In this work, time-depended Schrodinger equation described particles at matter (crystal, catalysis, metal) surface could be considered as propose of numerical control of quantum system. Accessing existing physical experimental results on the motion of particles (molecules, atoms) at surface, based on variational method of quantum control theory in Hilbert space, using density function theory (DFT), time-depended Schrodinger equation to proceed the investigation of computational approach. To do quantum calculation at surface, physically, first needs a concept as control goal: such as breaking a chemical bond as target; reducing energy of high intensity shaped laser pulse. Particles at surface is a kind of constrain control for spatial variable. Optimal control is to find and characterize the quantum optima for minimizing or maximizing the cost functional. Control methods contain selecting chemical reagent, designing chemical reaction, making control scope for a quantized system: time varying Schrodinger equation. Precisely, for general quadratic cost function, in two or three dimensional cases, a semi discrete (time continuous, spatial discrete) algorithm consisting of finite element method and conjugate gradient method, would be utilized for solving a numerical solution of state system, and obtaining quantum optimal control from a initial guess of control input. It is quite curious: what is the difference of control particles occurred at surface than control free particles? whether one can develop a suit of theory or methodology for quantum surface control? It is certainly expected to connect theoretical control, to numerical or computational control, and to experimental control as carrying out quantum system control of particles on the surface. It is desired that quantum control theory (QCT) for quantum dot at surface would be evidenced in visualization method, and attained confidential verification in the guidance of real-time computer-aided experiments in the viewpoint of chemistry and physics.
In this work, time-depended Schrodinger equation described particles at matter (crystal, catalysis, metal) surface could be considered as propose of numerical control of quantum system. Accessing existing physical experimental results on the motion of particles (molecules, atoms) at surface, based on variational method of quantum control theory in Hilbert space, using density function theory (DFT), time-depended Schrodinger equation to proceed the investigation of computational approach. To do quantum calculation at surface, physically, first needs a concept as control goal: such as breaking a chemical bond as target; reducing energy of high intensity shaped laser pulse. Particles at surface is a kind of constrain control for spatial variable. Optimal control is to find and characterize the quantum optima for minimizing or maximizing the cost functional. Control methods contain selecting chemical reagent, designing chemical reaction, making control scope for a quantized system: time varying Schrodinger equation. Precisely, for general quadratic cost function, in two or three dimensional cases, a semi discrete (time continuous, spatial discrete) algorithm consisting of finite element method and conjugate gradient method, would be utilized for solving a numerical solution of state system, and obtaining quantum optimal control from a initial guess of control input. It is quite curious: what is the difference of control particles occurred at surface than control free particles? whether one can develop a suit of theory or methodology for quantum surface control? It is certainly expected to connect theoretical control, to numerical or computational control, and to experimental control as carrying out quantum system control of particles on the surface. It is desired that quantum control theory (QCT) for quantum dot at surface would be evidenced in visualization method, and attained confidential verification in the guidance of real-time computer-aided experiments in the viewpoint of chemistry and physics.
In this work, time-depended Schrodinger equation described particles at matter (crystal, catalysis, metal) surface could be considered as propose of numerical control of quantum system. Accessing existing physical experimental results on the motion of particles (molecules, atoms) at surface, based on variational method of quantum control theory in Hilbert space, using density function theory (DFT), time-depended Schrodinger equation to proceed the investigation of computational approach. To do quantum calculation at surface, physically, first needs a concept as control goal: such as breaking a chemical bond as target; reducing energy of high intensity shaped laser pulse. Particles at surface is a kind of constrain control for spatial variable. Optimal control is to find and characterize the quantum optima for minimizing or maximizing the cost functional. Control methods contain selecting chemical reagent, designing chemical reaction, making control scope for a quantized system: time varying Schrodinger equation. Precisely, for general quadratic cost function, in two or three dimensional cases, a semi discrete (time continuous, spatial discrete) algorithm consisting of finite element method and conjugate gradient method, would be utilized for solving a numerical solution of state system, and obtaining quantum optimal control from a initial guess of control input. It is quite curious: what is the difference of control particles occurred at surface than control free particles? whether one can develop a suit of theory or methodology for quantum surface control? It is certainly expected to connect theoretical control, to numerical or computational control, and to experimental control as carrying out quantum system control of particles on the surface. It is desired that quantum control theory (QCT) for quantum dot at surface would be evidenced in visualization method, and attained confidential verification in the guidance of real-time computer-aided experiments in the viewpoint of chemistry and physics.
