Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ising formulations of many NP problems   We provide Ising formulations for many NP-complete and NP-hard problems,
including all of Karp's 21 NP-complete problems. This collects and extends
mappings to the Ising model from partitioning, covering and satisfiability. In
each case, the required number of spins is at most cubic in the size of the
problem. This work may be useful in designing adiabatic quantum optimization
algorithms.

20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess