Efficient decoupling schemes with bounded controls based on Eulerian orthogonal arrays

The task of decoupling, i.e., removing unwanted interactions in a system Hamiltonian and/or couplings with an environment (decoherence), plays an important role in controlling quantum systems. There are many efficient decoupling schemes based on combinatorial concepts like orthogonal arrays, difference schemes and Hadamard matrices. So far these (combinatorial) decoupling schemes have relied on the ability to effect sequences of instantaneous, arbitrarily strong control Hamiltonians (bang-bang controls). To overcome the shortcomings of bang-bang control Viola and Knill proposed a method called Eulerian decoupling that allows the use of bounded-strength controls for decoupling. However, their method was not directly designed to take advantage of the composite structure of multipartite quantum systems. In this paper we define a combinatorial structure called an Eulerian orthogonal array. It merges the desirable properties of orthogonal arrays and Eulerian cycles in Cayley graphs (that are the basis of Eulerian decoupling). We show that this structure gives rise to decoupling schemes with bounded-strength control Hamiltonians that can be applied to composite quantum systems with few body Hamiltonians and special couplings with the environment. Furthermore, we show how to construct Eulerian orthogonal arrays having good parameters in order to obtain efficient decoupling schemes.Comment: 8 pages, revte

Velocity Tails for Inelastic Maxwell Models

We study the velocity distribution function for inelastic Maxwell models, characterized by a Boltzmann equation with constant collision rate, independent of the energy of the colliding particles. By means of a nonlinear analysis of the Boltzmann equation, we find that the velocity distribution function decays algebraically for large velocities, with exponents that are analytically calculated.Comment: 4 pages, 2 figure

Correlated errors can lead to better performance of quantum codes

A formulation for evaluating the performance of quantum error correcting codes for a general error model is presented. In this formulation, the correlation between errors is quantified by a Hamiltonian description of the noise process. We classify correlated errors using the system-bath interaction: local versus nonlocal and two-body versus many-body interactions. In particular, we consider Calderbank-Shor-Steane codes and observe a better performance in the presence of correlated errors depending on the timing of the error recovery. We also find this timing to be an important factor in the design of a coding system for achieving higher fidelities.Comment: 5 pages, 3 figures. Replaced by the published version. Title change

Numerical Analysis of Boosting Scheme for Scalable NMR Quantum Computation

Among initialization schemes for ensemble quantum computation beginning at thermal equilibrium, the scheme proposed by Schulman and Vazirani [L. J. Schulman and U. V. Vazirani, in Proceedings of the 31st ACM Symposium on Theory of Computing (STOC'99) (ACM Press, New York, 1999), pp. 322-329] is known for the simple quantum circuit to redistribute the biases (polarizations) of qubits and small time complexity. However, our numerical simulation shows that the number of qubits initialized by the scheme is rather smaller than expected from the von Neumann entropy because of an increase in the sum of the binary entropies of individual qubits, which indicates a growth in the total classical correlation. This result--namely, that there is such a significant growth in the total binary entropy--disagrees with that of their analysis.Comment: 14 pages, 18 figures, RevTeX4, v2,v3: typos corrected, v4: minor changes in PROGRAM 1, conforming it to the actual programs used in the simulation, v5: correction of a typographical error in the inequality sign in PROGRAM 1, v6: this version contains a new section on classical correlations, v7: correction of a wrong use of terminology, v8: Appendix A has been added, v9: published in PR

Microscopic approach to pion-nucleus dynamics

Elastic scattering of pions from finite nuclei is investigated utilizing a contemporary, momentum--space first--order optical potential combined with microscopic estimates of second--order corrections. The calculation of the first--order potential includes:\ \ (1)~full Fermi--averaging integration including both the delta propagation and the intrinsic nonlocalities in the $\pi$-$N$ amplitude, (2)~fully covariant kinematics, (3)~use of invariant amplitudes which do not contain kinematic singularities, and (4)~a finite--range off--shell pion--nucleon model which contains the nucleon pole term. The effect of the delta--nucleus interaction is included via the mean spectral--energy approximation. It is demonstrated that this produces a convergent perturbation theory in which the Pauli corrections (here treated as a second--order term) cancel remarkably against the pion true absorption terms. Parameter--free results, including the delta--nucleus shell--model potential, Pauli corrections, pion true absorption, and short--range correlations are presented. (2 figures available from authors)Comment: 13 page

Decoherence under many-body system-environment interactions: a stroboscopic representation based on a fictitiously homogenized interaction rate

An environment interacting with portions of a system leads to multiexponential interaction rates. Within the Keldysh formalism, we fictitiously homogenize the system-environment interaction yielding a uniform decay rate facilitating the evaluation of the propagators. Through an injection procedure we neutralize the fictitious interactions. This technique justifies a stroboscopic representation of the system-environment interaction which is useful for numerical implementation and converges to the natural continuous process. We apply this procedure to a fermionic two-level system and use the Jordan-Wigner transformation to solve a two-spin swapping gate in the presence of a spin environment.Comment: 11 pages, 3 figures, title changed, some typos change

On high energy tails in inelastic gases

We study the formation of high energy tails in a one-dimensional kinetic model for granular gases, the so-called Inelastic Maxwell Model. We introduce a time- discretized version of the stochastic process, and show that continuous time implies larger fluctuations of the particles energies. This is due to a statistical relation between the number of inelastic collisions undergone by a particle and its average energy. This feature is responsible for the high energy tails in the model, as shown by computer simulations and by analytical calculations on a linear Lorentz model.Comment: 8 pages, 2 figures, submitted to physica

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