Fibonacci-Lucas SIC-POVMs

We present a conjectured family of SIC-POVMs which have an additional symmetry group whose size is growing with the dimension. The symmetry group is related to Fibonacci numbers, while the dimension is related to Lucas numbers. The conjecture is supported by exact solutions for dimensions d=4,8,19,48,124,323, as well as a numerical solution for dimension d=844.Comment: The fiducial vectors can be obtained from http://sicpovm.markus-grassl.de as well as from the source files. v2: precision for the numerical solution in dimension 844 increased to 150 digits and new exact solution for dimension 323 adde

Network Modelling of Fluid Retention Behaviour in Unsaturated Soils

The paper describes discrete modelling of the retention behaviour of unsaturated porous materials. A network approach is used within a statistical volume element (SVE), suitable for subsequent use in hydro-mechanical analysis and incorporation within multi-scale numerical modelling. The soil pore structure is modelled by a network of cylindrical pipes connecting spheres, with the spheres representing soil voids and the pipes representing inter-connecting throats. The locations of pipes and spheres are determined by a Voronoi tessellation of the domain. Original aspects of the modelling include a form of periodic boundary condition implementation applied for the first time to this type of network, a new pore volume scaling technique to provide more realistic modelling and a new procedure for initiating drying or wetting paths in a network model employing periodic boundary conditions. Model simulations, employing two linear cumulative probability distributions to represent the distributions of sphere and pipe radii, are presented for the retention behaviour reported from a mercury porosimetry test on a sandstone

Hydro-mechanical network modelling of particulate composites

Differential shrinkage in particulate quasi-brittle materials causes microcracking which reduces durability in these materials by increasing their mass transport properties. A hydro-mechanical three-dimensional periodic network approach was used to investigate the influence of particle and specimen size on the specimen permeability. The particulate quasi-brittle materials studied here consist of stiff elastic particles, and a softer matrix and interfacial transition zones between matrix and particles exhibiting nonlinear material responses. An incrementally applied uniform eigenstrain, along with a damage-plasticity constitutive model, are used to describe the shrinkage and cracking processes of the matrix and interfacial transition zones. The results showed that increasing particle diameter at constant volume fraction increases the crack widths and, therefore, permeability, which confirms previously obtained 2D modelling results. Furthermore, it was demonstrated that specimen thickness has, in comparison to the influence of particle size, a small influence on permeability increase due to microcracking

Structured Error Recovery for Codeword-Stabilized Quantum Codes

Codeword stabilized (CWS) codes are, in general, non-additive quantum codes that can correct errors by an exhaustive search of different error patterns, similar to the way that we decode classical non-linear codes. For an n-qubit quantum code correcting errors on up to t qubits, this brute-force approach consecutively tests different errors of weight t or less, and employs a separate n-qubit measurement in each test. In this paper, we suggest an error grouping technique that allows to simultaneously test large groups of errors in a single measurement. This structured error recovery technique exponentially reduces the number of measurements by about 3^t times. While it still leaves exponentially many measurements for a generic CWS code, the technique is equivalent to syndrome-based recovery for the special case of additive CWS codes.Comment: 13 pages, 9 eps figure

A micromechanics-enhanced finite element formulation for modelling heterogeneous materials

In the analysis of composite materials with heterogeneous microstructures, full resolution of the heterogeneities using classical numerical approaches can be computationally prohibitive. This paper presents a micromechanics-enhanced finite element formulation that accurately captures the mechanical behaviour of heterogeneous materials in a computationally efficient manner. The strategy exploits analytical solutions derived by Eshelby for ellipsoidal inclusions in order to determine the mechanical perturbation fields as a result of the underlying heterogeneities. Approximation functions for these perturbation fields are then incorporated into a finite element formulation to augment those of the macroscopic fields. A significant feature of this approach is that the finite element mesh does not explicitly resolve the heterogeneities and that no additional degrees of freedom are introduced. In this paper, hybrid-Trefftz stress finite elements are utilised and performance of the proposed formulation is demonstrated with numerical examples. The method is restricted here to elastic particulate composites with ellipsoidal inclusions but it has been designed to be extensible to a wider class of materials comprising arbitrary shaped inclusions.Comment: 28 pages, 12 figures, 2 table

On optimal quantum codes

We present families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over q-dimensional quantum systems, where q is an arbitrary prime power. It is shown that codes with parameters [[n,n-2d+2,d]]_q exist for all 3 <= n <= q and 1 <= d <= n/2+1. We also present quantum MDS codes with parameters [[q^2,q^2-2d+2,d]]_q for 1 <= d <= q which additionally give rise to shortened codes [[q^2-s,q^2-2d+2-s,d]]_q for some s.Comment: Accepted for publication in the International Journal of Quantum Informatio

Multiparticle entanglement purification for graph states

We introduce a class of multiparticle entanglement purification protocols that allow us to distill a large class of entangled states. These include cluster states, GHZ states and various error correction codes all of which belong to the class of two-colorable graph states. We analyze these schemes under realistic conditions and observe that they are scalable, i.e. the threshold value for imperfect local operations does not depend on the number of parties for many of these states. When compared to schemes based on bipartite entanglement purification, the protocol is more efficient and the achievable quality of the purified states is larger. As an application we discuss an experimental realization of the protocol in optical lattices which allows one to purify cluster states.Comment: 4 pages, 2 figures; V2: some typos corrected; V3: published versio

Corrosion induced cracking modelled by a coupled transport-structural approach

Transport of corrosion products into pores and cracks in concrete must be considered when predicting corrosion induced cracking in reinforced concrete structures, since this transport significantly delays the onset of cracking and spalling by reducing the amount of radial displacement imposed on the concrete at the steel/concrete interface. We aim to model this process by means of a coupled transport-structural approach, whereby the transport of corrosion products is determined by a pressure gradient generated by the confined volumetric expansion due to the transformation of steel into corrosion products. This pressure driven transport was studied by using both an axisymmetric thick-walled cylinder model and a network approach. The network approach was then applied to corrosion induced cracking experiments reported in the literature

Low-complexity quantum codes designed via codeword-stabilized framework

We consider design of the quantum stabilizer codes via a two-step, low-complexity approach based on the framework of codeword-stabilized (CWS) codes. In this framework, each quantum CWS code can be specified by a graph and a binary code. For codes that can be obtained from a given graph, we give several upper bounds on the distance of a generic (additive or non-additive) CWS code, and the lower Gilbert-Varshamov bound for the existence of additive CWS codes. We also consider additive cyclic CWS codes and show that these codes correspond to a previously unexplored class of single-generator cyclic stabilizer codes. We present several families of simple stabilizer codes with relatively good parameters.Comment: 12 pages, 3 figures, 1 tabl