Robust Logic Gates and Realistic Quantum Computation

The composite rotation approach has been used to develop a range of robust quantum logic gates, including single qubit gates and two qubit gates, which are resistant to systematic errors in their implementation. Single qubit gates based on the BB1 family of composite rotations have been experimentally demonstrated in a variety of systems, but little study has been made of their application in extended computations, and there has been no experimental study of the corresponding robust two qubit gates to date. Here we describe an application of robust gates to Nuclear Magnetic Resonance (NMR) studies of approximate quantum counting. We find that the BB1 family of robust gates is indeed useful, but that the related NB1, PB1, B4 and P4 families of tailored logic gates are less useful than initially expected.Comment: 6 pages RevTex4 including 5 figures (3 low quality to save space). Revised at request of referee and incorporting minor corrections and updates. Now in press at Phys Rev

Twelve-spin "Schrodinger cat"

Pseudopure "cat" state, a superposition of quantum states with all spins up and all spins down, is experimentally demonstrated for a system of twelve dipolar-coupled nuclear spins of fully 13C-labeled benzene molecule oriented in a liquid-crystalline matrix.Comment: Submitted to Applied Physics Letter

Study of localization in the quantum sawtooth map emulated on a quantum information processor

Quantum computers will be unique tools for understanding complex quantum systems. We report an experimental implementation of a sensitive, quantum coherence-dependent localization phenomenon on a quantum information processor (QIP). The localization effect was studied by emulating the dynamics of the quantum sawtooth map in the perturbative regime on a three-qubit QIP. Our results show that the width of the probability distribution in momentum space remained essentially unchanged with successive iterations of the sawtooth map, a result that is consistent with localization. The height of the peak relative to the baseline of the probability distribution did change, a result that is consistent with our QIP being an ensemble of quantum systems with a distribution of errors over the ensemble. We further show that the previously measured distributions of control errors correctly account for the observed changes in the probability distribution.Comment: 20 pages, 9 figure

Numerical Evidence for Divergent Burnett Coefficients

In previous papers [Phys. Rev. A {\bf 41}, 4501 (1990), Phys. Rev. E {\bf 18}, 3178 (1993)], simple equilibrium expressions were obtained for nonlinear Burnett coefficients. A preliminary calculation of a 32 particle Lennard-Jones fluid was presented in the previous paper. Now, sufficient resources have become available to address the question of whether nonlinear Burnett coefficients are finite for soft spheres. The hard sphere case is known to have infinite nonlinear Burnett coefficients (ie a nonanalytic constitutive relation) from mode coupling theory. This paper reports a molecular dynamics caclulation of the third order nonlinear Burnett coefficient of a Lennard-Jones fluid undergoing colour flow, which indicates that this term is diverges in the thermodynamic limit.Comment: 12 pages, 9 figure

Design and control of spin gates in two quantum dots arrays

We study the spin-spin interaction between quantum dots coupled through a two dimensional electron gas with spin-orbit interaction. We show that the interplay between transverse electron focusing and spin-orbit coupling allows to dynamically change the symmetry of the effective spin-spin Hamiltonian. That is, the interaction can be changed from Ising-like to Heisenberg-like and vice versa. The sign and magnitude of the coupling constant can also be tuned.Comment: 4 pages, 3 figure

Calculating error bars for neutrino mixing parameters

One goal of contemporary particle physics is to determine the mixing angles and mass-squared differences that constitute the phenomenological constants that describe neutrino oscillations. Of great interest are not only the best fit values of these constants but also their errors. Some of the neutrino oscillation data is statistically poor and cannot be treated by normal (Gaussian) statistics. To extract confidence intervals when the statistics are not normal, one should not utilize the value for chisquare versus confidence level taken from normal statistics. Instead, we propose that one should use the normalized likelihood function as a probability distribution; the relationship between the correct chisquare and a given confidence level can be computed by integrating over the likelihood function. This allows for a definition of confidence level independent of the functional form of the !2 function; it is particularly useful for cases in which the minimum of the !2 function is near a boundary. We present two pedagogic examples and find that the proposed method yields confidence intervals that can differ significantly from those obtained by using the value of chisquare from normal statistics. For example, we find that for the first data release of the T2K experiment the probability that chisquare is not zero, as defined by the maximum confidence level at which the value of zero is not allowed, is 92%. Using the value of chisquare at zero and assigning a confidence level from normal statistics, a common practice, gives the over estimation of 99.5%.Comment: 9 pages, 6 figure