In this theoretic work, trapped particles at matter surface to be considered as target system of quantum control. At the framework of variational method in Hilbert space, it would be quite interesting for us to explore particles which is trapped via optical lattice or other kinds of constraints at a matter surface (metal, crystal). The aim of this task is to survey theoretical control for quantum particles as they are appeared and trapped at matter surface (cf. [1]). The physical background of this work is laying on the specified particles motion or reaction under a certain chemical surface. As is well known, one can move a particle at surface smoothly through a point force above it or according to a proper angle, such quantum mechanical motion had already been achieved by the IBM team several years ago. At the viewpoint of quantum control, what is theoretic support? Can we make these control theoretically, computationally or experimentally? In fact, free trapped particles had been considered by scientists and researchers at worldwide scale. The most exciting things in this study is to take particle as target as it constrained on a surface. Theoretically, this work is to describe quantum control system consisting of time-varying Schrodinger equation at physical constraints condition. Then to apply control theory to quantum system of trapped particles, find and characterize optimal quantum control. Further, to compose optimality system (Euler-Lagrange system). Comprising of control free trapped particle, this work is focusing on control taking place at matter surface (on it particle is trapped), that is, try to discuss the external force constrain (e.g. optical lattice) and surface constrain are acting at particle together. Amazing result is desired in control of different multi-forces as control inputs, what would be happened as a particle changing its position, displacement or status under trapped situation? can we make a trapped chemical quantum well, or a physical optical lattice which worked using external force? what is extension of such kind of works at a variety of fields? whether the general quantum control is worked in this case? It is the purpose to solve these mysteries in this work, and report the initial conclusion of theoretic aspect for trapped particle at matter surface.
In this theoretic work, trapped particles at matter surface to be considered as target system of quantum control. At the framework of variational method in Hilbert space, it would be quite interesting for us to explore particles which is trapped via optical lattice or other kinds of constraints at a matter surface (metal, crystal). The aim of this task is to survey theoretical control for quantum particles as they are appeared and trapped at matter surface (cf. [1]). The physical background of this work is laying on the specified particles motion or reaction under a certain chemical surface. As is well known, one can move a particle at surface smoothly through a point force above it or according to a proper angle, such quantum mechanical motion had already been achieved by the IBM team several years ago. At the viewpoint of quantum control, what is theoretic support? Can we make these control theoretically, computationally or experimentally? In fact, free trapped particles had been considered by scientists and researchers at worldwide scale. The most exciting things in this study is to take particle as target as it constrained on a surface. Theoretically, this work is to describe quantum control system consisting of time-varying Schrodinger equation at physical constraints condition. Then to apply control theory to quantum system of trapped particles, find and characterize optimal quantum control. Further, to compose optimality system (Euler-Lagrange system). Comprising of control free trapped particle, this work is focusing on control taking place at matter surface (on it particle is trapped), that is, try to discuss the external force constrain (e.g. optical lattice) and surface constrain are acting at particle together. Amazing result is desired in control of different multi-forces as control inputs, what would be happened as a particle changing its position, displacement or status under trapped situation? can we make a trapped chemical quantum well, or a physical optical lattice which worked using external force? what is extension of such kind of works at a variety of fields? whether the general quantum control is worked in this case? It is the purpose to solve these mysteries in this work, and report the initial conclusion of theoretic aspect for trapped particle at matter surface.
