Energy landscape of 3D spin Hamiltonians with topological order

We explore the feasibility of a quantum self-correcting memory based on 3D spin Hamiltonians with topological quantum order in which thermal diffusion of topological defects is suppressed by macroscopic energy barriers. To this end we characterize the energy landscape of stabilizer code Hamiltonians with local bounded-strength interactions which have a topologically ordered ground state but do not have stringlike logical operators. We prove that any sequence of local errors mapping a ground state of such a Hamiltonian to an orthogonal ground state must cross an energy barrier growing at least as a logarithm of the lattice size. Our bound on the energy barrier is tight up to a constant factor for one particular 3D spin Hamiltonian.     

Commuting Pauli Hamiltonians as Maps between Free Modules

We study unfrustrated spin Hamiltonians that consist of commuting tensor products of Pauli matrices. Assuming translation-invariance, a family of Hamiltonians that belong to the same phase of matter is described by a map between modules over the translation-group algebra, so homological methods are applicable. In any dimension every point-like charge appears as a vertex of a fractal operator, and can be isolated with energy barrier at most logarithmic in the separation distance. For a topologically ordered system in three dimensions, there must exist a point-like nontrivial charge. A connection between the ground state degeneracy and the number of points on an algebraic set is discussed. Tools to handle local Clifford unitary transformations are given.     

Conditional detection of pure quantum states of light after storage in a Tm-doped waveguide

We demonstrate the conditional detection of time-bin qubits after storage in and retrieval from a photon-echo-based waveguide quantum memory. Each qubit is encoded into one member of a photon pair produced via spontaneous parametric down-conversion, and the conditioning is achieved by the detection of the other member of the pair. By performing projection measurements with the stored and retrieved photons onto different bases, we obtain an average storage fidelity of 0.885±0.020, which exceeds the relevant classical bounds and shows the suitability of our integrated light-matter interface for future applications of quantum information processing.     

Best Fidelity Conditions for Three Party Quantum Teleportation

Using the entangled three qubit states classified by Acin et al. we find the best fidelity conditions for quantum teleportation among three parties.