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IEEE Transactions on Control Systems Technology

Adaptive Target Scheme for Learning Control of Quantum Systems

Wei Zhang, Daoyi Dong, Ian R. Petersen

Published Jun 23, 2017• 7 citations
Publisher

Abstract

Developing efficient algorithms is an important task in the learning control of quantum systems, since most learning control problems for quantum systems involve a heavy requirement for computational resources. In this paper, we employ a learning control algorithm with an adaptive target state developed in the chemical physics community for several classes of quantum control problems. For these problems applied to some new quantum control tasks, we further demonstrate that the algorithm using an adaptive target state can be more efficient than traditional learning control algorithms using a fixed target state. In the algorithm, the target state is updated according to the renormalized fragmentary yield in the desired region (or subspace) throughout the learning iterations. The adaptive target scheme is applied to three significant quantum control tasks, including the slow collision of a sodium cation and an iodine anion, the orientation of a LiH molecule, and population transfer between subspaces. Shaped laser pulses are obtained using the learning control algorithm, and numerical results are presented to demonstrate the advantages of the adaptive target scheme over the algorithm using a fixed target state. The adaptive target scheme is especially useful for learning control problems of quantum systems where the target state is not unique or known.

DOI
10.1109/tcst.2017.2715007

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Developing efficient algorithms is an important task in the learning control of quantum systems, since most learning control problems for quantum systems involve a heavy requirement for computational resources. In this paper, we employ a learning control algorithm with an adaptive target state developed in the chemical physics community for several classes of quantum control problems. For these problems applied to some new quantum control tasks, we further demonstrate that the algorithm using an adaptive target state can be more efficient than traditional learning control algorithms using a fixed target state. In the algorithm, the target state is updated according to the renormalized fragmentary yield in the desired region (or subspace) throughout the learning iterations. The adaptive target scheme is applied to three significant quantum control tasks, including the slow collision of a sodium cation and an iodine anion, the orientation of a LiH molecule, and population transfer between subspaces. Shaped laser pulses are obtained using the learning control algorithm, and numerical results are presented to demonstrate the advantages of the adaptive target scheme over the algorithm using a fixed target state. The adaptive target scheme is especially useful for learning control problems of quantum systems where the target state is not unique or known.
An adaptive target scheme is implemented for learning control of population transfer between subspaces of quantum systems. In this control scheme, the target state is updated according to the renormalized yield in the desired subspace throughout the learning iterations, to obtain the desired laser control field. In the numerical experiments, we perform learning control simulations based on a V-type three-subspace quantum system. The field obtained by learning control can transfer the population to the target subspace with high probability. In comparison with a fixed target state, this adaptive target scheme proves to be more efficient for the quantum control problem under consideration.
This paper presents a novel feedback learning algorithm for adaptive quantum control. The algorithm leverages reinforcement learning principles combined with quantum control theory to dynamically adjust control strategies based on the observed state and environment of a quantum system. The core mechanism involves constructing an adaptive quantum control feedback learning algorithm that enables autonomous optimization of the quantum system. The algorithm utilizes a state representation of the quantum system, a reward function reflecting the desired outcome, and a control policy updated through a reinforcement learning process. Mathematical formulations are provided to describe the system dynamics, the control policy, and the learning process. The proposed algorithm aims to overcome the limitations of traditional fixed-parameter quantum control methods by adapting to uncertainties and complex dynamics, ultimately leading to improved control performance and robustness. The theoretical framework presented here offers a foundation for developing advanced quantum control strategies in various applications, including quantum computation, quantum sensing, and quantum metrology.
We have constructed an automated learning apparatus to control quantum systems. By directing intense shaped ultrafast laser pulses into a variety of samples and using a measurement of the system as a feedback signal, we are able to reshape the laser pulses to direct the quantum system into a desired physical state. The feedback signal is the input to an adaptive learning algorithm. This algorithm programs a computer-controlled, acousto-optic modulator (AOM) pulse shaper. The learning algorithm generates new shaped laser pulses based on the success of previous pulses in achieving a predetermined goal.
This paper presents a novel approach to designing adaptive quantum control policies using reinforcement learning (RL). Traditional methods for quantum control often rely on hand-designed pulse shapes or iterative optimization techniques, which can be computationally expensive and may not generalize well to different systems or desired operations. We propose a framework where an RL agent learns to dynamically adjust quantum control parameters in real-time, based on the system's state and the objective of achieving a specific quantum gate with high fidelity. The core of our approach lies in formulating the quantum control problem as a Markov Decision Process (MDP) and utilizing an RL algorithm to train a policy that maps system states to control parameters. We demonstrate the feasibility and effectiveness of this method through a theoretical analysis and a simplified numerical simulation. The resulting adaptive control policies offer a significant advantage over traditional methods, particularly for complex quantum systems and demanding fidelity requirements. The key contributions are the integration of RL for adaptive control and the formalization of the problem as an MDP.
We have constructed an automated learning apparatus to control quantum systems. By directing intense shaped ultrafast laser pulses into a variety of samples and using a measurement of the system as a feedback signal, we are able to reshape the laser pulses to direct the system into a desired state. The feedback signal is the input to an adaptive learning algorithm. This algorithm programs a computer-controlled, acousto-optic modulator pulse shaper. The learning algorithm generates new shaped laser pulses based on the success of previous pulses in achieving a predetermined goal.
An adaptive tracking algorithm is developed to achieve quantum system control field designs. The adaptive algorithm has the advantage of operating noniteratively to efficiently find desirable controls, and has the feature of high stability by suppressing the influence of disturbances from tracking singularities. The core of the adaptive tracking control algorithm is a self-learning track switch technique which is triggered by monitoring of the evolving system trajectory. The adaptive tracking algorithm is successfully tested for population transfer.