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arXiv:2410.14286

Smolyak algorithm assisted robust control for quantum systems with uncertainties

Zigui Zhang, Zibo Miao, Xiu–Hao Deng

Published Oct 18, 2024• 0 citations
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Abstract

Efficient and systematic numerical methods for robust control design are crucial in quantum systems due to inevitable uncertainties or disturbances. We propose a novel approach that models uncertainties as random variables and quantifies robustness using the expectation of infidelity by reformulating it as a weighted tensor product quadrature. We employ the Smolyak algorithm to develop a parametric robust quantum control scheme, which balances the reduction of computational cost with the enhancement of estimation accuracy. We demonstrate the effectiveness of our proposed algorithm by incorporating the Smolyak sparse grids into conventional gradient-based quantum optimal control methods such as GRAPE and GOAT. In robust control problems concerning quantum gate realization, low infidelity and strong robustness can be achieved. These results contribute to improving the reliability and security of quantum computing and communication systems in the presence of real-world imperfections.

DOI
10.48550/arxiv.2410.14286

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Efficient and systematic numerical methods for robust control design are crucial in quantum systems due to inevitable uncertainties or disturbances. We propose a novel approach that models uncertainties as random variables and quantifies robustness using the expectation of infidelity by reformulating it as a weighted tensor product quadrature. We employ the Smolyak algorithm to develop a parametric robust quantum control scheme, which balances the reduction of computational cost with the enhancement of estimation accuracy. We demonstrate the effectiveness of our proposed algorithm by incorporating the Smolyak sparse grids into conventional gradient-based quantum optimal control methods such as GRAPE and GOAT. In robust control problems concerning quantum gate realization, low infidelity and strong robustness can be achieved. These results contribute to improving the reliability and security of quantum computing and communication systems in the presence of real-world imperfections.
Efficient and systematic numerical methods for robust control design are crucial in quantum systems due to inevitable uncertainties or disturbances. We propose an approach that models uncertainties as random variables and quantifies robustness using the expectation of infidelity by reformulating it as a weighted tensor product quadrature. We employ the Smolyak algorithm to develop a parametric robust quantum control scheme, which balances the reduction of computational cost with the enhancement of estimation accuracy. We demonstrate the effectiveness of our proposed algorithm by incorporating the Smolyak sparse grids into conventional gradient-based quantum optimal control methods such as grape and goat. In robust control problems concerning quantum gate realization, low infidelity and strong robustness can be achieved. These results contribute to improving the reliability and security of quantum computing and communication systems in the presence of real-world imperfections.
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Abstract Efficient and systematic numerical methods for robust control design are crucial in quantum systems due to inevitable uncertainties or disturbances. We propose a novel approach that models uncertainties as random variables and quantifies robustness using the expectation of infidelity. By reformulating the robustness measure as a weighted tensor product quadrature, we employ the Smolyak sparse grid algorithm to develop a parametric robust quantum control scheme. This scheme significantly reduces computational cost while improving accuracy. We demonstrate the effectiveness of our Smolyak algorithm assisted gradient-based methods including \textbf{smGOAT} and \textbf{smGRAPE} in robust control problems regarding state transfer and quantum gate realization, with ultrahigh fidelity and strong robustness achieved. Our results contribute to improving the reliability and security of quantum computing and communication systems in the presence of real-world imperfections.
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Highly accurate and robust control of quantum operations is vital for the realization of error-correctible quantum computation. In this paper, we show that the robustness of high-precision controls can be remarkably enhanced through sampling-based stochastic optimization of a risk-sensitive (RS) loss function. Following the stochastic gradient-descent direction of this loss function, the optimization is guided to penalize poor-performance uncertainty samples in a tunable manner. We propose two algorithms, which are termed as the RS GRAPE and the adaptive RS GRAPE. Their effectiveness is demonstrated by numerical simulations, which is shown to be able to achieve high-control robustness while maintaining high fidelity.
High-precision operation of quantum computing systems must be robust to uncertainties and noises in the quantum hardware. We show that through a game played between the uncertainties (or noises) and the controls, adversarial uncertainty samples can be generated to find highly robust controls through the search for Nash equilibria. We propose a broad family of adversarial learning algorithms, namely a-GRAPE algorithms, which includes two effective learning schemes referred to as the best-response approach and the better-response approach within game-theoretic terminology, providing options for learning highly robust controls. Numerical experiments demonstrate that the balance between fidelity and robustness depends on the details of the chosen adversarial learning algorithm, which can effectively lead to a significant enhancement of control robustness while attaining high fidelity.