线性响应形式的量子最优控制理论
Quantum Optimal Control Theory in the Linear Response Formalism
摘要：
量子最优控制理论（QOCT）的目的是寻找一个驱动量子系统的外部场，以最优的方式实现一些预定义的目标。在实践中，这通常意味着优化一些可观察的值，即所谓的优值函数。因此，该理论的关键部分是一组方程，其提供了优值函数相对于控制驱动场形状的参数的梯度。我们表明，这些方程可以直接导出使用标准的线性响应理论，只需要一个小的概括-未扰动的哈密顿被允许是时间相关的。结果，上述梯度用某些响应函数来识别。这种识别导致一个自然的重新表述QOCT的Keldysh轮廓形式主义的量子多体理论。特别是，可以使用非平衡格林函数的图解技术计算的价值函数的梯度，这应该是有帮助的QOCT的应用程序中的计算困难的多电子问题。
英文摘要：
Quantum optimal control theory (QOCT) aims at finding an external field that drives a quantum system in such a way that optimally achieves some predefined target. In practice this normally means optimizing the value of some observable, a so called merit function. In consequence, a key part of the theory is a set of equations, which provides the gradient of the merit function with respect to parameters that control the shape of the driving field. We show that these equations can be straightforwardly derived using the standard linear response theory, only requiring a minor generalization -- the unperturbed Hamiltonian is allowed to be time-dependent. As a result, the aforementioned gradients are identified with certain response functions. This identification leads to a natural reformulation of QOCT in term of the Keldysh contour formalism of the quantum many-body theory. In particular, the gradients of the merit function can be calculated using the diagrammatic technique for non-equilibrium Green's functions, which should be helpful in the application of QOCT to computationally difficult many-electron problems.
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