Bounds on universal quantum computation with perturbed 2d cluster states

Motivated by the possibility of universal quantum computation under noise perturbations, we compute the phase diagram of the 2d cluster state Hamiltonian in the presence of Ising terms and magnetic fields. Unlike in previous analysis of perturbed 2d cluster states, we find strong evidence of a very well defined cluster phase, separated from a polarized phase by a line of 1st and 2nd order transitions compatible with the 3d Ising universality class and a tricritical end point. The phase boundary sets an upper bound for the amount of perturbation in the system so that its ground state is still useful for measurement-based quantum computation purposes. Moreover, we also compute the local fidelity with the unperturbed 2d cluster state. Besides a classical approximation, we determine the phase diagram by combining series expansions and variational infinite Projected entangled-Pair States (iPEPS) methods. Our work constitutes the first analysis of the non-trivial effect of few-body perturbations in the 2d cluster state, which is of relevance for experimental proposals.Comment: 7 pages, 4 figures, revised version, to appear in PR

Stable isotope paleoecology (d¹³C and d¹⁸O) of early Eocene <i>Zeauvigerina aegyptiaca</i> from the North Atlantic (DSDP Site 401)

Within the expanded and clay-enriched interval following the Paleocene-Eocene Thermal Maximum (PETM; ~55.8 Ma) at Deep Sea Drilling Project (DSDP) Site 401 (eastern North Atlantic), high abundances of well-preserved biserial planktic foraminifera such as Zeauvigerina aegyptiaca and Chiloguembelina spp. occur. The paleoecological preferences of these taxa are only poorly constrained, largely because existing records are patchy in time and space. The thin-walled Z. aegyptiaca is usually rather small (13C and d18O) study of well-preserved specimens of Z. aegyptiaca and several planktic foraminiferal species (Morozovella subbotinae, Subbotina patagonica, Chiloguembelina wilcoxensis) enabled us to determine the preferred depth habitat and mode of life for Z. aegyptiaca. Oxygen isotope values of Z. aegyptiaca range from -1.57‰ to -2.07‰ and overlap with those of M. subbotinae indicating that their habitat is (1) definitely planktic, which has been questioned by some earlier isotopic studies, and (2) probably within the lower surface mixed layer. Carbon isotope ratios range from 0.99‰ to 1.34‰ and are distinctly lower than values for non-biserial planktic species. This may indicate isotopic disequilibrium between ambient seawater and the calcareous tests of Z. aegyptiaca, which we relate to vital effects and to its opportunistic behavior. The observed isotopic signal of Z. aegyptiaca relative to the other planktic foraminiferal species is highly similar to many other microperforate bi- and triserial planktic genera that have appeared through geological time such as Heterohelix, Guembelitria, Chiloguembelina, Streptochilus and Gallitellia and we suggest that Z. aegyptiaca shares a similar ecology and habitat. Thus, in order for the opportunistic Z. aegyptiaca to bloom during the aftermath of the PETM, we assume that at that time, the surface waters at Site 401 were influenced by increased terrestrial run-off and nutrient availability

Joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles

The density function for the joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles is found in terms of a Painlev\'e II transcendent and its associated isomonodromic system. As a corollary, the density function for the spacing between these two eigenvalues is similarly characterized.The particular solution of Painlev\'e II that arises is a double shifted B\"acklund transformation of the Hasting-McLeod solution, which applies in the case of the distribution of the largest eigenvalue at the soft edge. Our deductions are made by employing the hard-to-soft edge transitions to existing results for the joint distribution of the first and second eigenvalue at the hard edge \cite{FW_2007}. In addition recursions under $a \mapsto a+1$ of quantities specifying the latter are obtained. A Fredholm determinant type characterisation is used to provide accurate numerics for the distribution of the spacing between the two largest eigenvalues.Comment: 26 pages, 1 Figure, 2 Table

A review of data on abundance, trends in abundance, habitat use and diet of ice-breeding seals in the Southern Ocean

The development of models of marine ecosystems in the Southern Ocean is becoming increasingly important as a means of understanding and managing impacts such as exploitation and climate change. Collating data from disparate sources, and understanding biases or uncertainties inherent in those data, are important first steps for improving ecosystem models. This review focuses on seals that breed in ice habitats of the Southern Ocean (i.e. crabeater seal, Lobodon carcinophaga; Ross seal, Ommatophoca rossii; leopard seal, Hydrurga leptonyx; and Weddell seal, Leptonychotes weddellii). Data on populations (abundance and trends in abundance), distribution and habitat use (movement, key habitat and environmental features) and foraging (diet) are summarised, and potential biases and uncertainties inherent in those data are identified and discussed. Spatial and temporal gaps in knowledge of the populations, habitats and diet of each species are also identified

The 1+1-dimensional Kardar-Parisi-Zhang equation and its universality class

We explain the exact solution of the 1+1 dimensional Kardar-Parisi-Zhang equation with sharp wedge initial conditions. Thereby it is confirmed that the continuum model belongs to the KPZ universality class, not only as regards to scaling exponents but also as regards to the full probability distribution of the height in the long time limit.Comment: Proceedings StatPhys 2

Finite-Element Discretization of Static Hamilton-Jacobi Equations Based on a Local Variational Principle

We propose a linear finite-element discretization of Dirichlet problems for static Hamilton-Jacobi equations on unstructured triangulations. The discretization is based on simplified localized Dirichlet problems that are solved by a local variational principle. It generalizes several approaches known in the literature and allows for a simple and transparent convergence theory. In this paper the resulting system of nonlinear equations is solved by an adaptive Gauss-Seidel iteration that is easily implemented and quite effective as a couple of numerical experiments show.Comment: 19 page

Convergence of simple adaptive Galerkin schemes based on h − h/2 error estimators

We discuss several adaptive mesh-refinement strategies based on (h − h/2)-error estimation. This class of adaptivemethods is particularly popular in practise since it is problem independent and requires virtually no implementational overhead. We prove that, under the saturation assumption, these adaptive algorithms are convergent. Our framework applies not only to finite element methods, but also yields a first convergence proof for adaptive boundary element schemes. For a finite element model problem, we extend the proposed adaptive scheme and prove convergence even if the saturation assumption fails to hold in general