Quantum simulations under translational symmetry

We investigate the power of quantum systems for the simulation of Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range interactions we determine time evolutions which can and those that can not be simulated. Whereas for general spin systems no finite universal set of generating interactions is shown to exist, universality turns out to be generic for quadratic bosonic and fermionic nearest-neighbor interactions when supplemented by all translationally invariant on-site Hamiltonians.Comment: 9 pages, 2 figures, references added, minor change

Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? We provide an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling n-qubit Hamiltonian and local unitaries. It follows that universal quantum computation can be performed using any entangling interaction and local unitary operations.Comment: Added references to NMR refocusing and to earlier work by Leung et al and Jones and Knil

Elementary gates for quantum computation

We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values $(x,y)$ to $(x,x \oplus y)$) is universal in the sense that all unitary operations on arbitrarily many bits $n$ (U($2^n$)) can be expressed as compositions of these gates. We investigate the number of the above gates required to implement other gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2) transformation to one input bit if and only if the logical AND of all remaining input bits is satisfied. These gates play a central role in many proposed constructions of quantum computational networks. We derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two-and three-bit quantum gates, the asymptotic number required for $n$-bit Deutsch-Toffoli gates, and make some observations about the number required for arbitrary $n$-bit unitary operations.Comment: 31 pages, plain latex, no separate figures, submitted to Phys. Rev. A. Related information on http://vesta.physics.ucla.edu:7777

Vacuum Polarization and Energy Conditions at a Planar Frequency Dependent Dielectric to Vacuum Interface

The form of the vacuum stress-tensor for the quantized scalar field at a dielectric to vacuum interface is studied. The dielectric is modeled to have an index of refraction that varies with frequency. We find that the stress-tensor components, derived from the mode function expansion of the Wightman function, are naturally regularized by the reflection and transmission coefficients of the mode at the boundary. Additionally, the divergence of the vacuum energy associated with a perfectly reflecting mirror is found to disappear for the dielectric mirror at the expense of introducing a new energy density near the surface which has the opposite sign. Thus the weak energy condition is always violated in some region of the spacetime. For the dielectric mirror, the mean vacuum energy density per unit plate area in a constant time hypersurface is always found to be positive (or zero) and the averaged weak energy condition is proven to hold for all observers with non-zero velocity along the normal direction to the boundary. Both results are found to be generic features of the vacuum stress-tensor and not necessarily dependent of the frequency dependence of the dielectric.Comment: 16 pages, 4 figures, Revtex style Minor typographic corrections to equations and tex

Continuous selections of multivalued mappings

This survey covers in our opinion the most important results in the theory of continuous selections of multivalued mappings (approximately) from 2002 through 2012. It extends and continues our previous such survey which appeared in Recent Progress in General Topology, II, which was published in 2002. In comparison, our present survey considers more restricted and specific areas of mathematics. Note that we do not consider the theory of selectors (i.e. continuous choices of elements from subsets of topological spaces) since this topics is covered by another survey in this volume

Correlation of mRNA and protein levels: Cell type-specific gene expression of cluster designation antigens in the prostate

Background: Expression levels of mRNA and protein by cell types exhibit a range of correlations for different genes. In this study, we compared levels of mRNA abundance for several cluster designation (CD) genes determined by gene arrays using magnetic sorted and laser-capture microdissected human prostate cells with levels of expression of the respective CD proteins determined by immunohistochemical staining in the major cell types of the prostate - basal epithelial, luminal epithelial, stromal fibromuscular, and endothelial - and for prostate precursor/stem cells and prostate carcinoma cells. Immunohistochemical stains of prostate tissues from more than 50 patients were scored for informative CD antigen expression and compared with cell-type specific transcriptomes. Results: Concordance between gene and protein expression findings based on 'present' vs. 'absent' calls ranged from 46 to 68%. Correlation of expression levels was poor to moderate (Pearson correlations ranged from 0 to 0.63). Divergence between the two data types was most frequently seen for genes whose array signals exceeded background (> 50) but lacked immunoreactivity by immunostaining. This could be due to multiple factors, e.g. low levels of protein expression, technological sensitivities, sample processing, probe set definition or anatomical origin of tissue and actual biological differences between transcript and protein abundance. Conclusion: Agreement between these two very different methodologies has great implications for their respective use in both molecular studies and clinical trials employing molecular biomarkers.This work was supported by grant DK63630 and DK069690 from NIDDK. Additional funding came from grants CA85859, CA98699 and CA111244 from NCI, and PM50 GMO76547/Center for Systems Biology

Quantum Inequalities and Singular Energy Densities

There has been much recent work on quantum inequalities to constrain negative energy. These are uncertainty principle-type restrictions on the magnitude and duration of negative energy densities or fluxes. We consider several examples of apparent failures of the quantum inequalities, which involve passage of an observer through regions where the negative energy density becomes singular. We argue that this type of situation requires one to formulate quantum inequalities using sampling functions with compact support. We discuss such inequalities, and argue that they remain valid even in the presence of singular energy densities.Comment: 18 pages, LaTex, 2 figures, uses eps

Europe as a multilevel federation

Peer reviewedPublisher PD

Faint High Latitude Carbon Stars Discovered by the Sloan Digital Sky Survey: Methods and Initial Results

We report the discovery of 39 Faint High Latitude Carbon Stars (FHLCs) from Sloan Digital Sky Survey commissioning data. The objects, each selected photometrically and verified spectroscopically, range over 16.6 < r* < 20.0, and show a diversity of temperatures as judged by both colors and NaD line strengths. At the completion of the Sloan Survey, there will be many hundred homogeneously selected and observed FHLCs in this sample. We present proper motion measures for each object, indicating that the sample is a mixture of extremely distant (>100 kpc) halo giant stars, useful for constraining halo dynamics, plus members of the recently-recognized exotic class of very nearby dwarf carbon (dC) stars. Motions, and thus dC classification, are inferred for 40-50 percent of the sample, depending on the level of statistical significance invoked. The new list of dC stars presented here, although selected from only a small fraction of the final SDSS, doubles the number of such objects found by all previous methods. (Abstract abridged).Comment: Accepted for publication in The Astronomical Journal, Vol. 124, Sep. 2002, 40 pages, 7 figures, AASTeX v5.