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Igor Semenikhin

Publications and source records attributed to Igor Semenikhin.

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Quantum register based on double quantum dots in semiconductor nanowires

An implementation of a universal solid-state quantum register based on electron space states in field-defined double quantum dots (a DQD possesses one electron in two adjacent tunnel bound dots) in an ultrathin semiconductor wire is discussed. To some extent, the structure resembles that of a field-effect transistor with multiple controlling electrodes (gates). Scalability is audible and it opens up a possibility of large-scale universal quantum computer fabricated by advanced silicon technology. Moreover, the structure could be developed into an ensemble quantum register where an array of nanowires with common controlling electrodes and contacts is fabricated. That register is much more resistant against environment noise. It is crucial that an individual qubit consists of two DQDs. The quantum information is encoded and processed inside the Hilbert subspace without charge transfer between dots. The filling factor of each quantum dot is permanently equal to 0.5. This guarantees a linear dynamics of qubits necessary for now existing quantum algorithms. Worth noting, the dynamics of qubits with altering charge state is more or less nonlinear due to interaction with surrounding dielectrics and metals (polaron effect). The basic two-qubit operations in the system are SWAP and sqrtSWAP. The latter operation is universal as well as CNOT. The two-qubit operations are performed by Coulomb interaction. Although that kind of interaction is incessant, the strength of its action depends on mutual states of interacting DQDs (in-resonance or off-resonance). In the proposed register any quantum algorithm could be effectuated via manipulation solely with digital voltage pulses on controlling electrodes that reminds a functioning of an integrated circuit. The final read-out of the register is performed after decoding into charge states of DQDs and a transmission of current through the wire.

cond-mat.mes-hall

Improving accuracy of the numerical solution of Maxwell's equations by processing edge singularities of the electromagnetic field

In this paper we present a methodology for increasing the accuracy and accelerating the convergence of numerical methods for solution of Maxwell's equations in the frequency domain by taking into account the be-havior of the electromagnetic field near the geometric edges of wedge-shaped structures. Several algorithms for incorporating treatment of singularities into methods for solving Maxwell's equations in two-dimensional structures by the examples of the analytical modal method and the spectral element method are discussed. In test calculations, for which we use diffraction gratings, the significant accuracy improvement and convergence ac-celeration were demonstrated. In the considered cases of spectral methods an enhancement of convergence from algebraic to exponential or close to exponential is observed. Diffraction efficiencies of the gratings, for which the conventional methods fail to converge due to the special values of permittivities, were calculated.

physics.comp-ph

Application of the iterative approach to modal methods for the solution of Maxwell's equations

In this work we discuss the possibility to reduce the computational complexity of modal methods, i.e. methods based on eigenmodes expansion, from the third power to the second power of the number of eigenmodes. The proposed approach is based on the calculation of the eigenmodes part by part by using shift-and-invert iterative technique and by applying the iterative approach to solve linear equations to compute eigenmodes expansion coefficients. As practical implementation, the iterative modal methods based on polynomials and trigonometric functions as well as on finite-difference scheme are developed. Alternatives to the scattering matrix (S-matrix) technique which are based on pure iterative or mixed direct-iteractive approaches allowing to markedly reduce the number of required numerical operations are discussed. Additionally, the possibility of diminishing the memory demand of the whole algorithm from second to first power of the number of modes by implementing the iterative approach is demonstrated. This allows to carry out calculations up to hundreds of thousands eigenmodes without using a supercomputer.

physics.comp-ph