Loading...

Topological color codes and two-body quantum lattice Hamiltonians

Kargarian, M | 2010

1042 Viewed
  1. Type of Document: Article
  2. DOI: 10.1088/1367-2630/12/2/025018
  3. Publisher: 2010
  4. Abstract:
  5. Topological color codes are among the stabilizer codes with remarkable properties from the quantum information perspective. In this paper, we construct a lattice, the so-called ruby lattice, with coordination number 4 governed by a two-body Hamiltonian. In a particular regime of coupling constants, in a strong coupling limit, degenerate perturbation theory implies that the low-energy spectrum of the model can be described by a many-body effective Hamiltonian, which encodes the color code as its ground state subspace. Ground state subspace corresponds to a vortex-free sector. The gauge symmetry Z2 ×Z2 of the color code could already be realized by identifying three distinct plaquette operators on the ruby lattice. All plaquette operators commute with each other and with the Hamiltonian being integrals of motion. Plaquettes are extended to closed strings or string-net structures. Non-contractible closed strings winding the space commute with Hamiltonian but not always with each other. This gives rise to exact topological degeneracy of the model. A connection to 2-colexes can be established via the coloring of the strings.We discuss it at the non-perturbative level. The particular structure of the two-body Hamiltonian provides a fruitful interpretation in terms of mapping onto bosons coupled to effective spins. We show that high-energy excitations of the model have fermionic statistics. They form three families of high-energy excitations each of one color. Furthermore, we show that they belong to a particular family of topological charges. The emergence of invisible charges is related to the string-net structure of the model
  6. Keywords:
  7. Coordination number ; Coupling constants ; Effective Hamiltonian ; Gauge symmetries ; High energy ; Integrals of motion ; Lattice Hamiltonians ; Low-energy spectra ; Many-body ; Net structures ; Perturbation theory ; Quantum Information ; Strong coupling ; Topological charges ; Topological degeneracies ; Color ; Color codes ; Ground state ; High energy physics ; Perturbation techniques ; Quantum optics ; Ruby ; Spectroscopy ; Topology ; Hamiltonians
  8. Source: New Journal of Physics ; Volume 12 , 2010 ; 13672630 (ISSN)
  9. URL: http://iopscience.iop.org/article/10.1088/1367-2630/12/2/025018/meta