Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Factorisation Algorithm in Adiabatic Quantum Computation   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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The categories of this paper are: cond-mat
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The categories of this paper are: stat
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex