Factorization of numbers with Gauss sums: I. Mathematical background

DOI10.1088/1367-2630/13/10/103007zbMath1448.11160arXiv1210.6474OpenAlexW2021012149MaRDI QIDQ5135217

Ilya Sh. Averbukh, Bertrand Girard, W. P. Schleich, Sabine Wölk, Wolfgang Merkel

Publication date: 19 November 2020

Published in: New Journal of Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.6474

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Quantum optics (81V80) Gauss and Kloosterman sums; generalizations (11L05)

Related Items (5)

Factorization of numbers with Gauss sums: II. Suggestions for implementation with chirped laser pulses ⋮ Factorization of numbers with Gauss sums: III. Algorithms with entanglement ⋮ Analogue algorithm for parallel factorization of an exponential number of large integers. II: Optical implementation ⋮ Analogue algorithm for parallel factorization of an exponential number of large integers. I: Theoretical description ⋮ Factorization with a logarithmic energy spectrum of a two-dimensional potential

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quantization of linear maps on a torus-Fresnel diffraction by a periodic grating
• Random renormalization in the semiclassical long-time limit of a precessing spin
• Quantum algorithms for algebraic problems
• Factoring Numbers with Waves
• Factorization of numbers with physical systems
• Factorization with exponential sums
• Renormalisation of curlicues
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Factorization of numbers with Gauss sums: II. Suggestions for implementation with chirped laser pulses
• Factorization of numbers with truncated Gauss sums at rational arguments
• New factorization algorithm based on a continuous representation of truncated Gauss sums
• CHIRPED PULSES, GAUSS SUMS AND THE FACTORIZATION OF NUMBERS

This page was built for publication: Factorization of numbers with Gauss sums: I. Mathematical background