Quantum Annealing for Prime Factorization

Jiang, Shuxian; Britt, Keith A.; McCaskey, Alexander J.; Humble, Travis S.; Kais, Sabre

doi:10.1038/s41598-018-36058-z

Title: Quantum Annealing for Prime Factorization

Journal Article · 04 December 2018 · Scientific Reports

DOI: https://doi.org/10.1038/s41598-018-36058-z · OSTI ID:1524891

Jiang, Shuxian ^[1];

^[2];

^[2]; Kais, Sabre ^[1]

Purdue Univ., West Lafayette, IN (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

We have developed a framework to convert an arbitrary integer factorization problem to an executable Ising model by first writing it as an optimization function then transforming the k-bit coupling (k ≥ 3) terms to quadratic terms using ancillary variables. Our resource-efficient method uses O(log²(N)) binary variables (qubits) for finding the factors of an integer N. We present how to factorize 15, 143, 59989, and 376289 using 4, 12, 59, and 94 logical qubits, respectively. This method was tested using the D-Wave 2000Q for finding an embedding and determining the prime factors for a given composite number. The method is general and could be used to factor larger integers as the number of available qubits increases, or combined with other ad hoc methods to achieve better performances for specific numbers.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1524891

Journal Information:: Scientific Reports, Journal Name: Scientific Reports Journal Issue: 1 Vol. 8; ISSN 2045-2322

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

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Cited By (2)

Integer factorization using stochastic magnetic tunnel junctions Borders, William A.; Pervaiz, Ahmed Z.; Fukami, Shunsuke Nature, Vol. 573, Issue 7774 https://doi.org/10.1038/s41586-019-1557-9	journal	September 2019
p-bits for probabilistic spin logic Camsari, Kerem Y.; Sutton, Brian M.; Datta, Supriyo Applied Physics Reviews, Vol. 6, Issue 1 https://doi.org/10.1063/1.5055860	journal	March 2019

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