Nonnegative/binary matrix factorization with a D-Wave quantum annealer

D-Wave quantum annealers represent a novel computational architecture and have attracted significant interest, but have been used for few real-world computations. Machine learning has been identified as an area where quantum annealing may be useful. Here, we show that the D-Wave 2X can be effectively used as part of an unsupervised machine learning method. This method can be used to analyze large datasets. The D-Wave only limits the number of features that can be extracted from the dataset. We apply this method to learn the features from a set of facial images

Comment on `Experimental and Theoretical Constraints of Bipolaronic Superconductivity in High TcT_{c} Materials: An Impossibility'

We show that objections raised by Chakraverty $et$ $al$ (Phys. Rev. Lett. 81, 433 (1998)) to the bipolaron model of superconducting cuprates are the result of an incorrect approximation for the bipolaron energy spectrum and misuse of the bipolaron theory. The consideration, which takes into account the multiband energy structure of bipolarons and the unscreened electron-phonon interaction clearly indicates that cuprates are in the Bose-Einstein condensation regime with mobile charged bosons.Comment: 1 page, no figure

High Temperature Superconductivity: the explanation

Soon after the discovery of the first high temperature superconductor by Georg Bednorz and Alex Mueller in 1986 the late Sir Nevill Mott answering his own question "Is there an explanation?" [Nature v 327 (1987) 185] expressed a view that the Bose-Einstein condensation (BEC) of small bipolarons, predicted by us in 1981, could be the one. Several authors then contemplated BEC of real space tightly bound pairs, but with a purely electronic mechanism of pairing rather than with the electron-phonon interaction (EPI). However, a number of other researchers criticized the bipolaron (or any real-space pairing) scenario as incompatible with some angle-resolved photoemission spectra (ARPES), with experimentally determined effective masses of carriers and unconventional symmetry of the superconducting order parameter in cuprates. Since then the controversial issue of whether the electron-phonon interaction (EPI) is crucial for high-temperature superconductivity or weak and inessential has been one of the most challenging problems of contemporary condensed matter physics. Here I outline some developments in the bipolaron theory suggesting that the true origin of high-temperature superconductivity is found in a proper combination of strong electron-electron correlations with a significant finite-range (Froehlich) EPI, and that the theory is fully compatible with the key experiments.Comment: 8 pages, 2 figures, invited comment to Physica Script

Key pairing interaction in layered doped ionic insulators

A controversial issue on whether the electron-phonon interaction (EPI) is crucial for high-temperature superconductivity or it is weak and inessential has remained one of the most challenging problems of contemporary condensed matter physics. We employ a continuum RPA approximation for the dielectric response function allowing for a selfconsistent semi-analytical evaluation of the EPI strength, electron-electron attractions, and the carrier mass renormalisation in layered high-temperature superconductors. We show that the Fr\"{o}hlich EPI with high-frequency optical phonons in doped ionic lattices is the key pairing interaction, which is beyond the BCS-Migdal-Eliashberg approximation in underdoped superconductors, and it remains a significant player in overdoped compounds.Comment: 4 pages, 4 figure

S-duality in Twistor Space

In type IIB string compactifications on a Calabi-Yau threefold, the hypermultiplet moduli space $M_H$ must carry an isometric action of the modular group SL(2,Z), inherited from the S-duality symmetry of type IIB string theory in ten dimensions. We investigate how this modular symmetry is realized at the level of the twistor space of $M_H$, and construct a general class of SL(2,Z)-invariant quaternion-Kahler metrics with two commuting isometries, parametrized by a suitably covariant family of holomorphic transition functions. This family should include $M_H$ corrected by D3-D1-D(-1)-instantons (with fivebrane corrections ignored) and, after taking a suitable rigid limit, the Coulomb branch of five-dimensional N=2 gauge theories compactified on a torus, including monopole string instantons. These results allow us to considerably simplify the derivation of the mirror map between type IIA and IIB fields in the sector where only D1-D(-1)-instantons are retained.Comment: 29 pages, 1 figur

Theory of SIS tunnelling in cuprates

We show that the single-particle polaron Green's function describes SIS tunnelling in cuprates, including the absence of Ohm's law at high voltages, the dip/hump features in the first derivative of the current, a substantial incoherent spectral weight beyond quasiparticle peaks and unusual shape of the peaks. The theory allows us to determine the characteristic phonon frequencies, normal and superconducting gaps, impurity scattering rate, and the electron-phonon coupling from the tunnelling data.Comment: 10 pages, 2 figure

Coherent `ab' and `c' transport theory of high-TcT_{c} cuprates

We propose a microscopic theory of the `$c$'-axis and in-plane transport of copper oxides based on the bipolaron theory and the Boltzmann kinetics. The fundamental relationship between the anisotropy and the spin susceptibility is derived, $\rho_{c}(T,x)/\rho_{ab}(T,x)\sim x/\sqrt{T}\chi_{s}(T,x)$. The temperature $(T)$ and doping $(x)$ dependence of the in-plane, $\rho_{ab}$ and out-of-plane, $\rho_{c}$ resistivity and the spin susceptibility, $\chi_{s}$ are found in a remarkable agreement with the experimental data in underdoped, optimally and overdoped $La_{2-x}Sr_{x}CuO_{4}$ for the entire temperature regime from $T_{c}$ up to $800K$. The normal state gap is explained and its doping and temperature dependence is clarified.Comment: 12 pages, Latex, 3 figures available upon reques

Parameter-free expression for superconducting Tc in cuprates

A parameter-free expression for the superconducting critical temperature of layered cuprates is derived which allows us to express Tc in terms of experimentally measured parameters. It yields Tc values observed in about 30 lanthanum, yttrium and mercury-based samples for different levels of doping. This remarkable agreement with the experiment as well as the unusual critical behaviour and the normal-state gap indicate that many cuprates are close to the Bose-Einstein condensation regime.Comment: 5 pages, 2 figures. Will be published in Physical Review