Local unitary invariants for multipartite quantum systems

A method is presented to obtain local unitary invariants for multipartite quantum systems consisting of fermions or distinguishable particles. The invariants are organized into infinite families, in particular, the generalization to higher dimensional single particle Hilbert spaces is straightforward. Many well-known invariants and their generalizations are also included.Comment: 13 page

All degree six local unitary invariants of k qudits

We give explicit index-free formulae for all the degree six (and also degree four and two) algebraically independent local unitary invariant polynomials for finite dimensional k-partite pure and mixed quantum states. We carry out this by the use of graph-technical methods, which provides illustrations for this abstract topic.Comment: 18 pages, 6 figures, extended version. Comments are welcom

Fault-ignorant Quantum Search

We investigate the problem of quantum searching on a noisy quantum computer. Taking a 'fault-ignorant' approach, we analyze quantum algorithms that solve the task for various different noise strengths, which are possibly unknown beforehand. We prove lower bounds on the runtime of such algorithms and thereby find that the quadratic speedup is necessarily lost (in our noise models). However, for low but constant noise levels the algorithms we provide (based on Grover's algorithm) still outperform the best noiseless classical search algorithm.Comment: v1: 15+8 pages, 4 figures; v2: 19+8 pages, 4 figures, published version (Introduction section significantly expanded, presentation clarified, results and order unchanged

Analysis of Surface Runoff

A mathematical model of surface runoff is presented which is of use in building a model of erosion processes. The method used for deriving the conceptual model of surface runoff is based on the mathematical expression of the basic laws of movement of water -- the equation of continuity and the equation of motion. Both equations form a system of nonlinear partial differential equations with two unknown functions expressing the depth and velocity of the movement of water along the slope, in dependence on their location on the slope, and time. The input variables of the model are the intensity and direction of the impinging raindrops, the intensity of infiltration and the physical characteristics of the slope (gradient, length and properties of soil surface). Extensive laboratory experiments have been carried out to determine the functional dependence of tangential stress on the depth and rate of runoff from different types of soil surfaces. Further, the conceptual model of surface runoff has been simplified to a kinematic one by using a simple relation between depth and rate of surface runoff instead of the equation of motion. Two empirical parameters of this relation have been determined by using data from the above mentioned laboratory experiments during calibration of the kinematic model. The kinematic model is recommended because of its simplicity with regard to simulation of the surface runoff formation from individual slopes within the watershed. The model is a multipurpose one. It may be used either for hydrological purposes (simulation of surface runoff characteristics) or for soil conservation purposes. The model outputs are surface characteristics (depth, velocity, rate). It is possible by comparing the surface runoff velocity with the critical nonscouring velocity for given field conditions to determine the critical slope length which is the basis for planning efficient soil conservation measures

Erosion and Water Quality as Modeled by Creams: A Case Study of the Sedlicky Catchment

In the process of verifying and validating the models of agricultural nonpoint source pollution at IIASA, a study was made of the Sedlicky brook (Bohemia, Czechoslovakia) case. The CREAMS model, verified at the Samsin research area (Czechoslovakia) has been used as the mathematical instrument. The validation results of the CREAMS model for the boundary conditions between the field level and the watershed level seem to show that under certain conditions, it can be applied to small watersheds. For large watersheds, modification of the hydrology submodel is necessary in order to describe the comprehensive hydrologic phenomena, particularly, the interflow and some of the subsurface flow