Microwave Simulation of Grover's Quantum Search Algorithm

An analog of a quantum search method, known as Grover's algorithm, is modeled without entanglement on the macroscopic level, using numerical simulation of microwave devices and methods. An array of microstrip annular-ring resonators simulates a quantum bit array. An oracle that performs a test to determine which element in the array is the answer to the search algorithm is provided by a microwave-frequency plane wave, modulated by a Gaussian pulse. A single annular ring with a resonant frequency identical to the frequency of the incident pulse serves as the answer to the search. It is shown that the number of Gaussian pulses needed to identify the answer element is equal to the radicN iterations predicted by the Grover algorithm. The decay in a microwave-resonator element is used to show that the quantum dual - a spontaneous decay of the excited energy level of a quantum bit, also described as its decoherence - can be a serious obstacle to the development of large quantum-bit data arrays     

The annular aperture antenna with a hemispherical center conductor extension

An annular aperture antenna mounted on an infinite ground plane and containing a hemispherical center conductor extension above the ground plane is investigated. A Green's function for the region above the ground plane is derived so as to be compatible with numerical solution techniques. A magnetic field integral equation is obtained in terms of the unknown tangential aperture electric field and is solved by the method of moments. A comparison between flush mounted and hemispherically extended annular aperture antennas is presented for the tangential aperture electric field, the coaxial line apparent input admittance, and the far radiated field.     

The time domain Green's function and propagator for Maxwell's equations

The free space time domain propagator and corresponding dyadic Green's function for Maxwell's differential equations are derived in one-, two-, and three-dimensions using the propagator method. The propagator method reveals terms that contribute in the source region, which to our knowledge have not been previously reported in the literature. It is shown that these terms are necessary to satisfy the initial condition, that the convolution of the Green's function with the field must identically approach the initial field as the time interval approaches zero. It is also shown that without these terms, Huygen's principle cannot be satisfied. To illustrate the value of this Green's function two analytical examples are presented, that of a propagating plane wave and of a radiating point source. An accurate propagator is the key element in the time domain path integral formulation for the electromagnetic field.     

The specificity of split renal membranes in hereditary nephritis

This study was undertaken to assess the specificity of split renal basement membranes in hereditary nephritis (HN). Thirteen specimens from eight patients with HN were mixed in a random fashion with specimens from control patients with either idiopathic nephrotic syndrome or various forms of glomerulonephritis and with specimens from patients with benign recurrent hematuria (BRH). Each biopsy specimen was scored for splitting of glomerular basement membranes (GBMs). Control and BRH specimens contained focal splitting in the GBMs; the biopsy specimens from HN patients had widespread lesions. Evaluation of split GBMs is useful in differentiating patients with HN from those with BRH and other renal diseases that may be confused with HN.     

Semi-orthogonal versus orthogonal wavelet basis sets for solvingintegral equations

The two categories of wavelets, orthogonal and semi-orthogonal, are compared and it is shown that the semi-orthogonal wavelet is best suited for integral equation applications. The Battle-Lemarie orthogonal wavelet and the spline generated semi-orthogonal wavelet are each used to solve for the current distribution on an infinite strip illuminated by a transverse magnetic (TM) plane wave and a straight thin wire illuminated by a normally incident plane wave. The grounds for comparison are accuracy in characterizing the current, matrix sparsity, computation time, and singularity extraction capability. The limitations and advantages of solving integral equations with each of the two wavelet categories are discussed     

A path integral time-domain method for electromagnetic scattering

A new full wave time-domain formulation for the electromagnetic field is obtained by means of a path integral. The path integral propagator is derived via a state variable approach starting with Maxwell's differential equations in tensor form. A numerical method for evaluating the path integral is presented and numerical dispersion and stability conditions are derived and numerical error is discussed. An absorbing boundary condition is demonstrated for the one-dimensional (1-D) case. It is shown that this time domain method is characterized by the unconditional stability of the path integral equations and by its ability to propagate an electromagnetic wave at the Nyquist limit, two numerical points per wavelength. As a consequence the calculated fields are not subject to numerical dispersion. Other advantages in comparison to presently popular time-domain techniques are that it avoids time interval interleaving and it does not require the methods of linear algebra such as basis function selection or matrix methods     

Corrections to `Radiation from a dielectric coated hemisphericalconductor fed by a coaxial transmission line' (Feb. 1989, 16-20)

The authors provide a corrected figure and title for the apparent input admittance in the above-titled paper (see ibid., vol.31, no.1, p.16-20, 1989)     

Lorenz, Lorentz, and the gauge

Briefly discusses work by L. Lorentz and H.A. Lorentz together with the concept of the Coulomb gauge     

Comparison of Lorentz and Coulomb gauge formulations fortransverse-electric wave scattering by two-dimensional surfaces ofarbitrary shape in the presence of a circular cylinder

Two forms of the so-called mixed-potential electric field integral equation (MPIE) are developed for two-dimensional perfectly conducting (PC) surfaces of arbitrary shape in the presence of an infinite PC cylinder of circular cross section subject to transverse-electric (TE) excitation. One of the MPIEs is based on the Coulomb gauge; the other uses the Lorentz gauge. In either case, the effect of the cylinder is incorporated in the integral equation by means of the appropriate Green's functions, leaving the current distribution on the arbitrary surface as the only unknown. The Green's functions are derived by the eigenfunction expansion technique. An existing well-established moment method procedure is adapted to solve both forms of the MPIE numerically. Computed results are presented for several cases of interest, and the relative merits of the Coulomb and Lorentz gauge MPIEs are discussed     

Edge diffraction in the vicinity of the tip of a composite wedge

The electromagnetic field due to a line source radiating in the presence of a two-dimensional composite wedge composed of a number of conducting and dielectric materials is obtained. The Fourier transform path integral method (FTPI) is described and used to perform the numerical analysis. An important feature of the FTPI method is that it is based on a global solution to the Helmholtz scalar wave equation. As such the method avoids numerical enforcement of boundary conditions and the necessity of reformulating the analytical/numerical equations for each geometric configuration. The total scattered field is presented for several cases where one of the dielectric wedge sections is lossy, including examples of microwave scattering from a crested ocean surface and an air-ocean-sea ice interface