Universal quantum computation with ordered spin-chain networks

It is shown that anisotropic spin chains with gapped bulk excitations and magnetically ordered ground states offer a promising platform for quantum computation, which bridges the conventional single-spin-based qubit concept with recently developed topological Majorana-based proposals. We show how to realize the single-qubit Hadamard, phase, and pi/8 gates as well as the two-qubit CNOT gate, which together form a fault-tolerant universal set of quantum gates. The gates are implemented by judiciously controlling Ising exchange and magnetic fields along a network of spin chains, with each individual qubit furnished by a spin-chain segment. A subset of single-qubit operations is geometric in nature, relying on control of anisotropy of spin interactions rather than their strength. We contrast topological aspects of the anisotropic spin-chain networks to those of p-wave superconducting wires discussed in the literature.Comment: 9 pages, 3 figure

Wave function engineering in quantum dot-ring nanostructures

Modern nanotechnology allows producing, depending on application, various quantum nanostructures with the desired properties. These properties are strongly influenced by the confinement potential which can be modified, e.g., by electrical gating. In this paper we analyze a nanostructure composed of a quantum dot surrounded by a quantum ring. We show that depending on the details of the confining potential the electron wave functions can be located in different parts of the structure. Since the properties of such a nanostructure strongly depend on the distribution of the wave functions, varying the applied gate voltage one can easily control them. In particular, we illustrate the high controllability of the nanostructure by demonstrating how its coherent, optical, and conducting properties can be drastically changed by a small modification of the confining potential.Comment: 8 pages, 10 figures, 2 tables, revte

Scanning Tunneling Microscope Operating as a Spin-diode

We theoretically investigate spin-polarized transport in a system composed of a ferromagnetic Scanning Tunneling Microscope (STM) tip coupled to an adsorbed atom (adatom) on a host surface. Electrons can tunnel directly from the tip to the surface or via the adatom. Since the tip is ferromagnetic and the host surface (metal or semiconductor) is non-magnetic we obtain a spin-diode effect when the adatom is in the regime of single occupancy. This effect leads to an unpolarized current for direct bias (V > 0) and polarized current for reverse (V < 0) bias voltages, if the tip is nearby the adatom. Within the nonequilibrium Keldysh technique we analyze the interplay between the lateral displacement of the tip and the intra adatom Coulomb interaction on the spindiode effect. As the tip moves away from the adatom the spin-diode effect vanishes and the currents become polarized for both V > 0 and V < 0. We also find an imbalance between the up and down spin populations in the adatom, which can be tuned by the tip position and the bias. Finally, due to the presence of the adsorbate on the surface, we observe spin-resolved Friedel oscillations in the current, which reflects the oscillations in the calculated LDOS of the subsystem surface+adatom.Comment: 11 pages, 4 figures. Submitte

Momentum dependence of the spin susceptibility in two dimensions: nonanalytic corrections in the Cooper channel

We consider the effect of rescattering of pairs of quasiparticles in the Cooper channel resulting in the strong renormalization of second-order corrections to the spin susceptibility in a two-dimensional electron system. We use the Fourier expansion of the scattering potential in the vicinity of the Fermi surface to find that each harmonic becomes renormalized independently. Since some of those harmonics are negative, the first derivative of the spin susceptibility is bound to be negative at small momenta, in contrast to the lowest order perturbation theory result, which predicts a positive slope. We present in detail an effective method to calculate diagrammatically corrections to the spin susceptibility to infinite order

Group Irregularity Strength of Connected Graphs

We investigate the group irregularity strength ($s_g(G)$) of graphs, i.e. the smallest value of $s$ such that taking any Abelian group \gr of order $s$, there exists a function f:E(G)\rightarrow \gr such that the sums of edge labels at every vertex are distinct. We prove that for any connected graph $G$ of order at least 3, $s_g(G)=n$ if $n\neq 4k+2$ and $s_g(G)\leq n+1$ otherwise, except the case of some infinite family of stars

Modelling and analysis of nonlinear guided waves interaction at a breathing crack using time-domain spectral finite element method

Published 20 June 2017This study proposes a time-domain spectral finite element (SFE) model and investigates nonlinear guided wave interaction at a breathing crack. An extended time-domain SFE method based on the Mindlin–Hermann rod and Timoshenko beam theory is proposed to predict the nonlinear guided wave generation at the breathing crack. An SFE crack element is proposed to simulate the mode-conversion effect, in which a bilinear crack mechanism is implemented to take into account the contact nonlinearity at the breathing crack. There is good agreement between the results calculated using the proposed time-domain SFE method and threedimensional finite element simulation. This demonstrates the accuracy of the proposed SFE method in simulating contact nonlinearity at the breathing crack. Parametric studies using the fundamental symmetric (S₀) and anti-symmetric (A₀) modes of guided waves are also carried out to provide physical insights into the higher harmonics generated due to the contact nonlinearity at the breathing crack. The magnitude of the higher harmonics generated as a function of the crack depth is investigated in detail. The results show that the mode-converted higher harmonic guided waves provide valuable information for damage detection.Shuai He and Ching Tai N