Stabilizing Entangled States with Quasi-Local Quantum Dynamical Semigroups

We provide a solution to the problem of determining whether a target pure state can be asymptotically prepared using dissipative Markovian dynamics under fixed locality constraints. Beside recovering existing results for a large class of physically relevant entangled states, our approach has the advantage of providing an explicit stabilization test solely based on the input state and constraints of the problem. Connections with the formalism of frustration-free parent Hamiltonians are discussed, as well as control implementations in terms of a switching output-feedback law.Comment: 11 pages, no figure

Efficient generation of universal two-dimensional cluster states with hybrid systems

We present a scheme to generate two-dimensional cluster state efficiently. The number of the basic gate-entangler-for the operation is in the order of the entanglement bonds of a cluster state, and could be reduced greatly if one uses them repeatedly. The scheme is deterministic and uses few ancilla resources and no quantum memory. It is suitable for large-scale quantum computation and feasible with the current experimental technology.Comment: 6 pages, 5 figure

Stabilization of solitons of the multidimensional nonlinear Schrodinger equation: Matter-wave breathers

We demonstrate that stabilization of solitons of the multidimensional Schrodinger equation with a cubic nonlinearity may be achieved by a suitable periodic control of the nonlinear term. The effect of this control is to stabilize the unstable solitary waves which belong to the frontier between expanding and collapsing solutions and to provide an oscillating solitonic structure, some sort of breather-type solution. We obtain precise conditions on the control parameters to achieve the stabilization and compare our results with accurate numerical simulations of the nonlinear Schrodinger equation. Because of the application of these ideas to matter waves these solutions are some sort of matter breathers

Classification of the phases of 1D spin chains with commuting Hamiltonians

We consider the class of spin Hamiltonians on a 1D chain with periodic boundary conditions that are (i) translational invariant, (ii) commuting and (iii) scale invariant, where by the latter we mean that the ground state degeneracy is independent of the system size. We correspond a directed graph to a Hamiltonian of this form and show that the structure of its ground space can be read from the cycles of the graph. We show that the ground state degeneracy is the only parameter that distinguishes the phases of these Hamiltonians. Our main tool in this paper is the idea of Bravyi and Vyalyi (2005) in using the representation theory of finite dimensional C^*-algebras to study commuting Hamiltonians.Comment: 8 pages, improved readability, added exampl

Efficient measurement-based quantum computing with continuous-variable systems

We present strictly efficient schemes for scalable measurement-based quantum computing using continuous-variable systems: These schemes are based on suitable non-Gaussian resource states, ones that can be prepared using interactions of light with matter systems or even purely optically. Merely Gaussian measurements such as optical homodyning as well as photon counting measurements are required, on individual sites. These schemes overcome limitations posed by Gaussian cluster states, which are known not to be universal for quantum computations of unbounded length, unless one is willing to scale the degree of squeezing with the total system size. We establish a framework derived from tensor networks and matrix product states with infinite physical dimension and finite auxiliary dimension general enough to provide a framework for such schemes. Since in the discussed schemes the logical encoding is finite-dimensional, tools of error correction are applicable. We also identify some further limitations for any continuous-variable computing scheme from which one can argue that no substantially easier ways of continuous-variable measurement-based computing than the presented one can exist.Comment: 13 pages, 3 figures, published versio

Detection of Symmetry Protected Topological Phases in 1D

A topological phase is a phase of matter which cannot be characterized by a local order parameter. It has been shown that gapped phases in 1D systems can be completely characterized using tools related to projective representations of the symmetry groups. We show how to determine the matrices of these representations in a simple way in order to distinguish between different phases directly. From these matrices we also point out how to derive several different types of non-local order parameters for time reversal, inversion symmetry and $Z_2 \times Z_2$ symmetry, as well as some more general cases (some of which have been obtained before by other methods). Using these concepts, the ordinary string order for the Haldane phase can be related to a selection rule that changes at the critical point. We furthermore point out an example of a more complicated internal symmetry for which the ordinary string order cannot be applied.Comment: 12 pages, 9 Figure