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.
Due to the unfavorable scaling of tensor network methods with the refinement parameter M, new approaches are necessary to improve the efficiency of numerical simulations based on such states in ...particular for gapless, strongly entangled systems. In one-dimensional DMRG, the use of Abelian symmetries has lead to large computational gain. In higher-dimensional tensor networks, this is associated with significant technical efforts and additional approximations. We explain a formalism to implement such symmetries in two-dimensional tensor network states and present benchmark results that confirm the validity of these approximations in the context of projected entangled-pair state algorithms.
We establish a relation between several entanglement properties in the Lipkin-Meshkov-Glick model, which is a system of mutually interacting spins embedded in a magnetic field. We provide analytical ...proofs that the single-copy entanglement and the global geometric entanglement of the ground state close to and at criticality behave as the entanglement entropy. These results are in deep contrast to what is found in one- dimensional spin systems where these three entanglement measures behave differently.
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.
The aim of this paper is to validate existing aeronautical fuselage multipath and previous assumptions, based on measurements from an experimental flight campaign. Particularly, the results of the ...study will be used to consolidate the on-going communication system design activities, in the frame of the European Space Agency (ESA) Iris Programme for Air Traffic Management via Satellite. The data analyses focus on the detection of strong fuselage multipath effects and on the characterization of the channel for the different flight phases. The campaign included several experimental flights from Amsterdam airport towards and around Accra, Ghana and from Amsterdam to Spitsbergen area, close to the North Pole. During the experimental flights, GPS L1 signal data was recorded using the Spirent Record & Playback GSS6400 equipment, as analogy to the L-band channel to be implemented for the operational service. This collected data was processed to characterise fuselage multipath effects during the en-route phase of flight at different elevation/azimuth. Results of carrier-to-multipath (C/M) ratio and fading (C/No) time-series at different satellite elevation angles are presented and compared with existing aeronautical fuselage models. Furthermore, electromagnetic simulations based on Method of Moments have been used to contrast the observations.
Phys. Rev. B 75, 104305 (2007) A generic method to investigate many-body continuous-variable systems is
pedagogically presented. It is based on the notion of matrix product states
(so-called MPS) and ...the algorithms thereof. The method is quite versatile and
can be applied to a wide variety of situations. As a first test, we show how it
provides reliable results in the computation of fundamental properties of a
chain of quantum harmonic oscillators achieving off-critical and critical
relative errors of the order of 10^(-8) and 10^(-4) respectively. Next, we use
it to study the ground state properties of the quantum rotor model in one
spatial dimension, a model that can be mapped to the Mott insulator limit of
the 1-dimensional Bose-Hubbard model. At the quantum critical point, the
central charge associated to the underlying conformal field theory can be
computed with good accuracy by measuring the finite-size corrections of the
ground state energy. Examples of MPS-computations both in the finite-size
regime and in the thermodynamic limit are given. The precision of our results
are found to be comparable to those previously encountered in the MPS studies
of, for instance, quantum spin chains. Finally, we present a spin-off
application: an iterative technique to efficiently get numerical solutions of
partial differential equations of many variables. We illustrate this technique
by solving Poisson-like equations with precisions of the order of 10^(-7).
Phys.Rev.Lett.98:060402,2007 An analytical expression for the von Neumann entropy of the Laughlin wave
function is obtained for any possible bipartition between the particles
described by this wave ...function, for filling fraction nu=1. Also, for filling
fraction nu=1/m, where m is an odd integer, an upper bound on this entropy is
exhibited. These results yield a bound on the smallest possible size of the
matrices for an exact representation of the Laughlin ansatz in terms of a
matrix product state. An analytical matrix product state representation of this
state is proposed in terms of representations of the Clifford algebra. For
nu=1, this representation is shown to be asymptotically optimal in the limit of
a large number of particles.
We investigate the stability of the topological phase of the toric code model in the presence of a uniform magnetic field by means of variational and high-order series expansion approaches. We find ...that when this perturbation is strong enough, the system undergoes a topological phase transition whose first- or second-order nature depends on the field orientation. When this transition is of second order, it is in the Ising universality class except for a special line on which the critical exponent driving the closure of the gap varies continuously, unveiling a new topological universality class.
Ionospheric Effects on GNSS Performance Beniguel, Y.; Angling, M.; Banfi, E. ...
2012 6th ESA Workshop on Satellite Navigation Technologies (Navitec 2012) & European Workshop on GNSS Signals and Signal Processing,
2012-Dec.
Conference Proceeding
This paper presents the features of the MONITOR project. This project initiated by ESA / ESTEC aims to increase the knowledge of the ionospheric effects and its impact on GNSS systems during active ...periods of solar activity. It includes the deployment of a set of GNSS-based ionospheric monitoring receivers worldwide distributed, the development of specific analysis software tools some of them integrated on a common platform, others distributed providing products routinely and a measurement campaign which will last beyond the peak of the current solar cycle.
