Enhancement of Entanglement Percolation in Quantum Networks via Lattice Transformations

We study strategies for establishing long-distance entanglement in quantum networks. Specifically, we consider networks consisting of regular lattices of nodes, in which the nearest neighbors share a pure, but non-maximally entangled pair of qubits. We look for strategies that use local operations and classical communication. We compare the classical entanglement percolation protocol, in which every network connection is converted with a certain probability to a singlet, with protocols in which classical entanglement percolation is preceded by measurements designed to transform the lattice structure in a way that enhances entanglement percolation. We analyze five examples of such comparisons between protocols and point out certain rules and regularities in their performance as a function of degree of entanglement and choice of operations.Comment: 12 pages, 17 figures, revtex4. changes from v3: minor stylistic changes for journal reviewer, minor changes to figures for journal edito

Scalable aggregation predictive analytics: a query-driven machine learning approach

We introduce a predictive modeling solution that provides high quality predictive analytics over aggregation queries in Big Data environments. Our predictive methodology is generally applicable in environments in which large-scale data owners may or may not restrict access to their data and allow only aggregation operators like COUNT to be executed over their data. In this context, our methodology is based on historical queries and their answers to accurately predict ad-hoc queries’ answers. We focus on the widely used set-cardinality, i.e., COUNT, aggregation query, as COUNT is a fundamental operator for both internal data system optimizations and for aggregation-oriented data exploration and predictive analytics. We contribute a novel, query-driven Machine Learning (ML) model whose goals are to: (i) learn the query-answer space from past issued queries, (ii) associate the query space with local linear regression & associative function estimators, (iii) define query similarity, and (iv) predict the cardinality of the answer set of unseen incoming queries, referred to the Set Cardinality Prediction (SCP) problem. Our ML model incorporates incremental ML algorithms for ensuring high quality prediction results. The significance of contribution lies in that it (i) is the only query-driven solution applicable over general Big Data environments, which include restricted-access data, (ii) offers incremental learning adjusted for arriving ad-hoc queries, which is well suited for query-driven data exploration, and (iii) offers a performance (in terms of scalability, SCP accuracy, processing time, and memory requirements) that is superior to data-centric approaches. We provide a comprehensive performance evaluation of our model evaluating its sensitivity, scalability and efficiency for quality predictive analytics. In addition, we report on the development and incorporation of our ML model in Spark showing its superior performance compared to the Spark’s COUNT method

Magnetic skyrmions and their lattices in triplet superconductors

Complete topological classification of solutions in SO(3) symmetric Ginzburg-Landau free energy has been performed and a new class of solutions in weak external magnetic field carrying two units of magnetic flux has been identified. These solutions, magnetic skyrmions, do not have singular core like Abrikosov vortices and at low magnetic field become lighter for strongly type II superconductors. As a consequence, the lower critical magnetic field Hc1 is reduced by a factor of log(kappa). Magnetic skyrmions repel each other as 1/r at distances much larger then magnetic penetration depth forming relatively robust triangular lattice. Magnetic induction near Hc1 increases gradually as (H-Hc1)^2. This agrees very well with experiments on heavy fermion superconductor UPt3. Newly discovered Ru based compounds Sr2RuO4 and Sr2YRu(1-x)Cu(x)O6 are other possible candidates to possess skyrmion lattices. Deviations from exact SO(3) symmetry are also studied.Comment: 23 pages, 10 eps figure

Interacting electrons on trilayer honeycomb lattices

Few-layer graphene systems come in various stacking orders. Considering tight-binding models for electrons on stacked honeycomb layers, this gives rise to a variety of low-energy band structures near the charge neutrality point. Depending on the stacking order these band structures enhance or reduce the role of electron-electron interactions. Here, we investigate the instabilities of interacting electrons on honeycomb multilayers with a focus on trilayers with ABA and ABC stackings theoretically by means of the functional renormalization group. We find different types of competing instabilities and identify the leading ordering tendencies in the different regions of the phase diagram for a range of local and non-local short-ranged interactions. The dominant instabilities turn out to be toward an antiferromagnetic spin-density wave (SDW), a charge density wave and toward quantum spin Hall (QSH) order. Ab-initio values for the interaction parameters put the systems at the border between SDW and QSH regimes. Furthermore, we discuss the energy scales for the interaction-induced gaps of this model study and put them into context with the scales for single-layer and Bernal-stacked bilayer honeycomb lattices. This yields a comprehensive picture of the possible interaction-induced ground states of few-layer graphene.Comment: 12 pages, 12 figure