Search results for: quantum master equation

Authors: A. R. Nezamabadi, M. Veiskarami

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This paper studies free vibration of simply supported functionally graded beams with piezoelectric layers based on the first order shear deformation theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. The governing equation is established. Resulting equation is solved using the Euler's equation. The effects of the constituent volume fractions, the influences of applied voltage on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: mechanical buckling, functionally graded beam, first order shear deformation theory, free vibration

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Authors: Somveer Singh, Vineet Kumar Singh

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This work contributes a numerical method based on Legendre wavelet approximation for the treatment of partial integro-differential equation (PIDE). Operational matrices of Legendre wavelets reduce the solution of PIDE into the system of algebraic equations. Some useful results concerning the computational order of convergence and error estimates associated to the suggested scheme are presented. Illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method.

Keywords: legendre wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: Sergio Tovar-Pérez, Sebastian Töpfer, Markus Gräfe

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The work proposes a technique that decreases the detection acquisition time of quantum holography schemes down to one-third; this allows the possibility to image moving objects. Since its invention, quantum holography with undetected photon schemes has gained interest in the scientific community. This is mainly due to its ability to tailor the detected wavelengths according to the needs of the scheme implementation. Yet this wavelength flexibility grants the scheme a wide range of possible applications; an important matter was yet to be addressed. Since the scheme uses digital phase-shifting techniques to retrieve the information of the object out of the interference pattern, it is necessary to acquire a set of at least four images of the interference pattern along with well-defined phase steps to recover the full object information. Hence, the imaging method requires larger acquisition times to produce well-resolved images. As a consequence, the measurement of moving objects remains out of the reach of the imaging scheme. This work presents the use and implementation of a spatial light modulator along with a digital holographic technique called quasi-parallel phase-shifting. This technique uses the spatial light modulator to build a structured phase image consisting of a chessboard pattern containing the different phase steps for digitally calculating the object information. Depending on the reduction in the number of needed frames, the acquisition time reduces by a significant factor. This technique opens the door to the implementation of the scheme for moving objects. In particular, the application of this scheme in imaging alive specimens comes one step closer.

Keywords: quasi-parallel phase shifting, quantum imaging, quantum holography, quantum metrology

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Authors: M. Zaïgouche, A. Kouvahe, F. Stefanelli

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IMPERTIO is a high technology based project aiming at offering efficient assistance help in communication for persons affected by Cerebral Palsy. The systems currently available are hardly used by these patients who are not satisfied by ergonomics and response time. The project rests upon the concept that, opposite to usual master-slave communication giving power to the entity with larger range of possibilities, providing conversely the mastery to the entity with smaller range of possibilities will allow a better understanding ground for both parties. Entirely customizable, the application developed from this idea gives full freedom to the user. Through pictograms (one button linked to a word or a sentence) and adapted keyboard, noticeable improvements are brought to the response time and ease to use ergonomics.

Keywords: cerebral palsy, master-slave relation, communication interface, virtual keyboard, word construction algorithm

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Authors: Erdem Elibol, Musa Cadırcı, Nedim Tutkun

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Recently, colloidal quantum dots (CQDs) have drawn increasing attention due to their unique size tunability, which makes them potential candidates for numerous applications including photovoltaic, LEDs, and imaging. However, the main challenge to exploit CQDs properly is that there has not been an effective method to produce them with highly crystalline form and narrow size dispersion. Hot injection method is one of the widely used techniques to produce high-quality nanoparticles. In this method, the key parameter is to reduce the time for injection of the precursors into each other, which yields fast and constant nucleation rate and hence to highly monodisperse QDs. In conventional hot injection method, the injection of precursors is carried out using standard lab syringes with long needles. However, this technique is relatively slow and thus will result in poor optical properties in QDs. In this work, highly luminescent CdTe QDs were synthesised by transferring hot precursors into each other using cannula method. Unlike regular syringe technique, with the help of high pressure difference between two precursors’ flasks and wide cross-section of cannula, the hot cannulation process is too short which yields narrow size distribution and high quantum yield of CdTe QDs. Here QDs with full width half maximum (FWHM) of 28 nm was achieved. In addition, the photoluminescence quantum yield of our samples was measured to be about 21 ± 0.9 which is at least twice the previous record values for CdTe QDs wherein syringe was used to transfer precursors.

