Engineering topics
Vahala, Linda
Publications and source records attributed to Vahala, Linda.
Qubit Lattice Algorithms Based on the Schrödinger-Dirac Representation of Maxwell Equations and Their Extensions
It is well known that Maxwell equations can be expressed in a unitary Schrodinger-Dirac representation for homogeneous media. However, difficulties arise when considering inhomogeneous media. A Dyson map points to a unitary field qubit basis, but the standard qubit lattice algorithm of interleaved unitary collision-stream operators must be augmented by some sparse non-unitary potential operators that recover the derivatives on the refractive indices. Here, the effect of the steepness of these derivatives on two-dimensional scattering is examined with simulations showing quite complex wavefronts emitted due to transmissions/reflections within the dielectric objects. Maxwell equations are extended to handle dissipation using Kraus operators. Then, our theoretical algorithms are extended to these open quantum systems. A quantum circuit diagram is presented as well as estimates on the required number of quantum gates for implementation on a quantum computer.
Qubit Lattice Algorithms based on the Schrodinger-Dirac representation of Maxwell Equations and their Extensions
It is well known that Maxwell equations can be expressed in a unitary Schrodinger-Dirac representation for homogeneous media. However, difficulties arise when considering inhomoge- neous media. A Dyson map points to a unitary field qubit basis, but the standard qubit lattice algorithm of interleaved unitary collision-stream operators must be augmented by some sparse non-unitary potential operators that recover the derivatives on the refractive indices. The effect of the steepness of these derivatives on two dimensional scattering is examined with simulations showing quite complex wavefronts emitted due to transmissions/reflections within the dielectric objects. Maxwell equations are extended to handle dissipation using Kraus operators. Then, our theoretical algorithms are extended to these open quantum systems. A quantum circuit diagram is presented as well as estimates on the required number of quantum gates for implementation on a quantum computer.
One and Two Dimensional Quantum Lattice Algorithms for Maxwell Equations in Inhomogeneous Scalar Dielectric Media. II: Simulations
Long time quantum lattice algorithm (QLA) simulations are performed for the mul- tiple reflection-transmission of an initial electromagnetic pulse propagating normally to a boundary layer region joining two media of different refractive index. For these one dimensional (1D) sim- ulations, there is excellent agreement between x-, y- and z- representations, as well as very good agreement with nearly all the standard plane wave boundary condition results for reflection and transmission off a dielectric discontinuity. In the QLA simulation, no boundary conditions are im- posed at the continuous, but sharply increasing, dielectic boundary layers. Two dimensional (2D) QLA scattering simulations in the x-z plane are performed for an electromagnetic pulse interacting with a conical dielectric obstacle for the 8-16 qubit model.
One and Two Dimensional Quantum Lattice Algorithms for Maxwell Equations in Inhomogeneous Scalar Dielectric Media I: Theory
A quantum lattice algorithm (QLA) is developed for Maxwell equations in scalar dielectric media using the Riemann-Silberstein representation on a Cartesian grid. For x-dependent and y-dependent dielectric inhomogeneities, the corresponding QLA requires a minimum of 8 qubits/spatial lattice site. This is because the corresponding Pauli spin matrices have off-diagonal components which permit the local collisional entanglement of these qubits. However, z-dependent inhomogeneities require a QLA with a minimum of 16 qubits/lattice site since the Pauli spin matrix σz is diagonal. For 2 dimensional inhomogeneities, one can readily couple the 8-8 qubit schemes for x-y variations. z-x and y-z variations can be treated by either a 16-8 qubit scheme or a 16-16 qubit representation.
