Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum adiabatic algorithm for Hilbert's tenth problem: I. The
  algorithm   We review the proposal of a quantum algorithm for Hilbert's tenth problem and
provide further arguments towards the proof that: (i) the algorithm terminates
after a finite time for any input of Diophantine equation; (ii) the final
ground state which contains the answer for the Diophantine equation can be
identified as the component state having better-than-even probability to be
found by measurement at the end time--even though probability for the final
ground state in a quantum adiabatic process need not monotonically increase
towards one in general. Presented finally are the reasons why our algorithm is
outside the jurisdiction of no-go arguments previously employed to show that
Hilbert's tenth problem is recursively non-computable.

36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int