Keywords: CdTe, hot injection method, luminescent, quantum dots

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Authors: Chao-Qing Dai

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Two families of exact travelling solutions for the discrete sine-Gordon equation are constructed based on the variable-coefficient Jacobian elliptic function method and different transformations. When the modulus of Jacobian elliptic function solutions tends to 1, soliton solutions can be obtained. Some soliton solutions degenerate into the known solutions in literatures. Moreover, dynamical properties of exact solutions are investigated. Our analysis and results may have potential values for certain applications in modern nonlinear science and textile engineering.

Keywords: exact solutions, variable-coefficient Jacobian elliptic function method, discrete sine-Gordon equation, dynamical behaviors

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Authors: Masoud Ghermezi

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Studying the sheet metals is one of the most important research areas in the field of metal forming due to their extensive applications in the aerospace industries. A useful method for determining the forming limit of these materials and consequently preventing the rupture of sheet metals during the forming process is the use of the forming limit curve (FLC). In addition to specifying the forming limit, this curve also delineates a boundary for the allowed values of strain in sheet metal forming; these characteristics of the FLC along with its accuracy of computation and wide range of applications have made this curve the basis of research in the present paper. This study presents a new model that not only agrees with the results obtained from the above mentioned theory, but also eliminates its shortcomings. In this theory, like in the M-K theory, a thin sheet with an inhomogeneity as a gradient thickness reduction with a sinusoidal function has been chosen and subjected to two-dimensional stress. Through analytical evaluation, ultimately, a governing differential equation has been obtained. The numerical solution of this equation for the range of positive strains (stretched region) yields the results that agree with the results obtained from M-K theory. Also the solution of this equation for the range of negative strains (tension region) completes the FLC curve. The findings obtained by applying this equation on two alloys with the hardening exponents of 0.4 and 0.24 indicate the validity of the presented equation.

Keywords: sheet metal, metal forming, forming limit curve (FLC), M-K theory

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Authors: Alexander P. Smirnov, Sergey A. Matveev, Dmitry A. Zheltkov, Eugene E. Tyrtyshnikov

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We propose a new computational technique for multidimensional (multicomponent) Smoluchowski coagulation equation. Using low-rank approximations in Tensor Train format of both the solution and the coagulation kernel, we accelerate the classical finite-difference Runge-Kutta scheme keeping its level of accuracy. The complexity of the taken finite-difference scheme is reduced from O(N^2d) to O(d^2 N log N ), where N is the number of grid nodes and d is a dimensionality of the problem. The efficiency and the accuracy of the new method are demonstrated on concrete problem with known analytical solution.

Keywords: tensor train decomposition, multicomponent Smoluchowski equation, runge-kutta scheme, convolution

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Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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Authors: Farid Nouioua, Abdelouaheb Ardjouni

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In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

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Authors: Shubham Jaiswal

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In the present article, a drive is taken to compute the solution of spatial fractional order advection-dispersion equation having source/sink term with given initial and boundary conditions. The equation is converted to a system of ordinary differential equations using second-kind shifted Chebyshev polynomials, which have finally been solved using finite difference method. The striking feature of the article is the fast transportation of solute concentration as and when the system approaches fractional order from standard order for specified values of the parameters of the system.

Keywords: spatial fractional order advection-dispersion equation, second-kind shifted Chebyshev polynomial, collocation method, conservative system, non-conservative system

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Authors: Amit Bhunia, Mohit Kumar Singh, Maryam Al Huwayz, Mohamed Henini, Shouvik Datta

