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arXiv:2005.13080 · IEEE Transactions on Control Systems Technology

Learning Control of Quantum Systems Using Frequency-Domain Optimization Algorithms

Daoyi Dong, Chuan‐Cun Shu, Jiangchao Chen, Xi Xing, Hailan Ma, Yu Guo, HERSCHEL A. RABITZ

Published Sep 2, 2020• 23 citations
arXivHTMLPDF

Abstract

We investigate two classes of quantum control problems by using frequency-domain optimization algorithms in the context of ultrafast laser control of quantum systems. In the first class of problems, the system model is known and a frequency-domain gradient-based optimization algorithm is applied for searching an optimal control field to selectively and robustly manipulate the population transfer in atomic rubidium. The other class of quantum control problems involves an experimental system with an unknown model. In this case, we introduce a differential evolution algorithm with a mixed strategy to search for optimal control fields and demonstrate the capability in an ultrafast laser control experiment for the fragmentation of Pr(hfac)3molecules.

DOI
10.1109/tcst.2020.3018500

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IEEE Transactions on Control Systems Technology•Jun 23, 2017•7 citations
We investigate two classes of quantum control problems by using frequency-domain optimization algorithms in the context of ultrafast laser control of quantum systems. In the first class of problems, the system model is known and a frequency-domain gradient-based optimization algorithm is applied for searching an optimal control field to selectively and robustly manipulate the population transfer in atomic rubidium. The other class of quantum control problems involves an experimental system with an unknown model. In this case, we introduce a differential evolution algorithm with a mixed strategy to search for optimal control fields and demonstrate the capability in an ultrafast laser control experiment for the fragmentation of Pr(hfac)3molecules.
Robust control design for quantum systems has been recognized as a key task in quantum information technology, molecular chemistry, and atomic physics. In this paper, an improved differential evolution algorithm, referred to as multiple-samples and mixed-strategy DE (msMS_DE), is proposed to search robust fields for various quantum control problems. In msMS_DE, multiple samples are used for fitness evaluation and a mixed strategy is employed for the mutation operation. In particular, the msMS_DE algorithm is applied to the control problems of: 1) open inhomogeneous quantum ensembles and 2) the consensus goal of a quantum network with uncertainties. Numerical results are presented to demonstrate the excellent performance of the improved machine learning algorithm for these two classes of quantum robust control problems. Furthermore, msMS_DE is experimentally implemented on femtosecond (fs) laser control applications to optimize two-photon absorption and control fragmentation of the molecule CH2BrI. The experimental results demonstrate the excellent performance of msMS_DE in searching for effective fs laser pulses for various tasks.
Achieving fast and efficient quantum state transfer is a fundamental task in physics, chemistry and quantum information science. However, the successful implementation of the perfect quantum state transfer also requires robustness under practically inevitable perturbative defects. Here, we demonstrate how an optimal and robust quantum state transfer can be achieved by shaping the spectral phase of an ultrafast laser pulse in the framework of frequency domain quantum optimal control theory. Our numerical simulations of the single dibenzoterrylene molecule as well as in atomic rubidium show that optimal and robust quantum state transfer via spectral phase modulated laser pulses can be achieved by incorporating a filtering function of the frequency into the optimization algorithm, which in turn has potential applications for ultrafast robust control of photochemical reactions.
Abstract This paper proposes a numerical approach to the problem of inverse quantum control with a focus on the automated formation of external laser control fields that ensure high-precision and controlled population transfer in multilevel quantum systems. The method is based on optimizing the parameters of control pulses using gradient algorithms in combination with automatic differentiation, which allows for effective control of the physical characteristics of laser fields and increases the stability of the transfer process. The obtained results provide a foundation for the development of more general quantum control methods focused on experimental implementation on real physical platforms.
Robust control design for quantum systems has been recognized as a key task in quantum information technology, molecular chemistry and atomic physics. In this paper, an improved differential evolution algorithm of msMS_DE is proposed to search robust fields for various quantum control problems. In msMS_DE, multiple samples are used for fitness evaluation and a mixed strategy is employed for mutation operation. In particular, the msMS_DE algorithm is applied to the control problem of open inhomogeneous quantum ensembles and the consensus problem of a quantum network with uncertainties. Numerical results are presented to demonstrate the excellent performance of the improved DE algorithm for these two classes of quantum robust control problems. Furthermore, msMS_DE is experimentally implemented on femtosecond laser control systems to generate good signals of two photon absorption and control fragmentation of halomethane molecules CH2BrI. Experimental results demonstrate excellent performance of msMS_DE in searching effective femtosecond laser pulses for various tasks.
We investigate the problem of control of quantum systems. Various notions of controllability of quantum systems are discussed and Lie algebraic techniques are employed to derive necessary and sufficient conditions for the resulting degrees of controllability. The results are employed to study the degree of controllability for various model systems. The problem of optimal control is formulated as a problem of maximisation of the expectation value of an observable of the system subject to dynamical constraints and costs. A class of iterative algorithms is discussed, and shown to converge to a solution of the Euler-Lagrange equations, which is a necessary condition for optimality of a solution. A numerical realisation of the algorithm is presented and potential implementation of the resulting control fields in the laboratory is discussed. The algorithm is applied to find optimal control fields for a variety of applications including selective and simultaneous excitation of individual quantum dots in a globally addressed ensemble, creation of superposition states, and selective excitation of certain vibrational modes of a simple molecule such as Hydrogen Fluoride. In each case we systematically explore the parameter space of the algorithm to select solutions with desirable physical features from the multitude of possible choices. As there are many possible optimal control fields which give similar yields the question of whether some are more robust than others is investigated. A number of optimal fields are analysed quantitatively in terms of robustness with regard to temporal and spectral noise affecting the fields, uncertainty in the model parameters and the effect of experimental limitations such as restrictions on the bandwidth of the fields. It is shown that whilst the solutions tend to be sensitive to uncertainty in the energy levels chosen for the model, they appear to be surprisingly tolerant to even severe bandwidth limitations.
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.