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International Joint Conference on Neural Networks (IJCNN)

Learning control of population transfer between subspaces of quantum systems using an adaptive target scheme

Wei Zhang, Daoyi Dong, Ian R. Petersen

Published Jul 1, 2016• 4 citations
Publisher

Abstract

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.

DOI
10.1109/ijcnn.2016.7727709

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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.
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In quantum dynamics of many-body systems, to identify the Hamiltonian becomes more difficult very rapidly as the number of degrees of freedom increases. In order to simplify the dynamics and to deduce dynamically relevant Hamiltonian information, it is desirable to control the dynamics to lie within a reduced space. With a judicious choice for the cost functional, the closed loop optimal control experiments can be manipulated efficiently to steer the dynamics to lie within a subspace of the system eigenstates without requiring any prior detailed knowledge about the system Hamiltonian. The procedure is simulated for optimally controlled population transfer experiments in the system of two degrees of freedom. To show the feasibility of steering the dynamics to lie in a specified subspace, the learning algorithms guiding the dynamics are presented along with frequency filtering. The results demonstrate that the optimal control fields derive the system to the desired target state through the desired subspace.
This paper investigates the ability of closed loop quantum learning control techniques to meet a posed physical objective while simultaneously steering the dynamics to lie in a specified subspace. Achievement of successful control with reduced space dynamics can have a number of benefits including a more easily understood control mechanism. Judicious choices for the cost functional may be introduced such that the closed loop optimal control experiments can steer the dynamics to lie within a subspace of the system eigenstates without requiring any prior detailed knowledge about the system Hamiltonian. Learning control with reduced space dynamics takes advantage of the expected existence of a multiplicity of fields that can all give acceptable quality control outcomes. The procedure eliminates the hard demands of following a specific dynamical path by only asking that the dynamics reside in a subspace. Additional measurements characterizing the subspace are necessary to monitor the system evolution during the control field learning process. This procedure is simulated for optimally controlled population transfer experiments in systems of one and two degrees of freedom. The results demonstrate that optimal control fields can be found that successfully derive the system to the target state while staying within the desired subspace.
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.
By using a quadratic Lyapunov function with un-known parameters and a particle swarm optimization (PSO) algorithm, this paper proposes a new Lyapunov control scheme for quantum systems. This approach can achieve high-probability population transfer to a given target state. For the case when the target state is an eigenstate of the internal Hamiltonian, we introduce a virtual control law into the system model and design corresponding control law. The stability of the system under the action of the Lyapunov control law is analyzed via the LaSalle invariance principle. For the case when the target state is a superposition state, we design a control law by performing a unitary transformation for the quantum system model under consideration. To achieve desired state transfer, we further introduce a PSO algorithm to search for the unknown parameters contained in the control law. Numerical results on a five-level quantum system and a three-qubit system are presented to demonstrate the effectiveness of the proposed approaches.
A gradient-based optimization approach combined with automatic differentiation is employed to ensure high accuracy and scalability when working with high-dimensional parameter spaces. Numerical simulations confirm the effectiveness of the proposed method: the population is reliably transferred to the target state with minimal occupation of intermediate levels, while the control pulses remain smooth and physically implementable. The developed framework serves as a universal and experimentally applicable tool for automated control pulse design in quantum systems. It is particularly useful in scenarios where analytical methods or manual parameter tuning--such as standard schemes like STIRAP--prove to be inefficient or inapplicable.