One of the central applications for quantum annealers is to find the
solutions of Ising problems. Suitable Ising problems, however, need to be
formulated such that they, on the one hand, respect the specific restrictions
of the hardware and, on the other hand, represent the original problems which
shall actually be solved. We evaluate sufficient requirements on such an
embedded Ising problem analytically and transform them into a linear
optimization problem. With an objective function aiming to minimize the maximal
absolute problem parameter, the precision issues of the annealers are
addressed. Due to the redundancy of several constraints, we can show that the
formally exponentially large optimization problem can be reduced and finally
solved in polynomial time for the standard embedding setting where the embedded
vertices induce trees. This allows to formulate provably equivalent embedded
Ising problems in a practical setup.Comment: 34 pages, 3 figure