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We report [https://arxiv.org/abs/2107.13518] experimental detection and control of Schrodinger’s Cat like macroscopically large, quantum coherent state of a two-component Bose-Einstein condensate of spatially indirect electron-hole pairs or excitons using a resonant tunneling diode of III-V Semiconductors. This provides access to millions of excitons as qubits to allow efficient, fault-tolerant quantum computation. In this work, we measure phase-coherent periodic oscillations in photo-generated capacitance as a function of an applied voltage bias and light intensity over a macroscopically large area. Periodic presence and absence of splitting of excitonic peaks in the optical spectra measured by photocapacitance point towards tunneling induced variations in capacitive coupling between the quantum well and quantum dots. Observation of negative ‘quantum capacitance’ due to a screening of charge carriers by the quantum well indicates Coulomb correlations of interacting excitons in the plane of the sample. We also establish that coherent resonant tunneling in this well-dot heterostructure restricts the available momentum space of the charge carriers within this quantum well. Consequently, the electric polarization vector of the associated indirect excitons collective orients along the direction of applied bias and these excitons undergo Bose-Einstein condensation below ~100 K. Generation of interference beats in photocapacitance oscillation even with incoherent white light further confirm the presence of stable, long-range spatial correlation among these indirect excitons. We finally demonstrate collective Rabi oscillations of these macroscopically large, ‘multipartite’, two-level, coupled and uncoupled quantum states of excitonic condensate as qubits. Therefore, our study not only brings the physics and technology of Bose-Einstein condensation within the reaches of semiconductor chips but also opens up experimental investigations of the fundamentals of quantum physics using similar techniques. Operational temperatures of such two-component excitonic BEC can be raised further with a more densely packed, ordered array of QDs and/or using materials having larger excitonic binding energies. However, fabrications of single crystals of 0D-2D heterostructures using 2D materials (e.g. transition metal di-chalcogenides, oxides, perovskites etc.) having higher excitonic binding energies are still an open challenge for semiconductor optoelectronics. As of now, these 0D-2D heterostructures can already be scaled up for mass production of miniaturized, portable quantum optoelectronic devices using the existing III-V and/or Nitride based semiconductor fabrication technologies.

Keywords: exciton, Bose-Einstein condensation, quantum computation, heterostructures, semiconductor Physics, quantum fluids, Schrodinger's Cat

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Authors: Kajal K. Patel, M. N. Mehta, T. R. Singh

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When water is injected in oil formatted area in secondary oil recovery process the instability occurs near common interface due to viscosity difference of injected water and native oil. The governing equation gives rise to the non-linear partial differential equation and its solution has been obtained by Homotopy analysis method with appropriate guess value of the solution together with some conditions and standard relations. The solution gives the average cross-sectional area occupied by the schematic fingers during the occurs of instability phenomenon. The numerical and graphical presentation has developed by using Maple software.

Keywords: capillary pressure, homotopy analysis method, instability phenomenon, viscosity

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Authors: Clarinda Vitorino Nhangumbe, Ercília Sousa

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Weather derivatives are financial products used to cover non catastrophic weather events with a weather index as the underlying asset. The rainfall weather derivative pricing model is modeled based in the assumption that the rainfall dynamics follows Ornstein-Uhlenbeck process, and the partial differential equation approach is used to derive the convection-diffusion two dimensional time dependent partial differential equation, where the spatial variables are the rainfall index and rainfall depth. To compute the approximation solutions of the partial differential equation, the appropriate boundary conditions are suggested, and an explicit numerical method is proposed in order to deal efficiently with the different choices of the coefficients involved in the equation. Being an explicit numerical method, it will be conditionally stable, then the stability region of the numerical method and the order of convergence are discussed. The model is tested for real precipitation data.

Keywords: finite differences method, ornstein-uhlenbeck process, partial differential equations approach, rainfall derivatives

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Authors: K. Senthil Kumar, A. Vasumalaikannan

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In this paper, teleoperation of the quadrotor using Internet with Force feedback is addressed. Teleoperation with Force feedback is the ability to remotely control a robot, where contact (obstacle) or environment (wind gust etc) information (force feedback) is communicated from the quadrotor to the master joystick and thus giving the operator a sense of telepresence. The stability and performance of such a teleoperator is highly dependent on the amount of time delay present in the control loop. This problem is further complicated given the fact that for network based communication the time delay is itself time varying and highly non deterministic. In this paper, a novel method using Neural based Smith Predictor at the master side the stability is achieved. The performance of the system even during worst case scenario is within acceptable.

Keywords: teleoperation, quadrotor, neural smith predictor, time delay

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Authors: S. A. M. Yatim, Z. B. Ibrahim, K. I. Othman, M. Suleiman

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The method of solving second order stiff ordinary differential equation (ODEs) that is based on backward differentiation formula (BDF) is considered in this paper. We derived the method by increasing the order of the existing method using an improved strategy in choosing the step size. Numerical results are presented to compare the efficiency of the proposed method to the MATLAB’s suite of ODEs solvers namely ode15s and ode23s. The method was found to be efficient to solve second order ordinary differential equation.

