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

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.

arXiv comment22 pages, 7 figures

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Cited by in corpus (7)

• Prime Number Decomposition using the Talbot Effect
• Factorization of numbers with Gauss sums: I. Mathematical background
• Chirped quasi-phase-matching with Gauss sums for production of biphotons
• Analogue algorithm for parallel factorization of an exponential number of large integers I. Theoretical description
• Factorization of numbers with Gauss sums: III. Algorithms with Entanglement
• Ghost factors in Gauss-sum factorization with transmon qubits
• Number-theoretic expressions obtained through analogy between prime factorization and optical interferometry