基于模型预测控制策略的鲁棒量子控制
Robust Quantum Control via a Model Predictive Control Strategy
AI总结：
本文提出基于时间最优模型预测控制（TOMPC）的鲁棒策略，通过迭代优化控制场并实施投影测量，在不确定性下实现两能级量子系统的高保真状态控制。
摘要：
本文提出了一种针对受有界不确定性影响的两能级量子系统的鲁棒控制策略，该策略采用时间最优模型预测控制（TOMPC）。在该方法中，控制场在有限时域内以标称量子系统为参考进行优化，然后施加第一时间间隔的最优控制，并对不确定系统实施投影测量。基于测量结果，下一时间间隔的新控制场将被迭代优化。我们给出了保证TOMPC算法稳定性的理论结果。我们还刻画了TOMPC策略在控制两能级系统时的鲁棒性和收敛速率。数值模拟进一步表明，在存在不确定性的情况下，我们的量子TOMPC算法增强了鲁棒性，并以高保真度将状态引导至期望状态。这项工作促进了模型预测控制在量子控制中的进展，并探索了其在量子技术实际应用中的潜力。
英文摘要：
This article presents a robust control strategy using Time-Optimal Model Predictive Control (TOMPC) for a two-level quantum system subject to bounded uncertainties. In this method, the control field is optimized over a finite horizon using a nominal quantum system as the reference and then the optimal control for the first time interval is applied and a projective measurement is implemented on the uncertain system. The new control field for the next time interval will be iteratively optimized based on the measurement result. We present theoretical results to guarantee the stability of the TOMPC algorithm. We also characterize the robustness and the convergence rate of the TOMPC strategy for the control of two-level systems. Numerical simulations further demonstrate that, in the presence of uncertainties, our quantum TOMPC algorithm enhances robustness and steers the state to the desired state with high fidelity. This work contributes to the progress of Model Predictive Control in quantum control and explores its potential in practical applications of quantum technology.
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