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We characterize the set of ground states that can be synthesized by classical2-body Ising Hamiltonians. We then construct simple Ising planar blocks thatsimulates efficiently a universal set of logic gates and connections, and henceany boolean function. We therefore provide a new method of encoding universalcomputation in the ground states of Ising lattices, and a simpler alternativedemonstration of the known fact that finding the ground state of a finite Isingspin glass model is NP complete. We relate this with our previous result aboutemergence properties in infinite lattices.

Encoding Universal Computation in the Ground States of Ising Lattices