Reflection and transmission of electromagnetic pulses at a planar dielectric interface -- theory and quantum lattice simulations
There is considerable interest in the application of quantum information science to advance computations in plasma physics. A particular point of curiosity is whether it is possible to take advantage of quantum computers to speed up numerical simulations relative to conventional computers. Many of the topics in fusion plasma physics are classical in nature. In order to implement them on quantum computers it will require couching a classical problem in the language of quantum mechanics. Electromagnetic waves are routinely used in fusion experiments to heat a plasma or to generate currents in the plasma. The propagation of electromagnetic waves is described by Maxwell equations with an appropriate description of the plasma as a dielectric medium. Before advancing to the tensor dielectric of a magnetized plasma, this paper considers electromagnetic wave propagation in a one-dimensional inhomogeneous scalar dielectric. The classic theory of scattering of plane electromagnetic waves at a planar interface, separating two different dielectric media, leads to Fresnel equations for reflection and transmission coefficients. In contrast to plane waves, this paper is on the reflection and transmission of a spatially confined electromagnetic pulse. Following an analytical formulation for the scattering of a Gaussian pulse, it is deduced that the maximum transmission coefficient for a pulse is $\sqrt{n_2/n_1}$ times that for a plane wave; the incident and transmitted pulses propagating in dielectric media with refractive indices $n_1$ and $n_2$, respectively. The analytical theory is complemented by numerical simulations using a quantum lattice algorithm for Maxwell equations. The algorithm, based on the Riemann-Silberstein-Weber representation of the electromagnetic fields and expressed in term of qubits, is an interleaved sequence of entangling operators at each lattice site and unitary streaming operators which transmit information from one site to an adjacent lattice site. Besides substantiating results from the theory for Gaussian pulses, numerical simulations show their validity for non-Gaussian pulses. Apart from their time-asymptotic forms, the simulations display an interplay between the incident, reflected, and transmitted pulses in the vicinity of the transition region between two dielectric media.
Building a Three-Dimensional Quantum Lattice Algorithm for Maxwell Equations
A three-dimensional quantum lattice algorithm (QLA) for electromagnetic wave propagation is being developed by stitching together the individual QLAs for 1D wave propagation in the three orthogonal Cartesian directions.
Building a three-dimensional quantum lattice algorithm for maxwell equations
We report a three-dimensional quantum lattice algorithm (QLA) for electromagnetic wave propagation is being developed by stitching together the individual QLAs for 1D wave propagation in the three orthogonal Cartesian directions
Unitary quantum lattice simulations for Maxwell equations in vacuum and in dielectric media
Utilizing the similarity between the spinor representation of the Dirac and the Maxwell equations that has been recognized since the early days of relativistic quantum mechanics, a quantum lattice algorithm (QLA) representation of unitary collision-stream operators of Maxwell's equations is derived for both homogeneous and inhomogeneous media. A second-order accurate 4-spinor scheme is developed and tested successfully for two-dimensional (2-D) propagation of a Gaussian pulse in a uniform medium whereas for normal (1-D) incidence of an electromagnetic Gaussian wave packet onto a dielectric interface requires 8-component spinors because of the coupling between the two electromagnetic polarizations. In particular, the well-known phase change, field amplitudes and profile widths are recovered by the QLA asymptotic profiles without the imposition of electromagnetic boundary conditions at the interface. The QLA simulations yield the time-dependent electromagnetic fields as the wave packet enters and straddles the dielectric boundary. QLA involves unitary interleaved non-commuting collision and streaming operators that can be coded onto a quantum computer: the non-commutation being the very reason why one perturbatively recovers the Maxwell equations.
Unitary Qubit Lattice Algorithm for Three-Dimensional Vortex Solitons in Hyperbolic Self-Defocusing Media
A qubit unitary lattice algorithm is developed for the 3D generalized Gross-Pitaevskii equation in which dark optical vortices are stabilized by a transverse bright soliton. It is shown how to generalize the unitary collision operator in order to switch the elliptic operator into a hyperbolic one. These unitary algorithms can be run on a quantum computer.
Unitary qubit lattice algorithm for three-dimensional vortex solitons in hyperbolic self-defocusing media
To obtain stable vortex structures in three-dimensional (3D) nonlinear optics, Efremidis et al. (2007) have introduced a generalized Nonlinear Schrodinger equation (NLS) in which the transverse quantum vortex components are stabilized by a longitudinal bright soliton: i.e., the elliptic operator ∇ 2 is replaced by its hyperbolic counterpart ∇ ⊥ 2 - ∂ 2 / ∂ z 2 . A new 3D mesoscopic qubit unitary lattice algorithm is developed for this generalized NLS. One introduces 2 qubits for each lattice site and entangles them with a local unitary collision operator. This entanglement is then spread throughout the lattice by nearest neighbor streaming. These interwined operators lead to an extremely well parallelized code on classical supcomputers while their unitary structure will permit encoding onto a quantum computer. Somewhat unexpectedly, the hyperbolic operator can be realized from variations in the collision operator, without introducing variations in the streaming operator. The initial line vortices are generated by Pade asymptotics. The energy constraint is conserved to 10 digit accuracy.
Topics in Plasma Physics
During the period 1998-2013, research under the auspices of the Department of Energy was performed on RF waves in plasmas. This research was performed in close collaboration with Josef Preinhaelter, Jakub Urban, Vladimir Fuchs, Pavol Pavlo and Frantisek Zacek (Czech Academy of Sciences), Martin Valovic and Vladimir Shevchenko (Culham). This research is detailed and all 38 papers which were published by this team are cited.
