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Communications and control engineering/Communications and control engineering series

Sampling-Based Learning Control of Quantum Systems with Uncertainties

Daoyi Dong, Ian R. Petersen

Published Jan 1, 2023• 7 citations
Publisher

Abstract

This chapter presents results on enhancing robustness of quantum systems with uncertainties using the sampling-based learning control (SLC) method. In Sect. 4.2, the SLCSampling-based learning control method is applied to state control of superconducting qubitsQubit, robust control of photoassociationPhotoassociation of O+H and synchronizing a laser with molecules for charge transfer $$^\text {a}$$ , $$^\text {b}$$ , $$^\text {c}$$ . Robust control based on SLC and b-GRAPE is presented for generating quantum gatesQuantum gate in Sect. 4.3 and SLC of open quantum systems is investigated in Sect. 4.4 $$^\text {d}$$ .

DOI
10.1007/978-3-031-20245-2_4

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This chapter presents results on enhancing robustness of quantum systems with uncertainties using the sampling-based learning control (SLC) method. In Sect. 4.2, the SLCSampling-based learning control method is applied to state control of superconducting qubitsQubit, robust control of photoassociationPhotoassociation of O+H and synchronizing a laser with molecules for charge transfer a^\text {a}a , b^\text {b}b , c^\text {c}c . Robust control based on SLC and b-GRAPE is presented for generating quantum gatesQuantum gate in Sect. 4.3 and SLC of open quantum systems is investigated in Sect. 4.4 d^\text {d}d .
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.
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 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.
In this paper, a sampling-based learning control (SLC) algorithm is used to find a robust control law that can steer a quantum system with uncertainties into a maximally entangled state. The quantum system under consideration consists of two two-level atoms interacting with a quantized electromagnetic field. In the sampling-based learning control method, an artificial system is constructed based on the quantum system with uncertainties and an optimal control law is learned for the artificial system. Some additional samples which are generated by sampling the uncertainty parameters are used to test the performance of the optimal control law. Numerical results demonstrate the effectiveness of the SLC method in finding a robust control law for entanglement generation between two atoms in a cavity in the presence of a quantized field.
Superconducting quantum systems are promising candidates for quantum information processing due to their scalability and design flexibility. However, the existence of defects, fluctuations, and inaccuracies is unavoidable for practical superconducting quantum circuits. In this paper, a sampling-based learning control (SLC) method is used to guide the design of control fields for manipulating superconducting quantum systems. Numerical results for one-qubit systems and coupled two-qubit systems show that the "smart" fields learned using the SLC method can achieve robust manipulation of superconducting qubits, even in the presence of large fluctuations and inaccuracies.