Matrix permanent and quantum entanglement of permutation invariant states

We point out that a geometric measure of quantum entanglement is related to the matrix permanent when restricted to permutation invariant states. This connection allows us to interpret the permanent as an angle between vectors. By employing a recently introduced permanent inequality by Carlen, Loss and Lieb, we can prove explicit formulas of the geometric measure for permutation invariant basis states in a simple way.Comment: 10 page

Longitudinal LASSO: Jointly Learning Features and Temporal Contingency for Outcome Prediction

Longitudinal analysis is important in many disciplines, such as the study of behavioral transitions in social science. Only very recently, feature selection has drawn adequate attention in the context of longitudinal modeling. Standard techniques, such as generalized estimating equations, have been modified to select features by imposing sparsity-inducing regularizers. However, they do not explicitly model how a dependent variable relies on features measured at proximal time points. Recent graphical Granger modeling can select features in lagged time points but ignores the temporal correlations within an individual's repeated measurements. We propose an approach to automatically and simultaneously determine both the relevant features and the relevant temporal points that impact the current outcome of the dependent variable. Meanwhile, the proposed model takes into account the non-{\em i.i.d} nature of the data by estimating the within-individual correlations. This approach decomposes model parameters into a summation of two components and imposes separate block-wise LASSO penalties to each component when building a linear model in terms of the past $\tau$ measurements of features. One component is used to select features whereas the other is used to select temporal contingent points. An accelerated gradient descent algorithm is developed to efficiently solve the related optimization problem with detailed convergence analysis and asymptotic analysis. Computational results on both synthetic and real world problems demonstrate the superior performance of the proposed approach over existing techniques.Comment: Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 201

On the Minimum Degree up to Local Complementation: Bounds and Complexity

The local minimum degree of a graph is the minimum degree reached by means of a series of local complementations. In this paper, we investigate on this quantity which plays an important role in quantum computation and quantum error correcting codes. First, we show that the local minimum degree of the Paley graph of order p is greater than sqrt{p} - 3/2, which is, up to our knowledge, the highest known bound on an explicit family of graphs. Probabilistic methods allows us to derive the existence of an infinite number of graphs whose local minimum degree is linear in their order with constant 0.189 for graphs in general and 0.110 for bipartite graphs. As regards the computational complexity of the decision problem associated with the local minimum degree, we show that it is NP-complete and that there exists no k-approximation algorithm for this problem for any constant k unless P = NP.Comment: 11 page

Multi-core job submission and grid resource scheduling for ATLAS AthenaMP

AthenaMP is the multi-core implementation of the ATLAS software framework and allows the efficient sharing of memory pages between multiple threads of execution. This has now been validated for production and delivers a significant reduction on the overall application memory footprint with negligible CPU overhead. Before AthenaMP can be routinely run on the LHC Computing Grid it must be determined how the computing resources available to ATLAS can best exploit the notable improvements delivered by switching to this multi-process model. A study into the effectiveness and scalability of AthenaMP in a production environment will be presented. Best practices for configuring the main LRMS implementations currently used by grid sites will be identified in the context of multi-core scheduling optimisation

Performance of an Operating High Energy Physics Data Grid: D0SAR-Grid

The D0 experiment at Fermilab's Tevatron will record several petabytes of data over the next five years in pursuing the goals of understanding nature and searching for the origin of mass. Computing resources required to analyze these data far exceed capabilities of any one institution. Moreover, the widely scattered geographical distribution of D0 collaborators poses further serious difficulties for optimal use of human and computing resources. These difficulties will exacerbate in future high energy physics experiments, like the LHC. The computing grid has long been recognized as a solution to these problems. This technology is being made a more immediate reality to end users in D0 by developing a grid in the D0 Southern Analysis Region (D0SAR), D0SAR-Grid, using all available resources within it and a home-grown local task manager, McFarm. We will present the architecture in which the D0SAR-Grid is implemented, the use of technology and the functionality of the grid, and the experience from operating the grid in simulation, reprocessing and data analyses for a currently running HEP experiment.Comment: 3 pages, no figures, conference proceedings of DPF04 tal

Number-Theoretic Nature of Communication in Quantum Spin Systems

The last decade has witnessed substantial interest in protocols for transferring information on networks of quantum mechanical objects. A variety of control methods and network topologies have been proposed, on the basis that transfer with perfect fidelity --- i.e. deterministic and without information loss --- is impossible through unmodulated spin chains with more than a few particles. Solving the original problem formulated by Bose [Phys. Rev. Lett. 91, 207901 (2003)], we determine the exact number of qubits in unmodulated chains (with XY Hamiltonian) that permit the transfer with fidelity arbitrarily close to 1, a phenomenon called pretty good state transfer. We prove that this happens if and only if the number of nodes is n=p-1, 2p-1, where p is a prime, or n=2^{m}-1. The result highlights the potential of quantum spin system dynamics for reinterpreting questions about the arithmetic structure of integers, and, in this case, primality.Comment: 6 pages, 1 EPS figur

A quantum Bose-Hubbard model with evolving graph as toy model for emergent spacetime

We present a toy model for interacting matter and geometry that explores quantum dynamics in a spin system as a precursor to a quantum theory of gravity. The model has no a priori geometric properties, instead, locality is inferred from the more fundamental notion of interaction between the matter degrees of freedom. The interaction terms are themselves quantum degrees of freedom so that the structure of interactions and hence the resulting local and causal structures are dynamical. The system is a Hubbard model where the graph of the interactions is a set of quantum evolving variables. We show entanglement between spatial and matter degrees of freedom. We study numerically the quantum system and analyze its entanglement dynamics. We analyze the asymptotic behavior of the classical model. Finally, we discuss analogues of trapped surfaces and gravitational attraction in this simple model.Comment: 23 pages, 6 figures; updated to published versio

Pretty good state transfer in qubit chains-The Heisenberg Hamiltonian

Pretty good state transfer in networks of qubits occurs when a continuous-time quantum walk allows the transmission of a qubit state from one node of the network to another, with fidelity arbitrarily close to 1. We prove that in a Heisenberg chain with n qubits, there is pretty good state transfer between the nodes at the jth and (n − j + 1)th positions if n is a power of 2. Moreover, this condition is also necessary for j = 1. We obtain this result by applying a theorem due to Kronecker about Diophantine approximations, together with techniques from algebraic graph theory

The maximally entangled symmetric state in terms of the geometric measure

The geometric measure of entanglement is investigated for permutation symmetric pure states of multipartite qubit systems, in particular the question of maximum entanglement. This is done with the help of the Majorana representation, which maps an n qubit symmetric state to n points on the unit sphere. It is shown how symmetries of the point distribution can be exploited to simplify the calculation of entanglement and also help find the maximally entangled symmetric state. Using a combination of analytical and numerical results, the most entangled symmetric states for up to 12 qubits are explored and discussed. The optimization problem on the sphere presented here is then compared with two classical optimization problems on the S^2 sphere, namely Toth's problem and Thomson's problem, and it is observed that, in general, they are different problems.Comment: 18 pages, 15 figures, small corrections and additions to contents and reference