Concatenated tensor network states

We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise entanglement and long-ranged correlations. We illustrate the approach for the enhancement of matrix product states, i.e. 1D tensor networks, where we replace each of the matrices of the original matrix product state with another 1D tensor network. This procedure yields a 2D tensor network, which includes -- already for tensor dimension two -- all states that can be prepared by circuits of polynomially many (possibly non-unitary) two-qubit quantum operations, as well as states resulting from time evolution with respect to Hamiltonians with short-ranged interactions. We investigate the possibility to efficiently extract information from these states, which serves as the basic step in a variational optimization procedure. To this aim we utilize known exact and approximate methods for 2D tensor networks and demonstrate some improvements thereof, which are also applicable e.g. in the context of 2D projected entangled pair states. We generalize the approach to higher dimensional- and tree tensor networks.Comment: 16 pages, 4 figure

Completeness of classical spin models and universal quantum computation

We study mappings between distinct classical spin systems that leave the partition function invariant. As recently shown in [Phys. Rev. Lett. 100, 110501 (2008)], the partition function of the 2D square lattice Ising model in the presence of an inhomogeneous magnetic field, can specialize to the partition function of any Ising system on an arbitrary graph. In this sense the 2D Ising model is said to be "complete". However, in order to obtain the above result, the coupling strengths on the 2D lattice must assume complex values, and thus do not allow for a physical interpretation. Here we show how a complete model with real -and, hence, "physical"- couplings can be obtained if the 3D Ising model is considered. We furthermore show how to map general q-state systems with possibly many-body interactions to the 2D Ising model with complex parameters, and give completeness results for these models with real parameters. We also demonstrate that the computational overhead in these constructions is in all relevant cases polynomial. These results are proved by invoking a recently found cross-connection between statistical mechanics and quantum information theory, where partition functions are expressed as quantum mechanical amplitudes. Within this framework, there exists a natural correspondence between many-body quantum states that allow universal quantum computation via local measurements only, and complete classical spin systems.Comment: 43 pages, 28 figure

Entanglement entropy of two disjoint intervals in c=1 theories

We study the scaling of the Renyi entanglement entropy of two disjoint blocks of critical lattice models described by conformal field theories with central charge c=1. We provide the analytic conformal field theory result for the second order Renyi entropy for a free boson compactified on an orbifold describing the scaling limit of the Ashkin-Teller (AT) model on the self-dual line. We have checked this prediction in cluster Monte Carlo simulations of the classical two dimensional AT model. We have also performed extensive numerical simulations of the anisotropic Heisenberg quantum spin-chain with tree-tensor network techniques that allowed to obtain the reduced density matrices of disjoint blocks of the spin-chain and to check the correctness of the predictions for Renyi and entanglement entropies from conformal field theory. In order to match these predictions, we have extrapolated the numerical results by properly taking into account the corrections induced by the finite length of the blocks to the leading scaling behavior.Comment: 37 pages, 23 figure

Performance of local orbital basis sets in the self-consistent Sternheimer method for dielectric matrices of extended systems

We present a systematic study of the performance of numerical pseudo-atomic orbital basis sets in the calculation of dielectric matrices of extended systems using the self-consistent Sternheimer approach of [F. Giustino et al., Phys. Rev. B 81 (11), 115105 (2010)]. In order to cover a range of systems, from more insulating to more metallic character, we discuss results for the three semiconductors diamond, silicon, and germanium. Dielectric matrices calculated using our method fall within 1-3% of reference planewaves calculations, demonstrating that this method is promising. We find that polarization orbitals are critical for achieving good agreement with planewaves calculations, and that only a few additional \zeta 's are required for obtaining converged results, provided the split norm is properly optimized. Our present work establishes the validity of local orbital basis sets and the self-consistent Sternheimer approach for the calculation of dielectric matrices in extended systems, and prepares the ground for future studies of electronic excitations using these methods.Comment: 10 pages, 8 figure

