线性光学问题的黎曼优化
Riemannian optimization for linear optical problems
- Universidad de Valladolid（瓦拉多利德大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文推导了干涉仪酉矩阵上可微函数的黎曼梯度解析公式，用于黎曼优化算法寻找最优配置，显著提升态制备成功概率并大幅加速计算。
AI中文摘要：
线性光学在量子科学中的许多应用涉及搜索多端口干涉仪的最优配置。例如，为了找到 heralded 态制备方案，可以优化干涉仪以最大化态制备的保真度和成功概率。在本文中，我们推导了定义在干涉仪酉矩阵上的任意可微函数的黎曼梯度的闭合解析公式。我们将该梯度用于黎曼优化算法（如梯度下降或 BFGS）中，以找到干涉仪的最优设置。作为一个有趣的应用案例，我们搜索线性光学态制备方案，改进了文献中报道的 NOON 态或光子催化制备的部分成功概率。最后，我们展示了我们的优化器比文献中的其他方法快数个数量级，为解决涉及更多模式和光子的线性光学问题打开了大门。
英文摘要：
Many applications of linear optics in quantum science involve searching for some optimal configuration of a multiport interferometer. For example, to find heralded state preparations, one can optimize the interferometer to maximize the fidelity and success probability of the state preparation. In this paper, we derive a closed analytical formula for the Riemannian gradient of any differentiable function defined over the interferometer unitaries. We use this gradient in Riemannian optimization algorithms, such as gradient descent or BFGS, to find the optimal setup of the interferometer. As an interesting use case, we search for linear optical state preparations, improving some of the success probabilities reported in the literature for NOON or photon catalysis preparations. Finally, we show that our optimizer is orders of magnitude faster than other methods in the literature, opening the door for solving linear optical problems involving more modes and photons.
