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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.<\/jats:p>","DOI":"10.22331\/q-2022-06-30-752","type":"journal-article","created":{"date-parts":[[2022,6,30]],"date-time":"2022-06-30T12:04:43Z","timestamp":1656590683000},"page":"752","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":11,"title":["Quantum advantage using high-dimensional twisted photons as quantum finite automata"],"prefix":"10.22331","volume":"6","author":[{"given":"Stephen Z. 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