Quantum finite automata (QFA) are basic computational devices that make binary decisions using quantum operations. They are known to be exponentially memory efficient compared to their classical counterparts. Here, we demonstrate an experimental implementation of multi-qubit QFAs using the orbital angular momentum (OAM) of single photons. We implement different high-dimensional QFAs encoded on a single photon, where multiple qubits operate in parallel without the need for complicated multi-partite operations. Using two to eight OAM quantum states to implement up to four parallel qubits, we show that a high-dimensional QFA is able to detect the prime numbers 5 and 11 while outperforming classical finite automata in terms of the required memory. Our work benefits from the ease of encoding, manipulating, and deciphering multi-qubit states encoded in the OAM degree of freedom of single photons, demonstrating the advantages structured photons provide for complex quantum information tasks.

中文翻译：

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使用高维扭曲光子作为量子有限自动机的量子优势

量子有限自动机 (QFA) 是使用量子运算做出二元决策的基本计算设备。与经典的同类产品相比，它们的内存效率呈指数级增长。在这里，我们使用单光子的轨道角动量 (OAM) 演示了多量子比特 QFA 的实验实现。我们实现了在单个光子上编码的不同高维 QFA，其中多个量子位并行运行，无需复杂的多部分运算。使用 2 到 8 个 OAM 量子态来实现多达 4 个并行量子位，我们表明高维 QFA 能够检测素数 5 和 11，同时在所需内存方面优于经典有限自动机。我们的工作得益于易于编码、操作、