition in a multi-level ladder system induced by a chirped laser pulse, (ii) a chirped one-photon transition in a two-level atom with a periodically modulated excited state, and (iii) a linearly chirped one-photon transition driven by a sequence of ultrashort pulses. For each of these quantum systems we show that the excitation probability amplitude is given by an appropriate Gauss sum. We provide rules how to encode the number N to be factored in our system and how to identify the factors of N in the fluorescence signal of the excited state.