Fate of the cluster state on the square lattice in a magnetic field

The cluster state represents a highly entangled state which is one central object for measurement-based quantum computing. Here we study the robustness of the cluster state on the two-dimensional square lattice at zero temperature in the presence of external magnetic fields by means of different types of high-order series expansions and variational techniques using infinite Projected Entangled Pair States (iPEPS). The phase diagram displays a first-order phase transition line ending in two critical end points. Furthermore, it contains a characteristic self-dual line in parameter space allowing many precise statements. The self-duality is shown to exist on any lattice topology.Comment: 12 pages, 9 figure

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

FIZIKĀLU PROCESU SKAITLISKĀ MODELĒŠANA PLĀNOS SLĀŅOS

Apakšzemes slāņainās sistēmās fizikālie parametri vertikālā virzienā ir konstanti lielumi, kuru vērtības mainās plānos slāņos ar lēcieniem. Ņemot vērā sistēmas kārtaino struktūru, aprēķinot fizikālos lielumus (temperatūru, koncentrāciju slāņos), lieto dažāda tipa viduvēšanas [3] vai režģa metodes, izvēloties katrā slānī vismaz vienu režģa līniju [1,2]. Līdz ar to iespējams samazināt risināmās problēmas dimensitāti: paraboliskā vai eliptiskā tipa parciālā diferenciālvienādojuma vietā var risināt 1. un 2. kārtas parasto diferencālvienādojumu sistēmu. Šīs metodes ir taišņu metodes pamatā. Svarīgi ir pēc iespējas samazināt parasto diferenciālvienādojumu skaitu nepieciešamās precizitātes sasniegšanai.Viduvēšanas rezultātā katrā slānī rodas viens diferenciālvienādojums, bet režģa metodē, lietojot integrēšanu un interpolāciju vai galīgo tilpumu elementus, vismaz viens diferenciālvienādojums (1.veida robežnosacījumu gadījumā) vai 3 vienādojumi (3.veida robežnosacījumu gadījumā). Izrādās, ka ar režģa metodi var iegūt 2 diferenciālvienādojumu sistēmu, kuri jāintegrē pa dažādu vidu saskares līnijām, pie tam precizitāte ir augstāka nekā vienkāršai viduvēšanas metodei. Konstantu koeficientu gadījumā ir iespējams iegūt analītiskos atrisinājumus formulu veidā

SIMULATION OF THE HEAT TRANSPORT PROBLEMS WITH RADIATION IN PLATE

In the literature [1 -5 ] simple and effective algorithms for mathematical modelling processes of distribution of heat in multilayered spaces are created. In the given work the way of improvement o f accuracy of algorithms is considered at approximation of integrals derivatives more the supreme orders are used

SIMPLE METHODS OF ENGINEERING CALCULATION FOR SOLVING STATIONARY 2 –D HEAT TRANSFER PROBLEMS IN MULTILAYER MEDIA

There are well-known different numerical methods for solving the boundary value problems for partial differential equations. Some of them are: finite difference method (FDM), finite element method (FEM), boundary element methods (BEM), and others. In the given work two methods FDM and BEM for the mathematical model of stationary distribution of heat in the multilayer media are considered. These methods were used for the reduction of the two-dimensional heat transfer problem described by a partial differential equation to a boundary – value problem for a system of ordinary differential equations. (ODEs). Such a procedure allows obtaining simple engineering algorithms for solving heat transfer equation in mulyilayer domain. In the case of three layers the system of ODEs is possible for solving analytically

Effective finite‐difference methods for the solutions of filtration problems in multilayer domains

In papers [1,2] there were consider different assumptions for averaging methods along the vertical coordinate.These methods were applied for the mathematical simulation of the mass transfer process in multilayered underground systems. A specific feature of these problems is that it is necessity to solve the 3‐D initial‐boundary‐value problems for parabolic type partial differential equations of second order with piece‐wise parameters in multilayer domain.Therefore here an effective finite‐difference method for solving a problem of the above type is developed.This method may be considered as a generalization of the method of finite volumes [3] for the layered systems. In the case of constant piece‐wise coefficients we obtain the exact discrete approximation of steady‐state 1‐D boundary‐value problem.This procedure allows to reduce the 3‐D problem to a system of 2‐D problems and the 2‐D problem to a system of 1‐D problems. First Published Online: 14 Oct 201

The exact finite‐difference scheme for vector boundary‐value problems with piece‐wise constant coefficients

We will consider the exact finite‐difference scheme for solving the system of differential equations of second order with piece‐wise constant coefficients. It is well‐known, that the presence of large parameters at first order derivatives or small parameters at second order derivatives in the system of hydrodynamics and magnetohydrodynamics (MHD) equations (large Reynolds, Hartmann and others numbers) causes additional difficulties for the applications of general classical numerical methods. Thus, important to work out special methods of solution, the so‐called uniform converging computational methods. This gives a basis for the development of special monotone finite vector‐difference schemes with perturbation coefficient of function‐matrix for solving the system of differential equations. Special finite‐difference approximations are constructed for a steady‐state boundary‐value problem, systems of parabolic type partial differential equations, a system of two MHD equations, 2‐D flows and MHD‐flows equations in curvilinear orthogonal coordinates. First Published Online: 14 Oct 201

Do Bullying Interventions Work? The Educators’ Perspective

This research examined the Olweus Bullying Prevention Program (OBPP) through the perspective of teachers located in a northeast Ohio county who received a grant to implement the program over a period of several years. The current investigation involved a Likert-style questions which were developed using the general implementation requirements of the OBPP. Teacher perception data were collected regarding implementation level, sustainability, support from other stakeholders, strengths, and weaknesses of the program, and whether they perceive it to reduce instances of bullying. Other moderators affecting perceptions were examined. These moderators include time, training, gender of teacher, years of experience, age of teacher, size of building, and general topology. Results include recommendations for practice

Increasing of accuracy for engineering calculation of heat transfer problems in two layer media

In this paper we study the simple algorithms for modelling the heat transfer problem in two layer media. The initial model which is based on a partial differential equation is reduced to ordinary differential equations (ODEs). The increase of accuracy is shown if instead of first order ODE initial value problem ([4, 5]) the second order differential equations is taken. Such a procedure allows us to obtain a simple engineering algorithm for solving heat transfer equations in two layered domain of Cartesian, cylindrical (with axial symmetry) and spherical coordinates (with radial symmetry). In a stationary case the exact finite difference scheme is obtained. Šiame straipsnyje yra nagrinejami paprasti dvisluoksnes srities šilumos laidumo problemos modeliavimo algoritmai, keičiant diferencialines lygtis dalinemis išvestinemis i paprastas diferencialines lygtis. Parodoma, kad didesnio tikslumo pasiekimui, vietoje pirmos eiles paprastu diferencialiniu lygčiu pradinio uždavinio nagrinejamos antros eiles diferencialines lygtys. Ši proced ura leidžia gauti paprasta inžinerini dvisluoksies srities šilumos laidumo lygties sprendini stačiakampeje, cilindrineje (su ašiu simetrija) ir sferineje (su spinduline simetrija) koordinačiu sistemoje. Tiksli baigtiniu skirtumu schema buvo sudaryta stacionariam atvejui. First Published Online: 14 Oct 201

Why are some South African children with Down syndrome not being offered cardiac surgery?

No Abstract. South African Medical Journal Vol. 96(9) (Part 2) 2006: 914-91