Coordinated optimization of visual cortical maps (II) Numerical studies

It is an attractive hypothesis that the spatial structure of visual cortical architecture can be explained by the coordinated optimization of multiple visual cortical maps representing orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we defined a class of analytically tractable coordinated optimization models and solved representative examples in which a spatially complex organization of the orientation preference map is induced by inter-map interactions. We found that attractor solutions near symmetry breaking threshold predict a highly ordered map layout and require a substantial OD bias for OP pinwheel stabilization. Here we examine in numerical simulations whether such models exhibit biologically more realistic spatially irregular solutions at a finite distance from threshold and when transients towards attractor states are considered. We also examine whether model behavior qualitatively changes when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. Our numerical results support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the spatially irregular architecture of the visual cortex. We discuss several alternative scenarios and additional factors that may improve the agreement between model solutions and biological observations.Comment: 55 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1102.335

A Compact Multiphoton 3D Imaging System for Recording Fast Neuronal Activity

We constructed a simple and compact imaging system designed specifically for the recording of fast neuronal activity in a 3D volume. The system uses an Yb:KYW femtosecond laser we designed for use with acousto-optic deflection. An integrated two-axis acousto-optic deflector, driven by digitally synthesized signals, can target locations in three dimensions. Data acquisition and the control of scanning are performed by a LeCroy digital oscilloscope. The total cost of construction was one order of magnitude lower than that of a typical Ti:sapphire system. The entire imaging apparatus, including the laser, fits comfortably onto a small rig for electrophysiology. Despite the low cost and simplicity, the convergence of several new technologies allowed us to achieve the following capabilities: i) full-frame acquisition at video rates suitable for patch clamping; ii) random access in under ten microseconds with dwelling ability in the nominal focal plane; iii) three-dimensional random access with the ability to perform fast volume sweeps at kilohertz rates; and iv) fluorescence lifetime imaging. We demonstrate the ability to record action potentials with high temporal resolution using intracellularly loaded potentiometric dye di-2-ANEPEQ. Our design proffers easy integration with electrophysiology and promises a more widespread adoption of functional two-photon imaging as a tool for the study of neuronal activity. The software and firmware we developed is available for download at http://neurospy.org/ under an open source license

Plant ecology meets animal cognition: impacts of animal memory on seed dispersal

We propose that an understanding of animal learning and memory is critical to predicting the impacts of animals on plant populations through processes such as seed dispersal, pollination and herbivory. Focussing on endozoochory, we review the evidence that animal memory plays a role in seed dispersal, and present a model which allows us to explore the fundamental consequences of memory for this process. We demonstrate that decision-making by animals based on their previous experiences has the potential to determine which plants are visited, which fruits are selected to be eaten from the plant and where seeds are subsequently deposited, as well as being an important determinant of animal survival. Collectively, these results suggest that the impact of animal learning and memory on seed dispersal is likely to be extremely important, although to date our understanding of these processes suffers from a conspicuous lack of empirical support. This is partly because of the difficulty of conducting appropriate experiments but is also the result of limited interaction between plant ecologists and those who work on animal cognition

SCAview: an Intuitive Visual Approach to the Integrative Analysis of Clinical Data in Spinocerebellar Ataxias

With SCAview, we present a prompt and comprehensive tool that enables scientists to browse large datasets of the most common spinocerebellar ataxias intuitively and without technical effort. Basic concept is a visualization of data, with a graphical handling and filtering to select and define subgroups and their comparison. Several plot types to visualize all data points resulting from the selected attributes are provided. The underlying synthetic cohort is based on clinical data from five different European and US longitudinal multicenter cohorts in spinocerebellar ataxia type 1, 2, 3, and 6 (SCA1, 2, 3, and 6) comprising > 1400 patients with overall > 5500 visits. First, we developed a common data model to integrate the clinical, demographic, and characterizing data of each source cohort. Second, the available datasets from each cohort were mapped onto the data model. Third, we created a synthetic cohort based on the cleaned dataset. With SCAview, we demonstrate the feasibility of mapping cohort data from different sources onto a common data model. The resulting browser-based visualization tool with a thoroughly graphical handling of the data offers researchers the unique possibility to visualize relationships and distributions of clinical data, to define subgroups and to further investigate them without any technical effort. Access to SCAview can be requested via the Ataxia Global Initiative and is free of charge