Towards topological quantum computer

One of the principal obstacles on the way to quantum computers is the lack of distinguished basis in the space of unitary evolutions and thus the lack of the commonly accepted set of basic operations (universal gates). A natural choice, however, is at hand: it is provided by the quantum R-matrices, the entangling deformations of non-entangling (classical) permutations, distinguished from the points of view of group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Observables in this case are (square modules of) the knot polynomials, and their pronounced integrality properties could provide a key to error correction. We suggest to use R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern-Simons theory, to build a topological version of quantum computing.Comment: 14 page

Models of G time variations in diverse dimensions

A review of different cosmological models in diverse dimensions leading to a relatively small time variation of the effective gravitational constant G is presented. Among them: 4-dimensional general scalar-tensor model, multidimensional vacuum model with two curved Einstein spaces, multidimensional model with multicomponent anisotropic "perfect fluid", S-brane model with scalar fields and two form field etc. It is shown that there exist different possible ways of explanation of relatively small time variation of the effective gravitational constant G compatible with present cosmological data (e.g. acceleration): 4-dimensional scalar-tensor theories or multidimensional cosmological models with different matter sources. The experimental bounds on G-dot may be satisfied ether in some restricted interval or for all allowed values of the synchronous time variable.Comment: 27 pages, Late

High-resolution radio imaging of two luminous quasars beyond redshift 4.5

Context. Radio-loud active galactic nuclei in the early Universe are rare. The quasars J0906+6930 at redshift z=5.47 and J2102+6015 at z=4.57 stand out from the known sample with their compact emission on milliarcsecond (mas) angular scale with high (0.1-Jy level) flux densities measured at GHz radio frequencies. This makes them ideal targets for very long baseline interferometry (VLBI) observations. Aims. By means of VLBI imaging we can reveal the inner radio structure of quasars and model their brightness distribution to better understand the geometry of the jet and the physics of the sources. Methods. We present sensitive high-resolution VLBI images of J0906+6930 and J2102+6015 at two observing frequencies, 2.3 and 8.6 GHz. The data were taken in an astrometric observing programme involving a global five-element radio telescope array. We combined the data from five different epochs from 2017 February to August. Results. For one of the highest redshift blazars known, J0906+6930, we present the first-ever VLBI image obtained at a frequency below 8 GHz. Based on our images at 2.3 and 8.6 GHz, we confirm that this source has a sharply bent helical inner jet structure within ~3 mas from the core. The quasar J2102+6015 shows an elongated radio structure in the east-west direction within the innermost ~2 mas that can be described with a symmetric three-component brightness distribution model at 8.6 GHz. Because of their non-pointlike mas-scale structure, these sources are not ideal as astrometric reference objects. Our results demonstrate that VLBI observing programmes conducted primarily with astrometric or geodetic goals can be utilized for astrophysical purposes as well.Comment: 8 pages, 3 figures, accepted for publication in Astronomy & Astrophysic

Hadronic Light-by-Light Scattering in the Muonium Hyperfine Splitting

We consider an impact of hadronic light-by-light scattering on the muonium hyperfine structure. A shift of the hyperfine interval $\Delta \nu({\rm Mu}) _{\rm\tiny HLBL}$ is calculated with the light-by-light scattering approximated by exchange of pseudoscalar and pseudovector mesons. Constraints from the operator product expansion in QCD are used to fix parameters of the model similar to the one used earlier for the hadronic light-by-light scattering in calculations of the muon anomalous magnetic moment. The pseudovector exchange is dominant in the resulting shift, $\Delta \nu({\rm Mu})_{\rm\tiny HLBL}= -0.0065(10) {Hz}$. Although the effect is tiny it is useful in understanding the level of hadronic uncertainties.Comment: 16 pages, 7 figures, a reference adde