Spectral difference Lanczos method for efficient time propagation in quantum control theory

2004 ◽  
Vol 120 (13) ◽  
pp. 5962-5967 ◽  
Author(s):  
John D. Farnum ◽  
David A. Mazziotti
Keyword(s):  
Control Theory ◽  
Quantum Control ◽  
Lanczos Method ◽  
Spectral Difference ◽  
Quantum Control Theory ◽  
Time Propagation

scholarly journals Quantum Control of Nano-Particles at Catalysis Surface

2021 ◽  
Author(s):  
Quan-Fang Wang
Keyword(s):  
Quantum Mechanics ◽  
Control Theory ◽  
Surface Science ◽  
Quantum Control ◽  
Control Object ◽  
Research Topic ◽  
Nano Particles ◽  
Theoretical Issue ◽  
Quantum Control Theory ◽  
Scale Particle

Quantum control is always interested in all the phenomena in the word. At the nano-scale, particle at catalysis surface is a research topic in connected of quantum mechanics and surface science. Nano-particles appeared at a certain crystals would be considered as control object in this regarding. Theoretical issue is taking account into control using quantum control theory. An exciting conclusion is attractive in this work ultimately

scholarly journals Quantum Numerical Control for Particles at Matter Surface

2021 ◽  
Author(s):  
Quan-Fang Wang
Keyword(s):  
Optimal Control ◽  
Schrödinger Equation ◽  
Control Theory ◽  
Quantum System ◽  
Schrodinger Equation ◽  
Quantum Control ◽  
Numerical Control ◽  
System Control ◽  
Control Input ◽  
Quantum Control Theory

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.

scholarly journals Quantum Numerical Control for Particles at Matter Surface

2021 ◽  
Author(s):  
Quan-Fang Wang
Keyword(s):  
Optimal Control ◽  
Schrödinger Equation ◽  
Control Theory ◽  
Quantum System ◽  
Schrodinger Equation ◽  
Quantum Control ◽  
Numerical Control ◽  
System Control ◽  
Control Input ◽  
Quantum Control Theory

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.

QUANTUM CONTROL THEORY FOR DECOHERENCE SUPPRESSION IN QUANTUM GATES

2007 ◽  
Vol 05 (01n02) ◽  
pp. 207-213 ◽  
Author(s):  
T. CALARCO ◽  
M. A. CIRONE ◽  
M. COZZINI ◽  
A. NEGRETTI ◽  
A. RECATI ◽  
...  
Keyword(s):  
Control Theory ◽  
Quantum Control ◽  
Optical Lattices ◽  
Impulsive Control ◽  
Iterative Algorithms ◽  
Optimization Methods ◽  
Quantum Gates ◽  
High Fidelity ◽  
Atom Chips ◽  
Quantum Control Theory

We show how quantum optimal control theory can help achieve high-fidelity quantum gates in real experimental settings. We discuss several optimization methods (from iterative algorithms to optimization by interference and to impulsive control) and different physical scenarios (from optical lattices to atom chips and to Rydberg atoms).

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