Topological color codes and two-body quantum lattice Hamiltonians

摘要: Topological color codes are among the stabilizer with remarkable properties from quantum information perspective. In this paper, we construct a lattice, so-called ruby coordination number 4 governed by two-body Hamiltonian. particular regime of coupling constants, in strong limit, degenerate perturbation theory implies that low-energy spectrum model can be described many-body effective Hamiltonian, which encodes code as its ground state subspace. Ground subspace corresponds to vortex-free sector. The gauge symmetry Z2×Z2 could already realized identifying three distinct plaquette operators on lattice. All commute each other and Hamiltonian being integrals motion. Plaquettes extended closed strings or string-net structures. Non-contractible winding space but not always other. This gives rise exact topological degeneracy model. A connection 2-colexes established via coloring strings. We discuss it at non-perturbative level. structure provides fruitful interpretation terms mapping onto bosons coupled spins. show high-energy excitations have fermionic statistics. They form families one color. Furthermore, they belong family charges. emergence invisible charges is related emerging fermions nontrivial fields. for 2-colexes, see background fluxes state. Also, use Jordan–Wigner transformation order test integrability introducing Majorana fermions. four-valent lattice prevents fermionized reduced quadratic owing interacting also propose another construction based between cluster states. corresponding defined bipartite spectrum, subsequent selective measurements give latter approach along