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Update: I was able to find an arxiv version of the paper: http://arxiv.org/pdf/1406.5955v1.pdf http://arxiv.org/pdf/1406.5955v1.pdf It seems that I wasn't wron
by gajomi 11y ago
Update: I was able to find an arxiv version of the paper: http://arxiv.org/pdf/1406.5955v1.pdf http://arxiv.org/pdf/1406.5955v1.pdf
It seems that I wasn't wrong about the context (indeed they focus on solving the full partition function, as opposed to just the ground state energy), but there is some additional information in the paper that is worth sharing.
The first is that their construction relies on a method where (1) the spins used to simulate a target Ising model are a subset of those taken in their universal model based on SAT and (2) that to make a correspondence between the energy levels in the universal mode and the target model one must throw away terms in the universal models partition function with energy larger than some Δ, so that the spectrum of the target model is a subset of the spectrum of the universal model. I think (1) is a neat trick, although maybe not too surprising if you are familiar with, e.g. hidden spin layers in neural network models. With respect to (2) they claim that this allows one to approximate the target model partition function with an error term of size O(exp(-Δ)). I would assume that this means that there can;t be too many states in the full model with with energy greater than Δ, since if they grew exponentially in number this could counteract the exponential damping in contribution in the partition function. Maybe someone who actually read the paper from start to finish can comment?
- btilly 11y agoOK, that does look like a lot less trivial a result than the article made it look like. :-)