A toolbox for lattice-spin models with polar molecules

There is growing interest in states of matter with topological order. These are characterized by highly stable ground states robust to perturbations that preserve the topology, and which support excitations with so-called anyonic statistics. Topologically ordered states can arise in two-dimensional lattice-spin models, which were proposed as the basis for a new class of quantum computation. Here, we show that the relevant hamiltonians for such spin lattice models can be systematically engineered with polar molecules stored in optical lattices, where the spin is represented by a single-valence electron of a heteronuclear molecule. The combination of microwave excitation with dipole - dipole interactions and spin - rotation couplings enables building a complete toolbox for effective two-spin interactions with designable range, spatial anisotropy and coupling strengths significantly larger than relevant decoherence rates. Finally, we illustrate two models: one with an energy gap providing for error-resilient qubit encoding, and another leading to topologically protected quantum memory.