Efficient quantum approximation : examining the efficiency of select universal gate sets in approximating 1-qubit quantum gates.

Quantum computation is of current ubiquitous interest in physics, computer science, and the public interest. In the not-so-distant future, quantum computers will be relatively common pieces of research equipment. Eventually, one can expect an actively quantum computer to be a common feature of life. In this work, I study the approximation efficiency of several common universal quantum gate sets at short sequence lengths using an implementation of the Solovay-Kitaev algorithm. I begin by developing from almost nothing the relevant formal mathematics to rigorously describe what one means by the terms universal gate set and covering efficiency. I then describe some interesting results on the asymptotic covering properties of certain classes of universal gate sets and discuss the theorem which the Solovay-Kitaev algorithm is based on. Moving from mathematical introduction to experimental method, I then describe how sets will be compared. I use the commonly studied sets H+T, Pauli+V, V, and Clifford+T to determine which is the most efficient at approximating randomly generated unitaries. By doing so, we get an understanding of how well each set would perform in the context of a general quantum computer processor. This was accomplished by using the same implementation of the Solovay-Kitaev algorithm throughout, with roughly equal-sized preprocessed libraries formed from each gate set, over approximations for 10,000 randomly generated unitary matrices at algorithm depth n=5. Ultimately, the Pauli+V and V sets were the most efficient and had similar performance qualities. On average the Pauli+V set produced approximations of length 15,491 and accuracy 0.0002686. The V basis produced approximations of average sequence length 16,403 and accuracy 0.0001465. This performance is about equal given this particular implementation of the Solovay-Kitaev algorithm. We conclude that this result is somewhat surprising as the general behavior and efficiency of these particular choices of gate set are expected to be similar. It is possible though that the asymptotic efficiencies of these gate sets vary by a relatively wide margin and this has effected the experiment. It is also possible that some aspect of a naive implementation of the Solovay-Kitaev algorithm resulted in the Hadamard gate based sets performing more poorly than the V basis sets overall. Due to constraints on computational power, this result could also be limited to this particular accuracy regime and could even out as tolerance is taken to be arbitrarily small. Further possibilities of this result as well as further work are then discussed

Le Boeuf a la Mode, Carte des Vins, 1792

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Characteristic trace fossils from Miocene brackish- water deposits in the Niger Delta, Nigeria

Miocene deposits in the eastern portion of the Greater Ughelli, Central Swamp and Coastal Swamp depobelts contain well-developed brackish-water trace fossil assemblages. Twelve ichnogenera have been identified, namely: Asterosoma, Bergaueria, Chondrites, Gyrolithes, Thalassinoides, Lockeia, Palaeophycus, ?Conichnus, Planolites, Siphonichnus, Skolithos and Diplocraterion. In addition, common non-descript, passively filled burrows and fugichnia (escape structures) have also been observed. The above-mentioned ichnogenera and associated non-descript structures can be arranged into six distinct and recurring ichnoassociations within the Greater Ughelli, Central Swamp and Coastal Swamp depobelts. Each ichnoassociation is comprised of a group of trace fossils which collectively reflect specific environmental conditions during deposition of these Miocene strata. All trace fossil assemblages illustrate deposition in nearshore, restricted settings. Ichnological and sedimentological criteria which may be utilized to recognise brackish-water deposits are discussed and illustrated in pictures of the cores studied

Large Amplitude Settlements of Oil Storage Tanks

The measured profile of large-amplitude settlements of an oil storage tank was analyzed by the finite element method. Both geometric and material nonlinearities were included in the finite element analysis. Stresses and deformations, based on available qualification criteria, were examined. The results showed that most criteria in use today for the tank shell and the bottom plate are overly conservative. The calculated response of the existing operational tank under the measured large-amplitude settlements confirmed such an observation

Holocene Environmental Change in the Frobisher Bay Area, Baffin Island, N.W.T.: Deglaciation, Emergence, and the Sequence of Vegetation and Climate

