Encoding universal computation in the ground states of Ising lattices.

We characterize the set of ground states that can be synthesized by classical two-body Ising Hamiltonians. We then construct simple Ising planar blocks that simulate efficiently a universal set of logic gates and connections, and hence any Boolean function. We therefore provide a new method of encoding universal computation in the ground states of Ising lattices and a simpler alternative demonstration of the known fact that finding the ground state of a finite Ising spin glass model is NP complete. We relate this with our previous result about emergent properties in infinite lattices.