On the Exact Evaluation of Certain Instances of the Potts Partition Function by Quantum Computers

We present an efficient quantum algorithm for the exact evaluation of either the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function Z for a family of graphs related to irreducible cyclic codes. This problem is related to the evaluation of the Jones and Tutte polynomials. We consider the connection between the weight enumerator polynomial from coding theory and Z and exploit the fact that there exists a quantum algorithm for efficiently estimating Gauss sums in order to obtain the weight enumerator for a certain class of linear codes. In this way we demonstrate that for a certain class of sparse graphs, which we call Irreducible Cyclic Cocycle Code (ICCC_\epsilon) graphs, quantum computers provide a polynomial speed up in the difference between the number of edges and vertices of the graph, and an exponential speed up in q, over the best classical algorithms known to date

A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements

The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of important mathematical concepts like, e.g., Fourier transforms, Galois fields and rings, finite and related projective geometries, and entanglement, to mention a few. Some applications of the theory to quantum information tasks are also mentioned.Comment: 20 pages, 1 figure to appear in Foundations of Physics, Nov. 2006 two more references adde

Eco-evolutionary dynamics on deformable fitness landscapes

Conventional approaches to modelling ecological dynamics often do not include evolutionary changes in the genetic makeup of component species and, conversely, conventional approaches to modelling evolutionary changes in the genetic makeup of a population often do not include ecological dynamics. But recently there has been considerable interest in understanding the interaction of evolutionary and ecological dynamics as coupled processes. However, in the context of complex multi-species ecosytems, especially where ecological and evolutionary timescales are similar, it is difficult to identify general organising principles that help us understand the structure and behaviour of complex ecosystems. Here we introduce a simple abstraction of coevolutionary interactions in a multi-species ecosystem. We model non-trophic ecological interactions based on a continuous but low-dimensional trait/niche space, where the location of each species in trait space affects the overlap of its resource utilisation with that of other species. The local depletion of available resources creates, in effect, a deformable fitness landscape that governs how the evolution of one species affects the selective pressures on other species. This enables us to study the coevolution of ecological interactions in an intuitive and easily visualisable manner. We observe that this model can exhibit either of the two behavioural modes discussed in the literature; namely, evolutionary stasis or Red Queen dynamics, i.e., continued evolutionary change. We find that which of these modes is observed depends on the lag or latency between the movement of a species in trait space and its effect on available resources. Specifically, if ecological change is nearly instantaneous compared to evolutionary change, stasis results; but conversely, if evolutionary timescales are closer to ecological timescales, such that resource depletion is not instantaneous on evolutionary timescales, then Red Queen dynamics result. We also observe that in the stasis mode, the overall utilisation of resources by the ecosystem is relatively efficient, with diverse species utilising different niches, whereas in the Red Queen mode the organisation of the ecosystem is such that species tend to clump together competing for overlapping resources. These models thereby suggest some basic conditions that influence the organisation of inter-species interactions and the balance of individual and collective adaptation in ecosystems, and likewise they also suggest factors that might be useful in engineering artificial coevolution

25 Years of Self-organized Criticality: Concepts and Controversies

Introduced by the late Per Bak and his colleagues, self-organized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a significant role in the development of complexity science. SOC, and more generally fractals and power laws, have attracted much comment, ranging from the very positive to the polemical. The other papers (Aschwanden et al. in Space Sci. Rev., 2014, this issue; McAteer et al. in Space Sci. Rev., 2015, this issue; Sharma et al. in Space Sci. Rev. 2015, in preparation) in this special issue showcase the considerable body of observations in solar, magnetospheric and fusion plasma inspired by the SOC idea, and expose the fertile role the new paradigm has played in approaches to modeling and understanding multiscale plasma instabilities. This very broad impact, and the necessary process of adapting a scientific hypothesis to the conditions of a given physical system, has meant that SOC as studied in these fields has sometimes differed significantly from the definition originally given by its creators. In Bak’s own field of theoretical physics there are significant observational and theoretical open questions, even 25 years on (Pruessner 2012). One aim of the present review is to address the dichotomy between the great reception SOC has received in some areas, and its shortcomings, as they became manifest in the controversies it triggered. Our article tries to clear up what we think are misunderstandings of SOC in fields more remote from its origins in statistical mechanics, condensed matter and dynamical systems by revisiting Bak, Tang and Wiesenfeld’s original papers

Performance of public private partnerships: an evolutionary perspective

PPPs are held to be a powerful way of mobilising private finance and resources to deliver public infrastructure. Theoretically, research into procurement has begun to acknowledge difficulties with the classification and assessment of different types of procurement, particularly those which do not sufficiently acknowledge variety within specific types of procurement methods. This paper advances a theoretical framework based on an evolutionary economic conceptualisation of a routine, which can accommodate the variety evident in procurement projects, in particular PPPs. The paper tests how the various elements of a PPP, as advanced in the theoretical framework, affect performance across 10 case studies. It concludes, that a limited number of elements of a PPP affect their performance, and provides strong evidence for the theoretical model advanced in this paper

Use of thin wall imaging in the diagnosis of laser heated hohlraums

High-Z, laser heated hohlraums can be made thick enough to contain thermal radiation, yet thin enough to let out x-rays >{approximately}6keV produced by hot, relatively dense blow-off plasma. The authors use such ``thin wall hohlraums`` to observe the physical location of hot, dense, laser produced hohlraum plasmas. This technique has allowed them to come to some understanding of laser transport/deposition, plasma stagnation and bulk plasma filling

The national ignition facility: Path to ignition in the laboratory

The National Ignition Facility (NIF) is a 192-beam laser facility presently under construction at LLNL. When completed, NIF will be a 1.8-MJ, 500-TW ultraviolet laser system. Its missions are to obtain fusion ignition and to perform high energy density experiments in support of the U.S. nuclear weapons stockpile. Four of the NIF beams have been commissioned to demonstrate laser performance and to commission the target area including target and beam alignment and laser timing. During this time, NIF demonstrated on a single-beam basis that it will meet its performance goals and demonstrated its precision and flexibility for pulse shaping, pointing, timing and beam conditioning. It also performed four important experiments for Inertial Confinement Fusion and High Energy Density Science. Presently, the project is installing production hardware to complete the project in 2009 with the goal to begin ignition experiments in 2010. An integrated plan has been developed including the NIF operations, user equipment such as diagnostics and cryogenic target capability, and experiments and calculations to meet this goal. This talk will provide NIF status, the plan to complete NIF, and the path to ignition