Entanglement and its Role in Shor's Algorithm

Entanglement has been termed a critical resource for quantum information processing and is thought to be the reason that certain quantum algorithms, such as Shor's factoring algorithm, can achieve exponentially better performance than their classical counterparts. The nature of this resource is still not fully understood: here we use numerical simulation to investigate how entanglement between register qubits varies as Shor's algorithm is run on a quantum computer. The shifting patterns in the entanglement are found to relate to the choice of basis for the quantum Fourier transform.Comment: 15 pages, 4 eps figures, v1-3 were for conference proceedings (not included in the end); v4 is improved following referee comments, expanded explanations and added reference

Atmospheric, climatic and environmental research

Work performed on the three tasks during the report period is summarized. The climate and atmospheric modeling studies included work on climate model development and applications, paleoclimate studies, climate change applications, and SAGE II. Climate applications of Earth and planetary observations included studies on cloud climatology and planetary studies. Studies on the chemistry of the Earth and the environment are briefly described. Publications based on the above research are listed; two of these papers are included in the appendices

An Observational Diagnostic for Distinguishing Between Clouds and Haze in Hot Exoplanet Atmospheres

The nature of aerosols in hot exoplanet atmospheres is one of the primary vexing questions facing the exoplanet field. The complex chemistry, multiple formation pathways, and lack of easily identifiable spectral features associated with aerosols make it especially challenging to constrain their key properties. We propose a transmission spectroscopy technique to identify the primary aerosol formation mechanism for the most highly irradiated hot Jupiters (HIHJs). The technique is based on the expectation that the two key types of aerosols -- photochemically generated hazes and equilibrium condensate clouds -- are expected to form and persist in different regions of a highly irradiated planet's atmosphere. Haze can only be produced on the permanent daysides of tidally-locked hot Jupiters, and will be carried downwind by atmospheric dynamics to the evening terminator (seen as the trailing limb during transit). Clouds can only form in cooler regions on the night side and morning terminator of HIHJs (seen as the leading limb during transit). Because opposite limbs are expected to be impacted by different types of aerosols, ingress and egress spectra, which primarily probe opposing sides of the planet, will reveal the dominant aerosol formation mechanism. We show that the benchmark HIHJ, WASP-121b, has a transmission spectrum consistent with partial aerosol coverage and that ingress-egress spectroscopy would constrain the location and formation mechanism of those aerosols. In general, using this diagnostic we find that observations with JWST and potentially with HST should be able to distinguish between clouds and haze for currently known HIHJs.Comment: 10 pages, 4 figures, accepted to ApJ Letter

Resonance bifurcations of robust heteroclinic networks

Robust heteroclinic cycles are known to change stability in resonance bifurcations, which occur when an algebraic condition on the eigenvalues of the system is satisfied and which typically result in the creation or destruction of a long-period periodic orbit. Resonance bifurcations for heteroclinic networks are more complicated because different subcycles in the network can undergo resonance at different parameter values, but have, until now, not been systematically studied. In this article we present the first investigation of resonance bifurcations in heteroclinic networks. Specifically, we study two heteroclinic networks in $\R^4$ and consider the dynamics that occurs as various subcycles in each network change stability. The two cases are distinguished by whether or not one of the equilibria in the network has real or complex contracting eigenvalues. We construct two-dimensional Poincare return maps and use these to investigate the dynamics of trajectories near the network. At least one equilibrium solution in each network has a two-dimensional unstable manifold, and we use the technique developed in [18] to keep track of all trajectories within these manifolds. In the case with real eigenvalues, we show that the asymptotically stable network loses stability first when one of two distinguished cycles in the network goes through resonance and two or six periodic orbits appear. In the complex case, we show that an infinite number of stable and unstable periodic orbits are created at resonance, and these may coexist with a chaotic attractor. There is a further resonance, for which the eigenvalue combination is a property of the entire network, after which the periodic orbits which originated from the individual resonances may interact. We illustrate some of our results with a numerical example.Comment: 46 pages, 20 figures. Supplementary material (two animated gifs) can be found on http://www.maths.leeds.ac.uk/~alastair/papers/KPR_res_net_abs.htm

