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A question that has been bugging my mind in quantum annealing is:

Assume we have a QUBO matrix $Q_{ij}$ with non-zero non-diagonal elements which have different signs, that is $Q_{ij}<0$ for some $i\neq j$ and $Q_{nm}>0$ for some $m\neq n$. How can these be mapped into an Ising model, where as far as I know, $J_{ij}$ (spin-spin coupling energy) have fixed signs (either ferromagnetic $J_{ij}<0$ or antiferromagnetic $J_{ij}>0,\,$ $\forall i,j$ but not both)? How can we account for this sign change in the mapping from QUBO to Ising?

Thanks in advance! :)

Nikolaos Petropoulos
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An Ising model need not have strictly ferromagnetic or antiferromagnetic interactions. Even purely in terms of the physics, models with competing interactions are of moderate interest, for example https://arxiv.org/abs/1906.09668.

Banach space fan
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