Igneous Rock Associations in Canada 3. Large Igneous Provinces (LIPs) in Canada and Adjacent Regions: 3 Ga to Present

Earth history is punctuated by numerous periods during which large volumes of mafic magma were emplaced. Such magmas not generated by a 'normal' spreading ridge or by subduction are termed Large Igneous Provinces (LIPs), and consist of continental flood basalts, volcanic rifted margins, oceanic plateaus, ocean basin flood basalts, submarine ridges, and seamount chains. Associated felsic rocks may also be present. LIPs of Mesozoic and Cenozoic age are typically the best preserved. Those of Paleozoic and Proterozoic age are usually more deeply eroded, and consist of flood basalt remnants and a deep-level plumbing system (of giant dyke swarms, sill provinces and layered intrusions). In the Archean the most promising LIP candidates are greenstone belts containing komatiites. Many LIPs have been linked to regional-scale uplift, continental rifting and breakup, and climatic crises. They can be used as precisely dated time markers in the stratigraphic record, and are key targets for Ni-Cu-PGE exploration. LIPs have also become a focus in the debate on the existence and nature of mantle plumes. Canada has a rich record of LIPs. At least 80 candidates are recognized in Canada and adjacent regions, with ages ranging from 3100 to 17 Ma. We review proposed links between the LIP record of Canada and mantle plumes, continental breakup, regional uplift, and ore deposits. However, given that many mafic units in Canada remain poorly characterized, a concerted geochronology campaign with integrated paleomagnetism and geochemistry would be invaluable in expanding the application of the Canadian LIP record to solving major geological problems. RÉSUMÉ L'histoire de la Terre est ponctuée de nombreuses périodes de mise en place de forts volumes de magma mafiques. De tels magmas qui ne sont pas issus de zones d'expansion « normale » ou de subduction sont appelés Grandes provinces ignées (GPI), et celles-ci sont constituées de basaltes d'épanchements continentaux, de marges de fosse volcaniques, de plateaux océaniques, d'épanchements de basaltes de bassins océaniques, de crêtes sous-marines, et de chaînes de monts sous-marines. Peuvent également y être associées des suites de roches felsiques. Généralement, les GPI du Mésozoïque et du Cénozoïque sont les mieux préservées. Celles du Protérozoïque et du Paléozoïque sont généralement plus fortement érodées et sont constituées de vestiges de basaltes d'épanchement et des réseaux de conduits d'origine (réseaux géants de dykes, provinces de filons-couches et d'intrusifs stratifiées). Dans l'Archéen, les meilleurs candidats sont représentés par les bandes de roches vertes à komatiites. De nombreuses GPI ont été associées à des épisodes de soulèvement régionaux, de dérives ou de fragmentations continentales, ainsi qu'à des crises climatiques. Elles peuvent servir de marqueurs temporels stratigraphiques et sont des cibles de première importance dans l'exploration de gisements de Cu-Ni-ÉGP. Les GPI sont aussi devenues des arguments très considérés dans le débat sur l'existence et la nature des panaches mantelliques. Le Canada possède de riches archives de GPI, et au moins 80 candidatures ont été isolées sur le territoire canadien et dans les régions adjacentes, leur âge délimitant une fourchette allant de 3 100 Ma à 17 Ma. Nous passons en revue les liens proposés entre la suite des GDI canadiennes d'une part, et celle des panaches mantelliques, des fragmentations continentales, des soulèvements régionaux, et des gisements minéraux, d'autre part. Toutefois, vu le piètre état de caractérisation des unités mafiques au Canada, une campagne de caractérisation géochronologique, paléomagnétique et géochimique serait d'une valeur inestimable pour favoriser l'utilisation des GDI canadiennes pour nous aider à solutionner de grands problèmes géologiques