论文标题
强大的量子控制：通过平均分析和合成
Robust Quantum Control: Analysis & Synthesis via Averaging
论文作者
论文摘要
基于经典的平均方法，提出了一种方法，用于鲁棒性分析和量子（统一）控制合成。结果是多次优化，以众所周知的鲁棒性衡量标称（不确定性）保真度竞争：相互作用（误差）哈密顿量的大小（误差），实质上是相互作用统一的马格努斯扩张的第一项。将其与高保真度的控制景观的拓扑结合在一起，由名义上的忠实Hessian的空空间确定，我们到达了一种新的两阶段算法。一旦标称忠诚度足够高，我们将标称保真度和鲁棒性度量近似为控制增量中的四倍体。通过解决每次迭代处的控制增量的凸优化，以保持名义忠诚度高并降低鲁棒性度量，从而获得了最佳解决方案。此外，通过将保真度与鲁棒性度量分开，可以使用更多的灵活性用于不确定性建模。
An approach is presented for robustness analysis and quantum (unitary) control synthesis based on the classic method of averaging. The result is a multicriterion optimization competing the nominal (uncertainty-free) fidelity with a well known robustness measure: the size of an interaction (error) Hamiltonian, essentially the first term in the Magnus expansion of an interaction unitary. Combining this with the fact that the topology of the control landscape at high fidelity is determined by the null space of the nominal fidelity Hessian, we arrive at a new two-stage algorithm. Once the nominal fidelity is sufficiently high, we approximate both the nominal fidelity and robustness measure as quadratics in the control increments. An optimal solution is obtained by solving a convex optimization for the control increments at each iteration to keep the nominal fidelity high and reduce the robustness measure. Additionally, by separating fidelity from the robustness measure, more flexibility is available for uncertainty modeling.
