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arXiv:1909.02296 · Physical Review A

Robust quantum control in games: An adversarial learning approach

Xiaozhen Ge, Haijin Ding, HERSCHEL A. RABITZ, Re-Bing Wu

Published May 11, 2020• 51 citations
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Abstract

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.

DOI
10.1103/physreva.101.052317

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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 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.