Universal quantum computation by discontinuous quantum walk

Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution under the Hamiltonian furnished by the adjacency matrix of the graph. We present a hybrid scheme for universal quantum computation in which a quantum walker takes discrete steps of continuous evolution. This `discontinuous' quantum walk employs perfect quantum state transfer between two nodes of specific subgraphs chosen to implement a universal gate set, thereby ensuring unitary evolution without requiring the introduction of an ancillary coin space. The run time is linear in the number of simulated qubits and gates. The scheme allows multiple runs of the algorithm to be executed almost simultaneously by starting walkers one timestep apart.Comment: 7 pages, revte

Symmetries and noise in quantum walk

We study some discrete symmetries of unbiased (Hadamard) and biased quantum walk on a line, which are shown to hold even when the quantum walker is subjected to environmental effects. The noise models considered in order to account for these effects are the phase flip, bit flip and generalized amplitude damping channels. The numerical solutions are obtained by evolving the density matrix, but the persistence of the symmetries in the presence of noise is proved using the quantum trajectories approach. We also briefly extend these studies to quantum walk on a cycle. These investigations can be relevant to the implementation of quantum walks in various known physical systems. We discuss the implementation in the case of NMR quantum information processor and ultra cold atoms.Comment: 19 pages, 24 figures : V3 - Revised version to appear in Phys. Rev. A. - new section on quantum walk in a cycle include

Higher Order Decompositions of Ordered Operator Exponentials

We present a decomposition scheme based on Lie-Trotter-Suzuki product formulae to represent an ordered operator exponential as a product of ordinary operator exponentials. We provide a rigorous proof that does not use a time-displacement superoperator, and can be applied to non-analytic functions. Our proof provides explicit bounds on the error and includes cases where the functions are not infinitely differentiable. We show that Lie-Trotter-Suzuki product formulae can still be used for functions that are not infinitely differentiable, but that arbitrary order scaling may not be achieved.Comment: 16 pages, 1 figur

Exploring the Cosmic Evolution of Habitability with Galaxy Merger Trees

We combine inferred galaxy properties from a semi-analytic galaxy evolution model incorporating dark matter halo merger trees with new estimates of supernova and gamma ray burst rates as a function of metallicity from stellar population synthesis models incorporating binary interactions. We use these to explore the stellar mass fraction of galaxies irradiated by energetic astrophysical transients and its evolution over cosmic time, and thus the fraction which is potentially habitable by life like our own. We find that 18 per cent of the stellar mass in the Universe is likely to have been irradiated within the last 260 Myr, with GRBs dominating that fraction. We do not see a strong dependence of irradiated stellar mass fraction on stellar mass or richness of the galaxy environment. We consider a representative merger tree as a Local Group analogue, and find that there are galaxies at all masses which have retained a high habitable fraction (>40 per cent) over the last 6 Gyr, but also that there are galaxies at all masses where the merger history and associated star formation have rendered galaxies effectively uninhabitable. This illustrates the need to consider detailed merger trees when evaluating the cosmic evolution of habitability.Comment: 11 page, 10 figures. MNRAS accepted 13th Dec 2017. Updated to match accepted version, with additional discussion of metallicity effect

Spin-1/2 particles moving on a 2D lattice with nearest-neighbor interactions can realize an autonomous quantum computer

What is the simplest Hamiltonian which can implement quantum computation without requiring any control operations during the computation process? In a previous paper we have constructed a 10-local finite-range interaction among qubits on a 2D lattice having this property. Here we show that pair-interactions among qutrits on a 2D lattice are sufficient, too, and can also implement an ergodic computer where the result can be read out from the time average state after some post-selection with high success probability. Two of the 3 qutrit states are given by the two levels of a spin-1/2 particle located at a specific lattice site, the third state is its absence. Usual hopping terms together with an attractive force among adjacent particles induce a coupled quantum walk where the particle spins are subjected to spatially inhomogeneous interactions implementing holonomic quantum computing. The holonomic method ensures that the implemented circuit does not depend on the time needed for the walk. Even though the implementation of the required type of spin-spin interactions is currently unclear, the model shows that quite simple Hamiltonians are powerful enough to allow for universal quantum computing in a closed physical system.Comment: More detailed explanations including description of a programmable version. 44 pages, 12 figures, latex. To appear in PR

LGP2 plays a critical role in sensitizing mda-5 to activation by double-stranded RNA.

The DExD/H box RNA helicases retinoic acid-inducible gene-I (RIG-I) and melanoma differentiation associated gene-5 (mda-5) sense viral RNA in the cytoplasm of infected cells and activate signal transduction pathways that trigger the production of type I interferons (IFNs). Laboratory of genetics and physiology 2 (LGP2) is thought to influence IFN production by regulating the activity of RIG-I and mda-5, although its mechanism of action is not known and its function is controversial. Here we show that expression of LGP2 potentiates IFN induction by polyinosinic-polycytidylic acid [poly(I:C)], commonly used as a synthetic mimic of viral dsRNA, and that this is particularly significant at limited levels of the inducer. The observed enhancement is mediated through co-operation with mda-5, which depends upon LGP2 for maximal activation in response to poly(I:C). This co-operation is dependent upon dsRNA binding by LGP2, and the presence of helicase domain IV, both of which are required for LGP2 to interact with mda-5. In contrast, although RIG-I can also be activated by poly(I:C), LGP2 does not have the ability to enhance IFN induction by RIG-I, and instead acts as an inhibitor of RIG-I-dependent poly(I:C) signaling. Thus the level of LGP2 expression is a critical factor in determining the cellular sensitivity to induction by dsRNA, and this may be important for rapid activation of the IFN response at early times post-infection when the levels of inducer are low

The human ehrlichioses in the United States.

The emerging tick-borne zoonoses human monocytic ehrlichiosis (HME) and human granulocytic ehrlichiosis (HGE) are under reported in the United States. From 1986 through 1997, 1,223 cases (742 HME, 449 HGE, and 32 not ascribed to a specific ehrlichial agent) were reported by state health departments. HME was most commonly reported from southeastern and southcentral states, while HGE was most often reported from northeastern and upper midwestern states. The annual number of reported cases increased sharply, from 69 in 1994 to 364 in 1997, coincident with an increase in the number of states making these conditions notifiable. From 1986 through 1997, 827 probable and confirmed cases were diagnosed by serologic testing at the Centers for Disease Control and Prevention, although how many of these cases were also reported by states is not known. Improved national surveillance would provide a better assessment of the public health importance of ehrlichiosis

Necessary Condition for the Quantum Adiabatic Approximation

A gapped quantum system that is adiabatically perturbed remains approximately in its eigenstate after the evolution. We prove that, for constant gap, general quantum processes that approximately prepare the final eigenstate require a minimum time proportional to the ratio of the length of the eigenstate path to the gap. Thus, no rigorous adiabatic condition can yield a smaller cost. We also give a necessary condition for the adiabatic approximation that depends on local properties of the path, which is appropriate when the gap varies.Comment: 5 pages, 1 figur