Quantum advantage using high-dimensional twisted photons as quantum finite automata

Stephen Z. D. Plachta1,2, Markus Hiekkamäki1, Abuzer Yakaryılmaz3,4, and Robert Fickler1

1Tampere University, Photonics Laboratory, Physics Unit, Tampere, FI-33720, Finland
2Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences, Vienna, Austria
3Center for Quantum Computer Science, Faculty of Computing, University of Latvia, Riga, Latvia
4QWorld Association, Tallinn, Estonia, https://qworld.net

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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.

Twisted photons, i.e., single quanta of light with a helically twisted wavefront and orbital angular momentum, have found various applications in quantum information science in addition to being interesting for fundamental studies in optics. Amongst the many benefits such states of light have, a particularly useful one is the encoding of quantum information which is not restricted to a single qubit per carrier, i.e., high-dimensional quantum states. The increased Hilbert space of such states can be used, e.g., to lift the requirement of having multiple qubit systems interacting with each other, a task notoriously hard for photons. Here, we use this feature of twisted photons and realize some quantum finite automata (QFAs) consisting of up to 4 parallel, separate qubits and demonstrate the quantum advantage of such basic computational devices in terms of resource efficiency. As such, our experiment shows the power of high-dimensional quantum states and twisted photons, while also demonstrating the superiority of QFAs over their classical counterparts.

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