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arXiv · 1808.02781

A Factorisation Algorithm in Adiabatic Quantum Computation

Tien D. Kieu
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Abstract

The problem of factorising positive integer $N$ into two integer factors $x$ and $y$ is first reformulated as an optimisation problem over the positive integer domain of either of the Diophantine polynomials $Q_N(x,y)=N^2(N-xy)^2 + x(x-y)^2$ or $R_N(x,y) = N^2(N-xy)^2 + (x-y)^2 + x$, of each of which the optimal solution is unique with $x\le \sqrt{N} \le y$, and $x=1$ if and only if $N$ is prime. An algorithm in the context of Adiabatic Quantum Computation is then proposed for the general factorisation problem.

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Tien D. Kieu. 2019-02-28. A Factorisation Algorithm in Adiabatic Quantum Computation. https://doi.org/10.1088/2399-6528%2Fab060d

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