In this work, quantum control of trapped Bose-Einstein-Condensates (BEC) is considered at matter surface. For particles at BEC status, quantum system is described by Gross-Pitaevskii equation, experimental control of BEC is happened at physics field, and achieved at laboratory. At theoretic aspect, control of trapped condensates is not sufficiently investigated at academic level. What we interest is applying control theory to BEC trapped on the surface (metallic, crystal). At optical lattice, particles are trapping by constrained forces at cooling technique, and temporally take the same quantum states, such kind of condensates phenomena had already been surveyed at a variety of areas. The most works are reported on free BEC particles, quite natural question is arising on the surface science: BEC particles created,detected, and placed on a certain chemical surface, control of trapped particles is difference or not? We are curious about optical and mechanical constraints take action together on particles. In the viewpoint of quantum control realm, our purpose is to apply optimal control theory (OCT) to trapped Bose-Einstein-Condensates as they are occurred at surface. In the framework of variational theory at complex Hilbert spaces, prove the existence of quantum optimal control, and characterize optimal control using optimality (Euler-Lagrange) system. Control variables for trapped BEC contain three functions: one is electro-magnetic force; another is external constraint from optical equipment (optical frequency, lattice number); third is quantum mechanics against gravitational force, which making BEC particles stay at surface stationary. Review the literatures, electro-magnetic-optical controls are extremely considered at last couple of years. Gravitational control is rarely considered. Further extension of the work is to do real-time computer-aided BEC control at matter surface. Computational approach for simulation of BEC control at two and three dimensions would be a promise direction.
In this work, quantum control of trapped Bose-Einstein-Condensates (BEC) is considered at matter surface. For particles at BEC status, quantum system is described by Gross-Pitaevskii equation, experimental control of BEC is happened at physics field, and achieved at laboratory. At theoretic aspect, control of trapped condensates is not sufficiently investigated at academic level. What we interest is applying control theory to BEC trapped on the surface (metallic, crystal). At optical lattice, particles are trapping by constrained forces at cooling technique, and temporally take the same quantum states, such kind of condensates phenomena had already been surveyed at a variety of areas. The most works are reported on free BEC particles, quite natural question is arising on the surface science: BEC particles created,detected, and placed on a certain chemical surface, control of trapped particles is difference or not? We are curious about optical and mechanical constraints take action together on particles. In the viewpoint of quantum control realm, our purpose is to apply optimal control theory (OCT) to trapped Bose-Einstein-Condensates as they are occurred at surface. In the framework of variational theory at complex Hilbert spaces, prove the existence of quantum optimal control, and characterize optimal control using optimality (Euler-Lagrange) system. Control variables for trapped BEC contain three functions: one is electro-magnetic force; another is external constraint from optical equipment (optical frequency, lattice number); third is quantum mechanics against gravitational force, which making BEC particles stay at surface stationary. Review the literatures, electro-magnetic-optical controls are extremely considered at last couple of years. Gravitational control is rarely considered. Further extension of the work is to do real-time computer-aided BEC control at matter surface. Computational approach for simulation of BEC control at two and three dimensions would be a promise direction.
The control of matter and energy at a fundamental level will be a cornerstone of new technologies for years to come. This idea is exemplified in a distilled form by controlling the dynamics of quantum mechanical systems via a time-dependent potential. The contributions detailed within this work focus on the computational aspects of formulating and solving quantum control problems efficiently.
The accurate numerical computation of optimal controls of infinite dimensional quantum control problems is a very difficult task that requires to take into account the features of the original infinite dimensional problem. An important issue is the choice of the functional space where the minimization process is defined. A systematic comparison of L2 versus H1 based minimization shows that the choice of the appropriate functional space matters and has many consequences in the implementation of some optimization techniques.
A matrix-free cascadic BFGS algorithm is introduced in the L 2 and H1 settings and it is demonstrated that the choice of H1 over L2 results in a substantial performance and robustness increase. A comparison between optimal control resulting from function space minimization and the control obtained by minimization over Chebyshev and POD basis function coefficients is presented.
A theoretical and computational framework is presented to obtain accurate controls for fast quantum state transitions that are needed in a host of applications such as nano electronic devices and quantum computing. This method is based on a reduced Hessian Krylov-Newton scheme applied to a norm-preserving discrete model of a dipole quantum control problem. The use of second-order numerical methods for solving the control problem is justified proving existence of optimal solutions and analyzing first- and second-order optimality conditions. Criteria for the discretization of the non-convex optimization problem and for the formulation of the Hessian are given to ensure accurate gradients and a symmetric Hessian. Robustness of the Newton approach is obtained using a globalization strategy with a robust linesearch procedure. Results of numerical experiments demonstrate that the Newton approach presented in this dissertation is able to provide fast and accurate controls for high-energy state transitions.
Control of bound-to-bound and bound-to-continuum transitions in open quantum systems and vector field control of two-dimensional systems is presented. An efficient space-time spectral discretization of the time-dependent Schrodinger equation and preconditioning strategy for a fast approximate solution with Krylov methods is outlined.