动态量子控制的鲁棒性：微分灵敏度界
Robustness of Dynamic Quantum Control: Differential Sensitivity Bound
AI总结：
该研究提出基于微分灵敏度的量子控制鲁棒性度量，建立参数不确定性下的性能保证，发现高保真控制中保真度与鲁棒性正相关而非此消彼长。
摘要：
通过优化的分段常数脉冲实现的动态控制是开环控制用于实现量子门的常用范式。尽管已有大量方法可用于合成此类控制，但关于所得控制方案在存在模型不确定性时的鲁棒性仍有许多悬而未决的问题；与经典控制不同，对于系统的不精确建模，通常不存在关于控制性能的解析保证。本文提出了一种基于门保真度误差对参数化（结构化）不确定性的微分灵敏度的新型鲁棒性度量，并利用参数化不确定性的微分灵敏度界，为多种量子门类型、系统规模和控制实现的最优控制器建立了性能保证。具体而言，本文展示了如何可靠地计算出能保证给定保真度误差的、针对一组哈密顿量不确定性的最大允许扰动。这种鲁棒性度量与标称工作条件下评估的保真度误差微分灵敏度的上界成反比。最后，结果表明，在广泛的问题和控制实现中，标称保真度误差与微分灵敏度上界呈正相关，这表明在高保真控制机制下，保真度与鲁棒性之间并非存在权衡关系，而是更高的标称门保真度与参数化不确定性下控制鲁棒性的提升呈正相关。
英文摘要：
Dynamic control via optimized, piecewise-constant pulses is a common paradigm for open-loop control to implement quantum gates. While numerous methods exist for the synthesis of such controls, there are many open questions regarding the robustness of the resulting control schemes in the presence of model uncertainty; unlike in classical control, there are generally no analytical guarantees on the control performance with respect to inexact modeling of the system. In this paper a new robustness measure based on the differential sensitivity of the gate fidelity error to parametric (structured) uncertainties is introduced, and bounds on the differential sensitivity to parametric uncertainties are used to establish performance guarantees for optimal controllers for a variety of quantum gate types, system sizes, and control implementations. Specifically, it is shown how a maximum allowable perturbation over a set of Hamiltonian uncertainties that guarantees a given fidelity error, can be reliably computed. This measure of robustness is inversely proportional to the upper bound on the differential sensitivity of the fidelity error evaluated under nominal operating conditions. Finally, the results show that the nominal fidelity error and differential sensitivity upper bound are positively correlated across a wide range of problems and control implementations, suggesting that in the high-fidelity control regime, rather than there being a trade-off between fidelity and robustness, higher nominal gate fidelities are positively correlated with increased robustness of the controls in the presence of parametric uncertainties.
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