The late-glacial and Holocene paleoenvironmental sequence for the Frobisher Bay area is outlined using glacial, sea level, and palynological evidence. A rapid retreat of ice from the late Foxe glacial maximum in the lower part of the bay after 11,000 BP was followed by a series of stillstands or minor readvances between ca. 8500 and 7000 BP and possibly later, before the final disappearance of the inland ice centred near Amadjuak Lake. Lithostratigraphy of three buried organic sections which together represent deposition occurring over the period from 5500 to 400 BP indicates a change from a relatively warm, moist environment before 5500 BP to neoglacial conditions, with the coldest phases centred around 5000, 2700, 1200 BP and probably sometime after 400 radiocarbon years BP. As evidenced by peat growth and pollen data, milder, wetter conditions prevailed from 4500 to 3000 BP and again from ca. 2600 to 1800 BP. Peat growth and soil organic fractions point to lesser mild intervals ca. 900 BP and 400 BP, but these are not apparent in the pollen assemblage. The pollen record does not extend to the last four centuries; however, lichenometric studies of neoglacial moraines by DOWDESWELL (1984) show that the maximum late Holocene advance of glaciers in the area occurred within the last century. Modern pollen samples indicate that the present vegetation of the inner Frobisher Bay area is comparable to that of the milder intervals of the late Holocene.La présente étude porte sur l'évolution paléoenvironnementale fini-glaciaire et holocène de la région de la baie de Frobisher et se fonde sur les niveaux marins ainsi que sur des témoins polliniques et glaciaires. Le retrait rapide des glaciers dans la partie intérieure de la baie depuis 11 000 BP a été suivi d'épisodes de stabilité et de récurrences mineures entre 8500 et 7000 ans BP. et peut-être plus tard, avant la disparition définitive des glaces continentales dont le centre se trouvait près du lac Amadjuak. L'analyse a porté sur trois sections de sol enfoui qui représentent les dépôts accumulés entre 5500 et 400 ans BP. La lithostratigraphie révèle le passage d'un climat relativement humide et chaud, il y a plus de 5500 ans, à un climat néoglaciaire dont les périodes les plus froides se situent vers 5000, 2700 et 1200 ans BP et probablement après 400 ans BP. La tourbe et les données polliniques témoignent de conditions climatiques plus douces et plus humides pour les périodes allant de 4500 à 3000 ans BP et d'environ 2600 à 1800 ans BP. Mais, contrairement aux associations polliniques, la tourbe et certaines portions organiques de sol font penser qu'ont existé des intervalles plus frais environ de 900 à 400 ans BP. Les données pollinique ne donnent aucun renseignement sur les quatre derniers siècles. Cependant, les études Ii-chénométriques que DOWDESWELL (1984) a faites sur les moraines néoglaciaires révèlent que, dans la région pendant l'Holocène supérieur, l'avancée maximale des glaces s'est produite au siècle dernier. Des échantillons polliniques récents démontrent que la végétation actuelle de l'intérieur de la baie de Frobisher ressemble à celle qu'on trouvait pendant les intervalles tempérés de l'Holocène supérieur.Die spàtglaziale und holozàne Abfolge des Palâomilieus im Gebiete der Frobisher Bucht wird durch glaziale, Meeresspiegel- und palynologische Beweise umrissen. Ein rasches Zurùckweichen des Eises aus dem niederen Teil der Bucht hat sich nach 11 000 BP ereignet. gefolgt von mehreren Stillstânden oder kleinerem Wiedervorrùcken zwischen etwa 8500 und 7000 BP oder evtl. spater, bevor das Inlandeis schliesslich verschwunden ist. Drei verdeckte Bodenprofile sind analysiert worden, die zu-sammen die Ablagerung der Zeit von 5500 bis 400 BP darstellen. Die Lithostratigraphie hat eine relativ warme, feuchte Umgebung vor 5500 BP ergeben, die sich alsdann zu neoglazialen Zustânden geàndert hat, mit dem Mittel der kâltesten Phasen um etwa 5000, 2700, und wahrscheinlich auch irgandwann nach 400 Radiokohlenstoffjahren BP. Torfwuchs sowie auch palynologische Daten zeigen, dass milde, feuchte Zustânde von 4500 bis 3000 BP und dann nochmals von etwa 2600 bis 1800 BP vorgeherrscht haben. Der Torfwuchs und der organische Anteil des Bodens deuten auch auf kleinere milde Zeitspannen um etwa 900 und 400 BP, aber dièse sind nicht aus der Pollenvergesellschaftung ersichtlich. Fur die jùngsten vier Jahrhunderte fehlen Pollenunterlagen; aber durch Untersuchung der Flechten auf neoglazialen Morânen hat DOWDESWELL (1984) fur dieses Gebiet ein spatholozànes Gletschervorrùcken wahrend des letzten Jahrhunderts belegen konnen. Pollenmuster beweisen. dass sich im Gebiet der inneren Frobisher Bucht die heutige Pflanzendecke gut mit der Vegetation mlldererer Spâtholozànintervalle vergleichen làsst

Steps for Shigella Gatekeeper Protein MxiC Function in Hierarchical Type III Secretion Regulation

Type III secretion systems are complex nanomachines used for injection of proteins from Gram-negative bacteria into eukaryotic cells. Although they are assembled when the environmental conditions are appropriate, they only start secreting upon contact with a host cell. Secretion is hierarchical. First, the pore-forming translocators are released. Second, effector proteins are injected. Hierarchy between these protein classes is mediated by a conserved gatekeeper protein, MxiC, in Shigella. As its molecular mechanism of action is still poorly understood, we used its structure to guide site-directed mutagenesis and to dissect its function. We identified mutants predominantly affecting all known features of MxiC regulation as follows: secretion of translocators, MxiC and/or effectors. Using molecular genetics, we then mapped at which point in the regulatory cascade the mutants were affected. Analysis of some of these mutants led us to a set of electron paramagnetic resonance experiments that provide evidence that MxiC interacts directly with IpaD. We suggest how this interaction regulates a switch in its conformation that is key to its functions

Circadian rhythm of hepatic cytosolic and nuclear estrogen receptors

The distribution of estrogen receptor between the cytosolic and nuclear compartments were evaluated in liver of male rats to determine whether a circadian rhythm exists. Cytosolic receptor reached a maximum level at 400 hours and a minimum at 2000 and 2400 hr. Nuclear receptor reached a maximum level at 800 hr and was lowest at 1600 and 2000 hr. Serum estradiol levels were also highest at 800 hr and lowest at 1600 hr. The variations in cytosolic and nuclear receptors are not reciprocal; in fact, the overall content of receptor in the liver is not constant and also displays a circadian rhythm. © 1986 Informa UK Ltd All rights reserved: reproduction in whole or part not permitted