3 years ago

# A Factorisation Algorithm in Adiabatic Quantum Computation.

Tien D. Kieu

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 the corresponding Diophantine polynomial $Q_N(x,y)=N^2(N-xy)^2 + x(x-y)^2$, 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.

Publisher URL: http://arxiv.org/abs/1808.02781

DOI: arXiv:1808.02781v2

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