https://doi.org/10.1140/epjp/s13360-024-05751-6
Regular Article
Discrete-time quantum walks in qudit systems
1
Atos, 411045, Pune, Maharashtra, India
2
A. K. Choudhury School of Information Technology, University of Calcutta, 700106, Kolkata, West Bengal, India
Received:
19
February
2024
Accepted:
17
October
2024
Published online:
5
November
2024
Quantum walks contribute significantly to developing quantum algorithms and quantum simulations. Here, we introduce a first of its kind one-dimensional quantum walk in the d-dimensional quantum domain, where 
, and show its equivalence for circuit realization in an arbitrary finite-dimensional quantum logic for utilizing the advantage of larger state space, which helps to reduce the run-time of the quantum walks as compared to the conventional binary quantum systems. We provide efficient quantum circuits for the implementation of discrete-time quantum walks (DTQW) in one-dimensional position space in any finite-dimensional quantum system when the dimension is odd using an appropriate logical mapping of the position space on which a walker evolves onto the multi-qudit states. With example circuits for various qudit state spaces, we also explore scalability in terms of n-qudit d-ary quantum systems. Further, the extension of one-dimensional DTQW to d-dimensional DTQW using 2d-dimensional coin space on d-dimensional lattice has been studied, where 
. Thereafter, the circuit design for the implementation of scalable d-dimensional DTQW in d-ary quantum systems has been portrayed. Lastly, we exhibit the circuit design for the implementation of DTQW using different coins on various search spaces.
Debasri Saha and Amlan Chakrabarti have contributed equally to this work.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
