Toric codes and quantum doubles from two-body Hamiltonians

Understand

We present a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the low-energy limits of entirely two-body Hamiltonians.

• Our construction makes use of a new type of perturbation gadget based on error-detecting subsystem codes.
• The procedure is motivated by a PEPS description of the target models, and reproduces the target models' behavior using only couplings which are natural in terms of the original Hamiltonians.
• This allows our construction to exactly capture the symmetries of the target models.