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Communications in Computational Physics

A Neural Network Approach to Sampling Based Learning Control for Quantum System with Uncertainty

Jingshi Li, Song Chen Song Chen, Yanzhao Cao, Zhao Sun

Published Oct 25, 2021• 2 citations
Publisher

Abstract

Robust control design for quantum systems with uncertainty is a key task for developing practical quantum technology. In this paper, we apply neural networks to learn the control of a quantum system with uncertainty. By exploiting the auto differentiation function developed for neural network models, our method avoids the manual computation of the gradient of the cost function as required in traditional methods. We implement our method using two algorithms. One uses neural networks to learn both the states and the controls and one uses neural networks to learn only the controls but solve the states by finite difference methods. Both algorithms incorporate the sampling-based learning process into the training of the networks. The performance of the algorithms is evaluated on a practical numerical example, followed by a detailed discussion about the advantage and trade-offs between our method and the other numerical schemes.

DOI
10.4208/cicp.oa-2020-0182

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Robust control design for quantum systems with uncertainty is a key task for developing practical quantum technology. In this paper, we apply neural networks to learn the control of a quantum system with uncertainty. By exploiting the auto differentiation function developed for neural network models, our method avoids the manual computation of the gradient of the cost function as required in traditional methods. We implement our method using two algorithms. One uses neural networks to learn both the states and the controls and one uses neural networks to learn only the controls but solve the states by finite difference methods. Both algorithms incorporate the sampling-based learning process into the training of the networks. The performance of the algorithms is evaluated on a practical numerical example, followed by a detailed discussion about the advantage and trade-offs between our method and the other numerical schemes.
Robust control design for quantum systems has been recognized as a key task in the development of practical quantum technology. In this paper, we present a systematic numerical methodology of sampling-based learning control (SLC) for control design of quantum systems with uncertainties. The SLC method includes two steps of training and testing. In the training step, an augmented system is constructed using artificial samples generated by sampling uncertainty parameters according to a given distribution. A gradient flow-based learning algorithm is developed to find the control for the augmented system. In the process of testing, a number of additional samples are tested to evaluate the control performance, where these samples are obtained through sampling the uncertainty parameters according to a possible distribution. The SLC method is applied to three significant examples of quantum robust control, including state preparation in a three-level quantum system, robust entanglement generation in a two-qubit superconducting circuit, and quantum entanglement control in a two-atom system interacting with a quantized field in a cavity. Numerical results demonstrate the effectiveness of the SLC approach even when uncertainties are quite large, and show its potential for robust control design of quantum systems.
High-fidelity quantum control is one of the key elements in quantum computing and information processing. In view of possible inaccuracies in quantum system modeling and inevitable errors in control fields, the design of robust control fields is of great importance. In this article, we propose a neural network-based robust control strategy that incorporates physics-informed neural networks (PINNs) and sampling-based learning control techniques for uncertain closed and open quantum systems. We employ the gradient descent algorithm with momentum for the network training, where two methods including direct calculation and automatic differentiation are used to compute the gradient of the loss function with respect to network weights. The direct calculation method demonstrates the internal mechanism of the gradient computation, while the automatic differentiation technology is easier to utilize. We provide some guidelines for the parameter selection of the sampling learning algorithm in the PINN robust control scheme to ensure good control performance. In particular, for open quantum systems with uncertainties, we point out the necessity of fast control. Some simulation experiments are conducted on closed and open systems with uncertainties and the results show the effectiveness of the proposed PINN control scheme in achieving high-fidelity state transfer of uncertain quantum systems.
Robust control design for quantum systems has been recognized as a key task in the development of practical quantum technology. In this paper, we present a systematic numerical methodology of sampling-based learning control (SLC) for control design of quantum systems with Hamiltonian uncertainties. The SLC method includes two steps of “training” and “testing and evaluation”. In the training step, an augmented system is constructed by sampling uncertainties according to possible distributions of uncertainty parameters. A gradient flow based learning and optimization algorithm is adopted to find the control for the augmented system. In the process of testing and evaluation, a number of samples obtained through sampling the uncertainties are tested to evaluate the control performance. Numerical results demonstrate the success of the SLC approach. The SLC method has potential applications for robust control design of quantum systems.
Robust quantum control with uncertainty plays a crucial role in practical quantum technologies. This paper presents a method for solving a quantum control problem by combining neural network and symplectic finite difference methods. The neural network approach provides a framework that is easy to establish and train. At the same time, the symplectic methods possess the norm-preserving property for the quantum system to produce a realistic solution in physics. We construct a general high dimensional quantum optimal control problem to evaluate the proposed method and an approach that combines a neural network with forward Euler’s method. Our analysis and numerical experiments confirm that the neural network-based symplectic method achieves significantly better accuracy and robustness against noises.
Robust control design for operation of quantum systems has been considered as a demanding and challenging task in the development of quantum technologies. In this paper, we apply the sampling-based learning control (SLC) approach to design a control law for manipulating two-level quantum systems with uncertainties. The gradient-based learning and optimization algorithm is adopted to find the optimal piece-wise control fields for an augmented system by sampling the domain of uncertainties. Numerical results demonstrate the effectiveness of the proposed method for unitary operation of two-level quantum systems even when there are large uncertainties.
Robust control design for quantum unitary transformations has been recognized as a fundamental and challenging task in the development of quantum information processing due to unavoidable decoherence or operational errors in the experimental implementation of quantum operations. In this paper, we extend the systematic methodology of sampling-based learning control (SLC) approach with a gradient flow algorithm for the design of robust quantum unitary transformations. The SLC approach first uses a "training" process to find an optimal control strategy robust against certain ranges of uncertainties. Then a number of randomly selected samples are tested and the performance is evaluated according to their average fidelity. The approach is applied to three typical examples of robust quantum transformation problems including robust quantum transformations in a three-level quantum system, in a superconducting quantum circuit, and in a spin chain system. Numerical results demonstrate the effectiveness of the SLC approach and show its potential applications in various implementation of quantum unitary transformations.