Classification and Prediction of RF Coupling inside A-320 and A-319 Airplanes using Feed Forward Neural Networks
Neural Network Modeling is introduced in this paper to classify and predict Interference Path Loss measurements on Airbus 319 and 320 airplanes. Interference patterns inside the aircraft are classified and predicted based on the locations of the doors, windows, aircraft structures and the communication/navigation system-of-concern. Modeled results are compared with measured data and a plan is proposed to enhance the modeling for better prediction of electromagnetic coupling problems inside aircraft.
Graphical Analysis of Electromagnetic Coupling on B-737 and B-757 Aircraft for VOR and LOC IPL Data
Electromagnetic coupling measurements were performed from numerous passenger cabin locations to aircraft instrument landing system localizer (LOC) and VHF Omni-Ranging (VOR) systems. This paper presents and compares the data for B-757 and B-737 airplanes, and provides a basis for fuzzy modeling of coupling patterns in different types of airplanes and airplanes with different antenna locations.
Comparative Analysis of Interference Pathloss Coupling Patterns on B-737 VS. B757 Airplanes
Portable wireless technology provides many benefits to modern day travelers. Over the years however, numerous reports have cited portable electronic devices (PEDs) as a possible cause of electromagnetic interference (EMI) to aircraft navigation and communication radio systems. PEDs may act as transmitters, both intentional and unintentional, and their signals may be detected by the various radio receiver antennas installed on the aircraft. Measurement of the radiated field coupling between passenger cabin locations and aircraft communication and navigation receivers, via their antennas is defined herein as interference path loss (IPL). IPL data is required for assessing the threat of PEDs to aircraft radios, and is very dependent upon airplane size, the interfering transmitter position within the airplane, and the location of the particular antenna for the aircraft system of concern. NASA Langley Research Center, Eagles Wings Inc., and United Airlines personnel performed extensive IPL measurements on several Boeing 737 airplanes. In the Spring of 2004, extensive IPL measurements were also taken on several Boeing 757 airplanes under a cooperative agreement between NASA Langley Research Center and Delta Airlines. The objective of this paper is to analyze IPL measurement data, to better understand the impact on coupling levels based on the different locations of the aircraft radio antennas on B-757 and B-737 airplanes, and to provide a basis for future fuzzy logic modeling of airplane IPL. This effort will build upon previous fuzzy modeling of IPL data for B-737 airplane data.
Graphical Analysis of B-737 Airplane Pathloss Data for GPS and Evaluation of Coupling Mitigation Techniques
The use of Portable Electronic Devices (PEDs) onboard commercial airliners is considered to be desirable for many passengers, However, the possibility of Electromagnetic Interference (EMI) caused by these devices may affect flight safety. PEDs may act as transmitters, both intentional and unintentional, and their signals may be detected by the various navigation and communication radios onboard the aircraft. Interference Pathloss (IPL) is defined as the measurement of the radiated field coupling between passenger cabin locations and aircraft communication and navigation receivers, via their antennas. This paper first focuses on IPL measurements for GPS, taken on an out-of-service United Airlines B-737-200. IPL pattern symmetry is verified by analyzing data obtained on the windows of the Port as well as the Starboard side of the aircraft. Further graphical analysis is performed with the door and exit seams sealed with conductive tape in order to better understand the effects of shielding on IPL patterns. Shielding effects are analyzed from window data for VHF and LOC systems. In addition the shielding benefit of applying electrically conductive film to aircraft windows is evaluated for GPS and TCAS systems.
Electromagnetic Propagation Prediction Inside Aircraft Cabins
Electromagnetic propagation models for signal strength prediction within aircraft cabins are essential for evaluating and designing a wireless communication system to be implemented onboard aircraft. A model was developed using Wireless Valley's SitePlanner; which is commercial grade software intended for predictions within office buildings. The performance of the model was evaluated through a comparison with test data measurements taken on several aircraft. The comparison concluded that the model can accurately predict power propagation within the cabin. This model can enhance researchers understanding of power propagation within aircraft cabins and will aid in future research.
Wireless Network Simulation in Aircraft Cabins
An electromagnetic propagation prediction tool was used to predict electromagnetic field strength inside airplane cabins. A commercial software package, Wireless Insite, was used to predict power levels inside aircraft cabins and the data was compared with previously collected experimental data. It was concluded that the software could qualitatively predict electromagnetic propagation inside the aircraft cabin environment.