Quantum control theory and applications: A survey <s> Closed-loop learning control <s> We simulate a method to teach a laser pulse sequences to excite specified molecular states. We use a learning procedure to direct the production of pulses based on fitness'' information provided by a laboratory measurement device. Over a series of pulses the algorithm learns an optimal sequence. The experimental apparatus, which consists of a laser, a sample of molecules and a measurement device, acts as an analog computer that solves Schroedinger's equation n/Iexactly, in real time. We simulate an apparatus that learns to excite specified rotational states in a diatomic molecule. <s> BIB001 </s> Quantum control theory and applications: A survey <s> Closed-loop learning control <s> A new iteration method is presented for achieving quantum optimal control over the expectation value of a positive definite operator. Theoretical analysis shows that this new algorithm exhibits quadratic and monotonic convergence. Numerical calculations verify that for this new algorithm, within a few steps, the optimized objective functional comes close to its converged limit. <s> BIB002 </s> Quantum control theory and applications: A survey <s> Closed-loop learning control <s> This review puts into perspective the present state and prospects for controlling quantum phenomena in atoms and molecules. The topics considered include the nature of physical and chemical control objectives, the development of possible quantum control rules of thumb, the theoretical design of controls and their laboratory realization, quantum learning and feedback control in the laboratory, bulk media influences, and the ability to utilize coherent quantum manipulation as a means for extracting microscopic information. The preview of the field presented here suggests that important advances in the control of molecules and the capability of learning about molecular interactions may be reached through the application of emerging theoretical concepts and laboratory technologies. <s> BIB003
Closed-loop learning control has achieved great successes in the control of laboratory chemical reactions BIB003 , BIB001 . The closed-loop learning control procedure generally involves three elements BIB003 : (i) a trial laser control input design, (ii) the laboratory generation of the control that is applied to the sample and subsequently observed for its impact, and (iii) a learning algorithm that considers the prior experiments and suggests the form of the next control input. The initial trial control input may be a well-designed laser pulse or a random control input. A feature of a good closed-loop learning control strategy is its insensitivity to the initial trials. An important task is to establish a good learning algorithm for ensuring that the closed-loop learning process converges to achieve a given control objective. Genetic algorithms and several rapid convergence algorithms have been employed for this task BIB001 , BIB002 . The control objective is usually formulated as an optimal control problem by converting the problem into a problem of optimizing a functional of the quantum states, control inputs, control time, etc. In the learning process, an optimal control problem is solved iteratively. First, one applies a trial input to a sample to be controlled and observes the result. Second, a learning algorithm suggests a better control input based on the prior experiments. Third, one applies a "better" control input to a new sample. This process continues in order to achieve the control objective. It is often easy to produce many identical-state samples in laboratory chemical reactions. If the control objective is well defined, there is a capability to apply specified control inputs to the samples. Then, if a sufficiently intelligent learning algorithm is applied to adjust the control inputs, this process will converge to optimize the required objective and an optimal control will be found BIB003 .