A Processor Core Model for Quantum Computing

We describe an architecture based on a processing 'core' where multiple qubits interact perpetually, and a separate 'store' where qubits exist in isolation. Computation consists of single qubit operations, swaps between the store and the core, and free evolution of the core. This enables computation using physical systems where the entangling interactions are 'always on'. Alternatively, for switchable systems our model constitutes a prescription for optimizing many-qubit gates. We discuss implementations of the quantum Fourier transform, Hamiltonian simulation, and quantum error correction.Comment: 5 pages, 2 figures; improved some arguments as suggested by a refere

Heteropolyacids supported on zirconia-doped γ, θ and α alumina: A physicochemical assessment and characterisation of supported solid acids

In this paper we carry out a surface study of promising supported solid acid catalysts commonly used for the production of high value chemicals derived from glycerol. In particular, γ, θ and α alumina (Al2O3) were modified by (i) grafting with 5 wt% zirconia, (ii) doping with 30 wt% silicotungstic acid (STA), and (iii) using both zirconia and STA. The aim is to rationalise the effect of these different parameters on structural properties and surface adsorption through a comprehensive multi-technique approach, including recently developed NMR relaxation techniques. XRD and laser Raman spectroscopy confirmed a strong interaction between STA and the γ-/θ-Al2O3 resulting in a distortion of the supported STA Keggin structure relative to that of bulk STA. Conversely, a much weaker interaction between the supported STA and α-Al2O3 was measured. NMR relaxation demonstrated that the STA doping increases the adsorption properties of the catalyst, particularly for γ-/θ-Al2O3. For catalysts based on α-Al2O3, such effect was negligible. Thermogravimetric/differential thermogravimetry (TGA/DTG) analysis suggested that zirconia-grafted and non-grafted θ-Al2O3 and γ-Al2O3 are suitable materials for increasing the thermal stability of STA whereas α-Al2O3 (both grafted and non-grafted) does not improve the thermal stability of STA

Humin Formation on SBA-15-pr-SO3H Catalysts during the Alcoholysis of Furfuryl Alcohol to Ethyl Levulinate: Effect of Pore Size on Catalyst Stability, Transport, and Adsorption

Herein, the alcoholysis of furfuryl alcohol in a series of SBA-15-pr-SO3H catalysts with different pore sizes is reported. Elemental analysis and NMR relaxation/diffusion methods show that changes in pore size have a significant effect on catalyst activity and durability. In particular, the decrease in catalyst activity after catalyst reuse is mainly due to carbonaceous deposition, whereas leaching of sulfonic acid groups is not significant. This effect is more pronounced in the largest-pore-size catalyst C3, which rapidly deactivates after one reaction cycle, whereas catalysts with a relatively medium and small average pore size (named, respectively, C2 and C1) deactivate after two reaction cycles and to a lesser extent. CHNS elemental analysis showed that C1 and C3 experience a similar amount of carbonaceous deposition, suggesting that the increased reusability of the small-pore-size catalyst can be attributed to the presence of SO3H groups mostly present on the external surface, as corroborated by results on pore clogging obtained by NMR relaxation measurements. The increased reusability of the C2 catalyst is attributed to a lower amount of humin being formed and, at the same time, reduced pore clogging, which helps to maintain accessible the internal pore space

Negative Impurity Magnetic Susceptibility and Heat Capacity in a Kondo Model with Narrow Peaks in the Local Density of Electron States

Temperature dependencies of the impurity magnetic susceptibility, entropy, and heat capacity have been obtained by the method of numerical renormalization group and exact diagonalization for the Kondo model with peaks in the electron density of states near the Fermi energy (in particular, with logarithmic Van Hove singularities). It is shown that these quantities can be {\it negative}. A new effect has been predicted (which, in principle, can be observed experimentally), namely, the decrease in the magnetic susceptibility and heat capacity of a nonmagnetic sample upon the addition of magnetic impurities into it

Short-range oscillators in power-series picture

A class of short-range potentials on the line is considered as an asymptotically vanishing phenomenological alternative to the popular confining polynomials. We propose a method which parallels the analytic Hill-Taylor description of anharmonic oscillators and represents all our Jost solutions non-numerically, in terms of certain infinite hypergeometric-like series. In this way the well known solvable Rosen-Morse and scarf models are generalized.Comment: 23 pages, latex, submitted to J. Phys. A: Math. Ge

On Convergence of the Inexact Rayleigh Quotient Iteration with the Lanczos Method Used for Solving Linear Systems

