Improved quantum algorithms for the ordered search problem via semidefinite programming

One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem using a constant factor fewer queries. However, the precise value of this constant is unknown. By characterizing a class of quantum query algorithms for ordered search in terms of a semidefinite program, we find new quantum algorithms for small instances of the ordered search problem. Extending these algorithms to arbitrarily large instances using recursion, we show that there is an exact quantum ordered search algorithm using 4 log_{605} N \approx 0.433 log_2 N queries, which improves upon the previously best known exact algorithm.Comment: 8 pages, 4 figure

Desorption of n-alkanes from graphene: a van der Waals density functional study

A recent study of temperature programmed desorption (TPD) measurements of small n-alkanes (CNH2N+2) from C(0001) deposited on Pt(111) shows a linear relationship of the desorption energy with increasing n-alkane chain length. We here present a van der Waals density functional study of the desorption barrier energy of the ten smallest n-alkanes (N = 1 to 10) from graphene. We find linear scaling with N, including a nonzero intercept with the energy axis, i.e., an offset at the extrapolation to N = 0. This calculated offset is quantitatively similar to the results of the TPD measurements. From further calculations of the polyethylene polymer we offer a suggestion for the origin of the offset.Comment: 3 pictures, 1 tabl

Dynamics and manipulation of entanglement in coupled harmonic systems with many degrees of freedom

Published versio

Evolution of turbulent spots in a parallel shear flow

The evolution of turbulent spots in a parallel shear flow is studied by means of full three-dimensional numerical simulations. The flow is bounded by free surfaces and driven by a volume force. Three regions in the spanwise spot cross-section can be identified: a turbulent interior, an interface layer with prominent streamwise streaks and vortices and a laminar exterior region with a large scale flow induced by the presence of the spot. The lift-up of streamwise streaks which is caused by non-normal amplification is clearly detected in the region adjacent to the spot interface. The spot can be characterized by an exponentially decaying front that moves with a speed different from that of the cross-stream outflow or the spanwise phase velocity of the streamwise roll pattern. Growth of the spots seems to be intimately connected to the large scale outside flow, for a turbulent ribbon extending across the box in downstream direction does not show the large scale flow and does not grow. Quantitatively, the large scale flow induces a linear instability in the neighborhood of the spot, but the associated front velocity is too small to explain the spot spreading.Comment: 10 pages, 10 Postscript figure

Generalized Toric Codes Coupled to Thermal Baths

We have studied the dynamics of a generalized toric code based on qudits at finite temperature by finding the master equation coupling the code's degrees of freedom to a thermal bath. As a consequence, we find that for qutrits new types of anyons and thermal processes appear that are forbidden for qubits. These include creation, annihilation and diffusion throughout the system code. It is possible to solve the master equation in a short-time regime and find expressions for the decay rates as a function of the dimension $d$ of the qudits. Although we provide an explicit proof that the system relax to the Gibbs state for arbitrary qudits, we also prove that above a certain crossing temperature, qutrits initial decay rate is smaller than the original case for qubits. Surprisingly this behavior only happens with qutrits and not with other qudits with $d>3$.Comment: Revtex4 file, color figures. New Journal of Physics' versio

Topological Color Codes and Two-Body Quantum Lattice Hamiltonians

Topological color codes are among the stabilizer codes with remarkable properties from quantum information perspective. In this paper we construct a four-valent lattice, the so called ruby lattice, governed by a 2-body Hamiltonian. In a particular regime of coupling constants, 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. The gauge symmetry $\mathbf{Z}_{2}\times\mathbf{Z}_{2}$ of color code could already be realized by identifying three distinct plaquette operators on the lattice. 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 giving rise to exact topological degeneracy of the model. Connection to 2-colexes can be established at the non-perturbative level. The particular structure of the 2-body Hamiltonian provides a fruitful interpretation in terms of mapping to 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. Also, we use Jordan-Wigner transformation in order to test the integrability of the model via introducing of Majorana fermions. The four-valent structure of the lattice prevents to reduce the fermionized Hamiltonian into a quadratic form due to interacting gauge fields. We also propose another construction for 2-body Hamiltonian based on the connection between color codes and cluster states. We discuss this latter approach along the construction based on the ruby lattice.Comment: 56 pages, 16 figures, published version

Phenomenon of declining blood pressure in elderly - high systolic levels are undervalued with Korotkoff method

<p>Abstract</p> <p>Background</p> <p>Systolic blood pressure (SBP) decline has been reported in octogenarians. The aim was to study if it could be observed while measuring SBP with two methods: Korotkoff (K-BP) and Strain-Gauge-Finger-Pletysmography (SG-BP), and which of them were more reliable in expressing vascular burden.</p> <p>Methods</p> <p>A cohort of 703 men from a population of Malmö, Sweden, were included in "Men born in 1914-study" and followed-up at ages: 68 and 81 years. 176 survivors were examined with K-BP and SG-BP at both ages, and 104 of them with Ambulatory Blood Pressure at age 81/82. Ankle Brachial Index (ABI) was measured on both occasions, and Carotid Ultrasound at age 81.</p> <p>Results</p> <p>From age 68 to 81, mean K-BP decreased in the cohort with mean 8.3 mmHg, while SG-BP increased with 13.4 mmHg. K-BP decreased in 55% and SG-BP in 31% of the subjects. At age 81, K-BP was lower than SG-BP in 72% of subjects, and correlated to high K-BP at age 68 (r = --.22; p < .05). SG-BP at age 81 was correlated with mean ambulatory 24-h SBP (r = .480; p < .0001), daytime SBP (r = .416; p < .0001), nighttime SBP (r = .395; p < .0001), and daytime and nighttime Pulse Pressure (r = .452; p < .0001 and r = .386; p < .0001). KB-BP correlated moderately only with nighttime SBP (r = .198; p = .044), and daytime and nightime pulse pressure (r = .225; p = .021 and r = .264; p = .007). Increasing SG-BP from age 68 to 81, but not K-BP, correlated with: 24-h, daytime and nighttime SBP, and mean daytime and nighttime Pulse Pressure. Increasing SG-BP was also predicted by high B-glucose and low ABI at age 68, and correlated with carotid stenosis and low ABI age 81, and the grade of ABI decrease over 13 years.</p> <p>Conclusion</p> <p>In contrast to K-BP, values of SG-BP in octogenarians strongly correlated with Ambulatory Blood Pressure. The SG-BP decline in the last decade was rare, and increasing SG-BP better than K-BP reflected advanced atherosclerosis. It should be aware, that K-BP underdetected 46% of subjects with SG-BP equal/higher than 140 mmHg at age 81, which may lead to biased associations with risk factors due to differential misclassification by age.</p