Keywords: backward differentiation formulae, block backward differentiation formulae, stiff ordinary differential equation, variable step size

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Authors: Erhan Zor, Funda Copur, Asli I. Dogan, Haluk Bingol

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Current trends in the wide-scale sensing technologies rely on the development of miniaturized, rapid and easy-to-use sensing platforms. Quantum dots (QDs) with strong and easily tunable luminescence and high emission quantum yields have become a well-established photoluminescent nanomaterials for sensor applications. Although the majority of the reports focused on the cadmium-based QDs which have toxic effect on biological systems and eventually would cause serious environmental problems, carbon-based quantum dots (CQDs) that do not contain any toxic class elements have attracted substantial research interest in recent years. CQDs are small carbon nanostructures (less than 10 nm in size) with various unique properties and are widely-used in different fields during the last few years. In this respect, chiral nanostructures have become a promising class of materials in various areas such as pharmacology, catalysis, bioanalysis and (bio)sensor technology due to the vital importance of chirality in living systems. We herein report the synthesis of chiral CQDs with D- or L-tartaric acid as precursor materials. The optimum experimental conditions were examined and the purification procedure was performed using ethanol/water by column chromatography. The purified chiral CQDs were characterized by UV-Vis, FT-IR, XPS, PL and TEM techniques. The resultants display different photoluminescent characteristics due to the size and conformational difference. Considering the results, it can be concluded that chiral CQDs is expected to be used as optical chiral sensor in different platforms.

Keywords: carbon quantum dots, chirality, sensor, tartaric acid

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Authors: Tatsuya Otoshi, Masayuki Murata

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With the development and diversification of applications on the Internet, applications that require high responsiveness, such as video streaming, are becoming mainstream. Application responsiveness is not only a matter of communication delay but also a matter of time required to grasp changes in network conditions. The tradeoff between accuracy and measurement time is a challenge in network control. We people make countless decisions all the time, and our decisions seem to resolve tradeoffs between time and accuracy. When making decisions, people are known to make appropriate choices based on relatively small samples. Although there have been various studies on models of human decision-making, a model that integrates various cognitive biases, called ”quantum decision-making,” has recently attracted much attention. However, the modeling of small samples has not been examined much so far. In this paper, we extend the model of quantum decision-making to model decision-making with a small sample. In the proposed model, the state is updated by value-based probability amplitude amplification. By analytically obtaining a lower bound on the number of samples required for decision-making, we show that decision-making with a small number of samples is feasible.

Keywords: quantum decision making, small sample, MPEG-DASH, Grover's algorithm

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Authors: Akhmylovskaia Larisa, Barysh Andriana

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The present paper is introducing the translation score developing methodology and methods in the cross-cultural communication. The ideas and examples presented by the authors illustrate the universal character of translation score developing methods under analysis. Personal experience in the international theatre-making projects, opera laboratories, cross-cultural master-classes, movie and theatre festivals give more opportunities to single out the conditions, forms, means and principles of translation score developing as well as the translator/interpreter’s functions as cultural liaison for multiethnic collaboration.

Keywords: methodology of translation score developing, pre-production, analysis, production, post-production, ethnic scene theory, theatre anthropology, laboratory, master-class, educational project, academic project, Stanislavski terminology meta-language, super-objective, participant observation

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Authors: Raphael Zanella

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This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under the axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit march-in-time. The code is verified by space and time convergence tests using a manufactured solution. The solving of an example problem with an axisymmetric formulation is compared to that with a full-3D formulation. Both formulations lead to the same result, but the code based on the axisymmetric formulation is much faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest in using an axisymmetric formulation when it is possible.

Keywords: axisymmetric problem, continuous finite elements, heat equation, weak formulation

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Authors: Razieh Khalafi

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The brain is the information processing centre of the human body. Stimuli in the form of information are transferred to the brain and then brain makes the decision on how to respond to them. In this research, we propose a new partial differential equation which analyses the EEG signals and make a relationship between the incoming stimuli and the brain response to them. In order to test the proposed model, a set of external stimuli applied to the model and the model’s outputs were checked versus the real EEG data. The results show that this model can model the EEG signal well. The proposed model is useful not only for modelling of EEG signal in case external stimuli but it can be used for modelling of brain response in case of internal stimuli.

