Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graver Bases via Quantum Annealing with Application to Non-Linear
  Integer Programs   We propose a novel hybrid quantum-classical approach to calculate Graver
bases, which have the potential to solve a variety of hard linear and
non-linear integer programs, as they form a test set (optimality certificate)
with very appealing properties. The calculation of Graver bases is
exponentially hard (in general) on classical computers, so they not used for
solving practical problems on commercial solvers. With a quantum annealer,
however, it may be a viable approach to use them. We test two hybrid
quantum-classical algorithms (on D-Wave)--one for computing Graver basis and a
second for optimizing non-linear integer programs that utilize Graver bases--to
understand the strengths and limitations of the practical quantum annealers
available today. Our experiments suggest that with a modest increase in coupler
precision--along with near-term improvements in the number of qubits and
connectivity (density of hardware graph) that are expected--the ability to
outperform classical best-in-class algorithms is within reach, with respect to
non-linear integer optimization.

34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol