Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing the Noncomputable   We explore in the framework of Quantum Computation the notion of
computability, which holds a central position in Mathematics and Theoretical
Computer Science. A quantum algorithm that exploits the quantum adiabatic
processes is considered for the Hilbert's tenth problem, which is equivalent to
the Turing halting problem and known to be mathematically noncomputable.
Generalised quantum algorithms are also considered for some other mathematical
noncomputables in the same and of different noncomputability classes. The key
element of all these algorithms is the measurability of both the values of
physical observables and of the quantum-mechanical probability distributions
for these values. It is argued that computability, and thus the limits of
Mathematics, ought to be determined not solely by Mathematics itself but also
by physical principles.

28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio