Steve Flammia, University of Washington
Abstract
Perturbation gadgets are a generic tool for reproducing the relevant physics in the ground state of a k-body Hamiltonian by using only two-body interactions. Most interesting Hamiltonians, such as those with topological order, have a large (extensive) number of local symmetries as well as some global symmetries. However, the existing gadgets do not preserve these symmetries even approximately. Here we begin an investigation of symmetry preserving perturbation gadgets. As a case study, we present a procedure to obtain the Hamiltonians of the toric code and all the Kitaev quantum double models as the low-energy limits of entirely two-body Hamiltonians. Our construction makes use error-detecting subsystem codes as well as the formalism of projected entangled pair states (PEPS). The gadgets reproduce the target models’ behavior using only couplings which are natural in terms of the original Hamiltonians, and we maintain an extensive number of symmetries from the target models.