Comparison of time optimal control for two level quantum systems

Abstract

The time optimal problem for a two level quantum system is studied. We compare two different control strategies of bang-bang control and the geometric control, respectively, especially in the case of minimizing the time of steering the state from North Pole to South Pole on the Bloch sphere with bounded control. The time performances are compared for different parameters by the individual numerical simulation experiments, and the experimental results are analyzed. The results show that the geometric control spends less time than the bang-bang control does.

Switching optimal adaptive trajectory tracking control of quantum systems

“…() In particular, the optimal control can manipulate the quantum systems to achieve the control objective while additional features of the transition process, such as power expenditure, the energy function, the transfer time, and the fidelity are optimized. () Accordingly, many studies have published on developing new optimal control techniques for quantum control systems, ie, optimal population transfer in the limit of large transfer time,() time optimal control of quantum systems,() a study on critical points of the optimal quantum control, Pareto optimal quantum control for simultaneous control of an arbitrary number of quantum observable expectation values, optimal control for quantum systems despite the feedback delay, robust optimal control of quantum systems in the presence of the disturbances and the uncertainties, numerical cascade nonlinear conjugate gradient scheme, and nonlinear conjugate gradient scheme . Moreover, several numerical methods have been presented to solve the optimization problem in optimal quantum control including a symmetric split operator method, a semidiscrete paradigm composed of finite element method and conjugate gradient method, the pseudospectral method, a gradient descent algorithm equipped with adaptive step size selection, and greedy algorithms .…”