Structure of fish assemblages on coastal rocky shores of the Azores

Bol. Mus. Mun. Funchal, Sup. N.º 6: 127-138, 2001The structure of fish assemblages was investigated from the surface down to 25 m depth on Azorean rocky shores. A total of 57 fish species was recorded by visual censuses, most species (66%) occurring in the whole depth range studied. Fish abundance was dominated by 11 species, mainly sparids, labrids, carangids and pomacentrids, which constituted over 88% of the total number of individuals recorded. The trophic structure of the fish assemblages studied in the Azores was characterized by the dominance of benthic mesocarnivores and high proportions of herbivores and pelagic macrocarnivores.A estrutura das comunidades ictiológicas dos fundos rochosos dos Açores foi estudada desde a superfície até aos 25 m de profundidade. Um total de 57 espécies de peixes foi identificado com recurso a censos visuais. A maioria das espécies (66%) ocorreu em toda a gama de profundidades estudada. A fauna ictiológica era dominada, em termos de abundância, por 11 espécies, principalmente pertencentes às famílias Sparidae, Labridae, Carangidae e Pomacentridae, os quais constituíram mais de 88% do número total de indivíduos observados. A estrutura trófica das comunidades ictiológicas estudadas nos Açores apresentouse dominada por meso-carnívoros bentónicos e proporções elevadas de herbívoros e macro-carnívoros pelágico

The effect of symmetry breaking on the dynamics near a structurally stable heteroclinic cycle between equilibria and a periodic orbit

The effect of small forced symmetry breaking on the dynamics near a structurally stable heteroclinic cycle connecting two equilibria and a periodic orbit is investigated. This type of system is known to exhibit complicated, possibly chaotic dynamics including irregular switching of sign of various phase space variables, but details of the mechanisms underlying the complicated dynamics have not previously been investigated. We identify global bifurcations that induce the onset of chaotic dynamics and switching near a heteroclinic cycle of this type, and by construction and analysis of approximate return maps, locate the global bifurcations in parameter space. We find there is a threshold in the size of certain symmetry-breaking terms below which there can be no persistent switching. Our results are illustrated by a numerical example

Preliminary results on production and calcification of coral reefs communities of Tikehau atoll

The carbon and oxygen metabolism of some coral reef communities of Tikehau atoll were studied in November 1989. Calcification, photosynthèse and respiration were measured during incubation experiments in transparent plastic bags. Over 24 hours period, we observed a net calcification rate for the three studied communities. However, only #Halimeda$ community presented an excess production. (Résumé d'auteur

Basic Parameter Estimation of Binary Neutron Star Systems by the Advanced LIGO/Virgo Network

Within the next five years, it is expected that the Advanced LIGO/Virgo network will have reached a sensitivity sufficient to enable the routine detection of gravitational waves. Beyond the initial detection, the scientific promise of these instruments relies on the effectiveness of our physical parameter estimation capabilities. The majority of this effort has been towards the detection and characterization of gravitational waves from compact binary coalescence, e.g. the coalescence of binary neutron stars. While several previous studies have investigated the accuracy of parameter estimation with advanced detectors, the majority have relied on approximation techniques such as the Fisher Matrix. Here we report the statistical uncertainties that will be achievable for optimal detection candidates (SNR = 20) using the full parameter estimation machinery developed by the LIGO/Virgo Collaboration via Markov-Chain Monte Carlo methods. We find the recovery of the individual masses to be fractionally within 9% (15%) at the 68% (95%) credible intervals for equal-mass systems, and within 1.9% (3.7%) for unequal-mass systems. We also find that the Advanced LIGO/Virgo network will constrain the locations of binary neutron star mergers to a median uncertainty of 5.1 deg^2 (13.5 deg^2) on the sky. This region is improved to 2.3 deg^2 (6 deg^2) with the addition of the proposed LIGO India detector to the network. We also report the average uncertainties on the luminosity distances and orbital inclinations of ideal detection candidates that can be achieved by different network configurations.Comment: Second version: 15 pages, 9 figures, accepted in Ap