Optical networks implementing single-qudit quantum gates may exhibit superior properties to those for qubits as each optical element in the network can work in parallel on many optical modes simultaneously. We present a class of such networks that implements in a deterministic and efficient way the quantum Fourier transform (QFT) in an arbitrarily high dimension. These networks redistribute the initial quantum state into the orbital angular momentum (OAM) and path degrees of freedom and offer two modes of operation. Either the OAM-only QFT can be implemented, which uses the path as an internal auxiliary degree of freedom, or the path-only QFT is implemented, which uses the OAM as the auxiliary degree of freedom. The resources for both schemes scale linearly $O(d)$ with the dimension $d$ of the system, beating the best known bounds for the path-encoded QFT. While the QFT of the orbital-angular-momentum states of single photons has been applied in a multitude of experiments, these schemes require specially designed elements with nontrivial phase profiles. In contrast, we propose a different approach that utilizes only conventional optical elements.

中文翻译：

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单光子的轨道角动量的傅立叶变换

由于网络中的每个光学元件可以同时在多种光学模式下并行工作，因此实现单量子量子门的光网络可能会表现出优于量子比特的性能。我们提出了一类这样的网络，它以确定性和有效的方式在任意高维中实现量子傅立叶变换（QFT）。这些网络将初始量子态重新分配到轨道角动量（OAM）和路径自由度中，并提供两种操作模式。既可以实施仅OAM的QFT，将路径用作内部辅助自由度，也可以实施仅路径的QFT，其将OAM作为辅助自由度。两种方案的资源均呈线性增长$Ø（d）$ 与尺寸 $d$系统的性能，超越了路径编码QFT的最著名界限。虽然单光子的轨道角动量态的QFT已在众多实验中得到应用，但这些方案需要具有非平凡相位分布的特殊设计元素。相反，我们提出了一种仅使用常规光学元件的不同方法。