Keywords: brain, stimuli, partial differential equation, response, EEG signal

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Authors: H. Vargova, J. Strecka, N. Tomasovicova

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A rigorous analytical treatment, with the help of a concept of negativity, is used to study the quantum and thermal entanglement in an isotropic mixed spin-(1/2,S) Heisenberg dimer. The effect of the spin-S magnitude, as well as the effect of diversity between Landé g-factors of magnetic constituents on system entanglement, is exhaustively analyzed upon the variation of the external magnetic and electric field, respectively. It was identified that the increasing magnitude of the spin-S species in a mixed spin-(1/2,S) Heisenberg dimer with comparative Landé g-factors have always a reduction effect on a degree of the quantum entanglement, but it strikingly shifts the thermal entanglement to the higher temperatures. Surprisingly, out of the limit of identical Landé g-factors, the increasing magnitude of spin-S entities can enhance the system entanglement in both low and high magnetic fields. Besides this, we identify that the analyzed dimer with a high-enough magnitude of the spin-S entities at a sufficiently high magnetic field can exhibit unconventional thermally driven re-entrance between the entangled and unentangled mixed state. The importance of the electric-field stimuli is also discussed in detail.

Keywords: quantum and thermal entantanglement, mixed spin Heisenberg model, negativity, reentrant phase transition

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Authors: U. V. S. Seshavatharam, S. Lakshminarayana

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In a unified approach observed cosmic red shift can be re-interpreted as an index of cosmological galactic atomic light emission phenomenon. By increasing the applications of Hubble volume in cosmology as well as in quantum physics, concepts of ‘Black Hole Cosmology’ can be well-confirmed. Clearly speaking ‘quantum mechanics’ can be shown to be a branch of ‘black hole cosmology’. In Big Bang Model, confirmation of all the observations directly depend on the large scale galactic distances that are beyond human reach and raise ambiguity in all respects. The subject of modern black hole physics is absolutely theoretical. Advantage of Black hole cosmology lies in confirming its validity through the ground based atomic and nuclear experimental results.

Keywords: Hubble volume, black hole cosmology, CMBR energy density, Planck’s constant, fine structure ratio, cosmic time, nuclear charge radius, unification

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Authors: Narges Solaymani

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Definition of Nurse: Nurse: A person who is educated and skilled in the field of scientific principles and professional skills of health care, treatment, and medical training of patients. Nursing is a very important profession in the societies of the world. Although in the past, all caregivers of the sick and disabled were called nurses, nowadays, a nurse is a person who has a university education in this field. There are nurses in bachelor's, master's, and doctoral degrees in nursing. New courses have been launched in the master's degree based on duty-oriented nurses. A nurse cannot have an independent treatment center but is a member of the treatment team in established treatment centers such as hospitals, clinics, or offices. Nurses can establish counseling centers and provide nursing services at home. According to the standards, the number of nurses should be three times the number of doctors or twice the number of hospital beds, or there should be three nurses for every thousand people. Also, international standards show that in the internal and surgical department, every 4 to 6 patients should have a nurse.

Keywords: nurse, intensive care, CPR, bandage

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Authors: Ya-Fen Lee, Yun-Yao Chi

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The study aims to explore the relationship between risk perceptions of rockfall and revisit intention using a Structural Equation Modelling (SEM) analysis. A total of 573 valid questionnaires are collected from travelers to Taroko National Park, Taiwan. The findings show the majority of travellers have the medium perception of rockfall risk, and are willing to revisit the Taroko National Park. The revisit intention to Taroko National Park is influenced by hazardous preferences, willingness-to-pay, obstruction and attraction. The risk perception has an indirect effect on revisit intention through influencing willingness-to-pay. The study results can be a reference for mitigation the rockfall disaster.

Keywords: risk perception, rockfall, revisit intention, structural equation modelling

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Authors: Carla E. O. de Moraes, Gladson O. Antunes, Mauro A. Rincon

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The aim of this paper is to study the internal stabilization of the Bernoulli-Euler equation numerically. For this, we consider a square plate subjected to a feedback/damping force distributed only in a subdomain. An algorithm for obtaining an approximate solution to this problem was proposed and implemented. The numerical method used was the Finite Difference Method. Numerical simulations were performed and showed the behavior of the solution, confirming the theoretical results that have already been proved in the literature. In addition, we studied the validation of the numerical scheme proposed, followed by an analysis of the numerical error; and we conducted a study on the decay of the energy associated.

