  Many-body entangled systems, in particular topologically ordered spin systems
proposed as resources for quantum information processing tasks, often involve
highly non-local interaction terms. While one may approximate such systems
through two-body interactions perturbatively, these approaches have a number of
drawbacks in practice. Here, we propose a scheme to simulate many-body spin
Hamiltonians with two-body Hamiltonians non-perturbatively. Unlike previous
approaches, our Hamiltonians are not only exactly solvable with exact ground
state degeneracy, but also support completely localized quasi-particle
excitations, which are ideal for quantum information processing tasks. Our
construction is limited to simulating the toric code and quantum double models,
but generalizations to other non-local spin Hamiltonians may be possible.
