A Factorisation Algorithm in Adiabatic Quantum Computation

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.

11 pages, 3 figures

References in corpus (1)

• The Travelling Salesman Problem and Adiabatic Quantum Computation: An Algorithm

Cited by in corpus (2)

• The Travelling Salesman Problem and Adiabatic Quantum Computation: An Algorithm
• A Class of Time-Energy Uncertainty Relations for Time-dependent Hamiltonians