Minimal instances for toric code ground states

A decade ago Kitaev's toric code model established the new paradigm of topological quantum computation. Due to remarkable theoretical and experimental progress, the quantum simulation of such complex many-body systems is now within the realms of possibility. Here we consider the question, to which extent the ground states of small toric code systems differ from LU-equivalent graph states. We argue that simplistic (though experimentally attractive) setups obliterate the differences between the toric code and equivalent graph states; hence we search for the smallest setups on the square- and triangular lattice, such that the quasi-locality of the toric code hamiltonian becomes a distinctive feature. To this end, a purely geometric procedure to transform a given toric code setup into an LC-equivalent graph state is derived. In combination with an algorithmic computation of LC-equivalent graph states, we find the smallest non-trivial setup on the square lattice to contain 5 plaquettes and 16 qubits; on the triangular lattice the number of plaquettes and qubits is reduced to 4 and 9, respectively.Comment: 14 pages, 11 figure

Surface Roughness Parameter Uncertainties on Radar Based Soil Moisture Retrievals

Surface roughness variations are often assumed to be negligible for the retrieval of sol moisture. Although previous investigations have suggested that this assumption is reasonable for natural vegetation covers (i.e. Moran et al. 2002), in-situ measurements over plowed agricultural fields (i.e. Callens et al. 2006) have shown that the soil surface roughness can change considerably due to weathering induced by rain

Fermi-surface induced modulation in an optimally doped YBCO superconductor

We have observed a Fermi-surface (FS) induced lattice modulation in a YBCO superconductor with a wavevector along CuO chains, {\it i.e.} ${\bf q}_1$=(0,$\delta$,0). The value of $\delta\sim0.21$ is twice the Fermi wavevector ($2{\bf k}_F$) along {\bf b*} connecting nearly nested FS `ridges'. The ${\bf q}_1$ modulation exists only within O-vacancy-ordered islands (characterized by ${\bf q}_0$=$(\frac14,0,0))$ and persists well above and below $T_c$. Our results are consistent with the presence of a FS-induced charge-density wave

Nonlinear current-induced forces in Si atomic wires

We report first-principles calculations of current-induced forces in Si atomic wires as a function of bias and wire length. We find that these forces are strongly nonlinear as a function of bias due to the competition between the force originating from the scattering states and the force due to bound states. We also find that the average force in the wire is larger the shorter the wire, suggesting that atomic wires are more difficult to break under current flow with increasing length. The last finding is in agreement with recent experimental data.Comment: 4 figure

Modular differential equations for torus one-point functions

It is shown that in a rational conformal field theory every torus one-point function of a given highest weight state satisfies a modular differential equation. We derive and solve these differential equations explicitly for some Virasoro minimal models. In general, however, the resulting amplitudes do not seem to be expressible in terms of standard transcendental functions.Comment: 19 pages, LaTeX; reference adde

Simulations of Weighted Tree Automata

Simulations of weighted tree automata (wta) are considered. It is shown how such simulations can be decomposed into simpler functional and dual functional simulations also called forward and backward simulations. In addition, it is shown in several cases (fields, commutative rings, Noetherian semirings, semiring of natural numbers) that all equivalent wta M and N can be joined by a finite chain of simulations. More precisely, in all mentioned cases there exists a single wta that simulates both M and N. Those results immediately yield decidability of equivalence provided that the semiring is finitely (and effectively) presented.Comment: 17 pages, 2 figure

Current-Induced Effects in Nanoscale Conductors

We present an overview of current-induced effects in nanoscale conductors with emphasis on their description at the atomic level. In particular, we discuss steady-state current fluctuations, current-induced forces, inelastic scattering and local heating. All of these properties are calculated in terms of single-particle wavefunctions computed using a scattering approach within the static density-functional theory of many-electron systems. Examples of current-induced effects in atomic and molecular wires will be given and comparison with experimental results will be provided when available.Comment: revtex, 10 pages, 8 figure

Propensity assessment of tensile surface structures to water ponding

This paper has been created with the financial support of the specific university research project granted by the Brno University of Technology, registered under the number FAST-J-23-8326

Chromium at High Pressures: Weak Coupling and Strong Fluctuations in an Itinerant Antiferromagnet

The spin- and charge-density-wave order parameters of the itinerant antiferromagnet chromium are measured directly with non-resonant x-ray diffraction as the system is driven towards its quantum critical point with high pressure using a diamond anvil cell. The exponential decrease of the spin and charge diffraction intensities with pressure confirms the harmonic scaling of spin and charge, while the evolution of the incommensurate ordering vector provides important insight into the difference between pressure and chemical doping as means of driving quantum phase transitions. Measurement of the charge density wave over more than two orders of magnitude of diffraction intensity provides the clearest demonstration to date of a weakly-coupled, BCS-like ground state. Evidence for the coexistence of this weakly-coupled ground state with high-energy excitations and pseudogap formation above the ordering temperature in chromium, the charge-ordered perovskite manganites, and the blue bronzes, among other such systems, raises fundamental questions about the distinctions between weak and strong coupling.Comment: 11 pages, 9 figures (8 in color

Visual Affect Around the World: A Large-scale Multilingual Visual Sentiment Ontology

Every culture and language is unique. Our work expressly focuses on the uniqueness of culture and language in relation to human affect, specifically sentiment and emotion semantics, and how they manifest in social multimedia. We develop sets of sentiment- and emotion-polarized visual concepts by adapting semantic structures called adjective-noun pairs, originally introduced by Borth et al. (2013), but in a multilingual context. We propose a new language-dependent method for automatic discovery of these adjective-noun constructs. We show how this pipeline can be applied on a social multimedia platform for the creation of a large-scale multilingual visual sentiment concept ontology (MVSO). Unlike the flat structure in Borth et al. (2013), our unified ontology is organized hierarchically by multilingual clusters of visually detectable nouns and subclusters of emotionally biased versions of these nouns. In addition, we present an image-based prediction task to show how generalizable language-specific models are in a multilingual context. A new, publicly available dataset of >15.6K sentiment-biased visual concepts across 12 languages with language-specific detector banks, >7.36M images and their metadata is also released.Comment: 11 pages, to appear at ACM MM'1