Keywords: Bernoulli-Euler plate equation, numerical simulations, stability, energy decay, finite difference method

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Authors: Shigeyuki Haruyama, Ken Kaminishi, Junji Kaneko, Tadayuki Kyoutani, Siti Ruhana Omar, Oke Oktavianty

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This study is used as a definition method to the value and function in manufacturing sector. In concurrence of discussion about present condition of modeling method, until now definition of 1D-CAE is ambiguity and not conceptual. Across all the physics fields, those methods are defined with the formulation of differential algebraic equation which only applied time derivation and simulation. At the same time, we propose semi-acausal modeling concept and differential algebraic equation method as a newly modeling method which the efficiency has been verified through the comparison of numerical analysis result between the semi-acausal modeling calculation and FEM theory calculation.

Keywords: system model, physical models, empirical models, conservation law, differential algebraic equation, object-oriented

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Authors: M. K. Yusuf, W. O. Hamman, U. E. Umana, S. B. Oladele

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Background: Dilatation of the inferior vena cava (IVC) is used as the ultrasonic diagnostic feature in patients suspected of congestive heart failure. The IVC diameter has been reported to vary among the various body mass indexes (BMI) and body shape indexes (ABSI). Knowledge of these variations is useful in precision diagnoses of CHF by imaging scientists. Aim: The study aimed to establish an equation for predicting the ultrasonic mean diameter of the IVC among the various BMI/ABSI of inhabitants of Azare, Bauchi State-Nigeria. Methodology: Two hundred physically healthy adult subjects of both sexes were classified into under, normal, over, and obese weights using their BMIs after selection using a structured questionnaire following their informed consent for an abdominal ultrasound scan. The probe was placed on the midline of the body, halfway between the xiphoid process and the umbilicus, with the marker on the probe directed towards the patient's head to obtain a longitudinal view of the IVC. The maximum IVC diameter was measured from the subcostal view using the electronic caliper of the scan machine. The mean value of each group was obtained, and the results were analysed. Results: A novel equation {(IVC Diameter = 1.04 +0.01(X) where X= BMI} has been generated for determining the IVC diameter among the populace. Conclusion: An equation for predicting the IVC diameter from individual BMI values in apparently healthy subjects has been established.

Keywords: equation, ultrasonic, IVC diameter, body adiposities

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Authors: Jonny, T. Yuri M. Zagloel

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This paper is made to present an Indonesian Healthcare model. Currently, there are nine TQM (Total Quality Management) practices in healthcare industry. However, these practices are not integrated yet. Therefore, this paper aims to integrate these practices as a model by using Structural Equation Modeling (SEM). After administering about 210 questionnaires to various stakeholders of this industry, a LISREL program was used to evaluate the model's fitness. The result confirmed that the model is fit because the p-value was about 0.45 or above required 0.05. This has signified that previously mentioned of nine TQM practices are able to be integrated as an Indonesian healthcare model.

Keywords: healthcare, total quality management (TQM), structural equation modeling (SEM), linear structural relations (LISREL)

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Authors: Damir Latypov

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A hybrid classical-quantum algorithm to solve boundary integral equations (BIE) arising in problems of electromagnetic and acoustic scattering is proposed. The quantum speed-up is due to a Quantum Linear System Algorithm (QLSA). The original QLSA of Harrow et al. provides an exponential speed-up over the best-known classical algorithms but only in the case of sparse systems. Due to the non-local nature of integral operators, matrices arising from discretization of BIEs, are, however, dense. A QLSA for dense matrices was introduced in 2017. Its runtime as function of the system's size N is bounded by O(√Npolylog(N)). The run time of the best-known classical algorithm for an arbitrary dense matrix scales as O(N².³⁷³). Instead of exponential as in case of sparse matrices, here we have only a polynomial speed-up. Nevertheless, sufficiently high power of this polynomial, ~4.7, should make QLSA an appealing alternative. Unfortunately for the QLSA, the asymptotic separability of the Green's function leads to high compressibility of the BIEs matrices. Classical fast algorithms such as Multilevel Fast Multipole Method (MLFMM) take advantage of this fact and reduce the runtime to O(Nlog(N)), i.e., the QLSA is only quadratically faster than the MLFMM. To be truly impactful for computational electromagnetics and acoustics engineers, QLSA must provide more substantial advantage than that. We propose a computational scheme which combines elements of the classical fast algorithms with the QLSA to achieve the required performance.

Keywords: quantum linear system algorithm, boundary integral equations, dense matrices, electromagnetic scattering theory

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