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A factorisation algorithm in Adiabatic Quantum Computation
T. Kieu·August 8, 2018·DOI: 10.1088/2399-6528/ab060d
MathematicsPhysics
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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 ≤ N ≤ 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.