For the Hermitian inexact Rayleigh quotient iteration (RQI), the author has established new local general convergence results, independent of iterative solvers for inner linear systems. The theory shows that the method locally converges quadratically under a new condition, called the uniform positiveness condition. In this paper we first consider the local convergence of the inexact RQI with the unpreconditioned Lanczos method for the linear systems. Some attractive properties are derived for the residuals, whose norms are $\xi_{k+1}$'s, of the linear systems obtained by the Lanczos method. Based on them and the new general convergence results, we make a refined analysis and establish new local convergence results. It is proved that the inexact RQI with Lanczos converges quadratically provided that $\xi_{k+1}\leq\xi$ with a constant $\xi\geq 1$. The method is guaranteed to converge linearly provided that $\xi_{k+1}$ is bounded by a small multiple of the reciprocal of the residual norm $\|r_k\|$ of the current approximate eigenpair. The results are fundamentally different from the existing convergence results that always require $\xi_{k+1}<1$, and they have a strong impact on effective implementations of the method. We extend the new theory to the inexact RQI with a tuned preconditioned Lanczos for the linear systems. Based on the new theory, we can design practical criteria to control $\xi_{k+1}$ to achieve quadratic convergence and implement the method more effectively than ever before. Numerical experiments confirm our theory.Comment: 20 pages, 8 figures. arXiv admin note: text overlap with arXiv:0906.223

Hitting Time of Quantum Walks with Perturbation

The hitting time is the required minimum time for a Markov chain-based walk (classical or quantum) to reach a target state in the state space. We investigate the effect of the perturbation on the hitting time of a quantum walk. We obtain an upper bound for the perturbed quantum walk hitting time by applying Szegedy's work and the perturbation bounds with Weyl's perturbation theorem on classical matrix. Based on the definition of quantum hitting time given in MNRS algorithm, we further compute the delayed perturbed hitting time (DPHT) and delayed perturbed quantum hitting time (DPQHT). We show that the upper bound for DPQHT is actually greater than the difference between the square root of the upper bound for a perturbed random walk and the square root of the lower bound for a random walk.Comment: 9 page

Detection and imaging in strongly backscattering randomly layered media

Abstract. Echoes from small reflectors buried in heavy clutter are weak and difficult to distinguish from the medium backscatter. Detection and imaging with sensor arrays in such media requires filtering out the unwanted backscatter and enhancing the echoes from the reflectors that we wish to locate. We consider a filtering and detection approach based on the singular value decomposition of the local cosine transform of the array response matrix. The algorithm is general and can be used for detection and imaging in heavy clutter, but its analysis depends on the model of the cluttered medium. This paper is concerned with the analysis of the algorithm in finely layered random media. We obtain a detailed characterization of the singular values of the transformed array response matrix and justify the systematic approach of the filtering algorithm for detecting and refining the time windows that contain the echoes that are useful in imaging

Tunable Silver-Functionalized Porous Frameworks for Antibacterial Applications

Healthcare-associated infections and the rise of drug-resistant bacteria pose significant challenges to existing antibiotic therapies. Silver nanocomposites are a promising solution to the current crisis, however their therapeutic application requires improved understanding of underpinning structure-function relationships. A family of chemically and structurally modified mesoporous SBA-15 silicas were synthesized as porous host matrices to tune the physicochemical properties of silver nanoparticles. Physicochemical characterization by transmission electron microscopy (TEM), X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), X-ray absorption near-edge spectroscopy (XANES) and porosimetry demonstrate that functionalization by a titania monolayer and the incorporation of macroporosity both increase silver nanoparticle dispersion throughout the silica matrix, thereby promoting Ag₂CO₃ formation and the release of ionic silver in simulated tissue fluid. The Ag₂CO₃ concentration within functionalized porous architectures is a strong predictor for antibacterial efficacy against a broad spectrum of pathogens, including C. difficile and methicillin-resistant Staphylococcus aureus (MRSA)

Density-matrix functional theory of the Hubbard model: An exact numerical study

A density functional theory for many-body lattice models is considered in which the single-particle density matrix is the basic variable. Eigenvalue equations are derived for solving Levy's constrained search of the interaction energy functional W, which is expressed as the sum of Hartree-Fock energy and the correlation energy E_C. Exact results are obtained for E_C of the Hubbard model on various periodic lattices. The functional dependence of E_C is analyzed by varying the number of sites, band filling and lattice structure. The infinite one-dimensional chain and one-, two-, or three-dimensional finite clusters with periodic boundary conditions are considered. The properties of E_C are discussed in the limits of weak and strong electronic correlations, as well as in the crossover region. Using an appropriate scaling we observe a pseudo-universal behavior which suggests that the correlation energy of extended systems could be obtained quite accurately from finite cluster calculations. Finally, the behavior of E_C for repulsive (U>0) and attractive (U<0) interactions are contrasted.Comment: Phys. Rev. B (1999), in pres