Detecting Topological Order with Ribbon Operators

We introduce a numerical method for identifying topological order in two-dimensional models based on one-dimensional bulk operators. The idea is to identify approximate symmetries supported on thin strips through the bulk that behave as string operators associated to an anyon model. We can express these ribbon operators in matrix product form and define a cost function that allows us to efficiently optimize over this ansatz class. We test this method on spin models with abelian topological order by finding ribbon operators for $\mathbb{Z}_d$ quantum double models with local fields and Ising-like terms. In addition, we identify ribbons in the abelian phase of Kitaev's honeycomb model which serve as the logical operators of the encoded qubit for the quantum error-correcting code. We further identify the topologically encoded qubit in the quantum compass model, and show that despite this qubit, the model does not support topological order. Finally, we discuss how the method supports generalizations for detecting nonabelian topological order.Comment: 15 pages, 8 figures, comments welcom

Thermalization, Error-Correction, and Memory Lifetime for Ising Anyon Systems

We consider two-dimensional lattice models that support Ising anyonic excitations and are coupled to a thermal bath. We propose a phenomenological model for the resulting short-time dynamics that includes pair-creation, hopping, braiding, and fusion of anyons. By explicitly constructing topological quantum error-correcting codes for this class of system, we use our thermalization model to estimate the lifetime of the quantum information stored in the encoded spaces. To decode and correct errors in these codes, we adapt several existing topological decoders to the non-Abelian setting. We perform large-scale numerical simulations of these two-dimensional Ising anyon systems and find that the thresholds of these models range between 13% to 25%. To our knowledge, these are the first numerical threshold estimates for quantum codes without explicit additive structure.Comment: 34 pages, 9 figures; v2 matches the journal version and corrects a misstatement about the detailed balance condition of our Metropolis simulations. All conclusions from v1 are unaffected by this correctio

Efficient quantum state tomography

Quantum state tomography, the ability to deduce the state of a quantum system from measured data, is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger systems it becomes infeasible because the number of quantum measurements and the amount of computation required to process them grows exponentially in the system size. Here we show that we can do exponentially better than direct state tomography for a wide range of quantum states, in particular those that are well approximated by a matrix product state ansatz. We present two schemes for tomography in 1-D quantum systems and touch on generalizations. One scheme requires unitary operations on a constant number of subsystems, while the other requires only local measurements together with more elaborate post-processing. Both schemes rely only on a linear number of experimental operations and classical postprocessing that is polynomial in the system size. A further strength of the methods is that the accuracy of the reconstructed states can be rigorously certified without any a priori assumptions.Comment: 9 pages, 4 figures. Combines many of the results in arXiv:1002.3780, arXiv:1002.3839, and arXiv:1002.4632 into one unified expositio

Variation and correlations between sexual, asexual and natural enemy resistance life-history traits in a natural plant pathogen population

BackgroundUnderstanding the mechanisms by which diversity is maintained in pathogen populations is critical for epidemiological predictions. Life-history trade-offs have been proposed as a hypothesis for explaining long-term maintenance of variation in pathogen populations, yet the empirical evidence supporting trade-offs has remained mixed. This is in part due to the challenges of documenting successive pathogen life-history stages in many pathosystems. Moreover, little is understood of the role of natural enemies of pathogens on their life-history evolution.ResultsWe characterize life-history-trait variation and possible trade-offs in fungal pathogen Podosphaera plantaginis infecting the host plant Plantago lanceolata. We measured the timing of both asexual and sexual stages, as well as resistance to a hyperparasite of seven pathogen strains that vary in their prevalence in nature. We find significant variation among the strains in their life-history traits that constitute the infection cycle, but no evidence for trade-offs among pathogen development stages, apart from fast pathogen growth coninciding with fast hyperparasite growth. Also, the seemingly least fit pathogen strain was the most prevalent in the nature.ConclusionsWe conclude that in the nature environmental variation, and interactions with the antagonists of pathogens themselves may maintain variation in pathogen populations.Peer reviewe

Hilbert Spaces from Path Integrals

It is shown that a Hilbert space can be constructed for a quantum system starting from a framework in which histories are fundamental. The Decoherence Functional provides the inner product on this "History Hilbert space". It is also shown that the History Hilbert space is the standard Hilbert space in the case of non-relativistic quantum mechanics.Comment: 22 pages. Minor updates to match published versio

The analysis of European lacquer : optimization of thermochemolysis temperature of natural resins

In order to optimize chromatographic analysis of European lacquer, thermochemolysis temperature was evaluated for the analysis of natural resins. Five main ingredients of lacquer were studied: sandarac, mastic, colophony, Manila copal and Congo copal. For each, five temperature programs were tested: four fixed temperatures (350, 480, 550, 650 degrees C) and one ultrafast thermal desorption (UFD), in which the temperature rises from 350 to 660 degrees C in 1 min. In total, the integrated signals of 27 molecules, partially characterizing the five resins, were monitored to compare the different methods. A compromise between detection of compounds released at low temperatures and compounds formed at high temperatures was searched. 650 degrees C is too high for both groups, 350 degrees C is best for the first, and 550 degrees C for the second. Fixed temperatures of 480 degrees C or UFD proved to be a consensus in order to detect most marker molecules. UFD was slightly better for the molecules released at low temperatures, while 480 degrees C showed best compounds formed at high temperatures

Síntese e avaliação catalítica de catalisadores microporoso, mesoporosos e micro-mesoporosos

As propriedades e potencialidades dos materiais porosos estão em constantes estudos e usos nas mais variadas áreas da ciência. Esses materiais são atribuídos em classes de acordo com o ordenamento dos seus blocos estruturantes. Suas propriedades estão intrinsecamente relacionadas pela sua capacidade de catalisar as reações químicas. Neste trabalho, catalisadores do tipo HAlZSM-12, HAlMCM-41, HAlMCM-48, AlSBA-15 (Si/Al= 25, 50, 75) e HAlZSM-12/HAlMCM-41, HAlZSM-12/HAlMCM-48, HAlZSM-12/AlSBA-15 foram sintetizados pelo método hidrotérmico, submetidas a processos de calcinação e troca iônica e caracterizados por difratometria de raios-X. No presente trabalho também avaliou-se o potencial catalítico dos catalisadores na pirólise catalítica do ácido oléico em escala de bancada usando a termogravimetria. _________________________________________________________________________________________ ABSTRACT: The properties and potential of porous materials are in constant studies and uses in various areas of science. These materials are attributed to classes according to their structural ordering of blocks. Their properties are intrinsically related by their ability to catalyze chemical reactions. In this study, catalysts of type HAlZSM-12, HAlMCM-41, HAlMCM-48, AlSBA-15 (Si/Al 25, 50, 75) and composites HAlZSM-12/HAlMCM-41, HAlZSM-12/HAlMCM-48, HAlZSM-12/AlSBA-15 were synthesized by hydrothermal method, subjected to calcination and ion exchange processes and characterized by X-ray diffraction. In this study also were evaluated the catalytic potential of catalysts in the catalytic pyrolysis of oleic acid in micro-scale tests using thermogravimetric (TG)