Generalised Quantum Gates for Qudits and their Application in Quantum Fourier Transform

Abstract:Quantum computing with qudits, quantum systems with $d > 2$ levels, offers a powerful extension beyond qubits, expanding the computational possibilities of quantum systems, allowing the simplification of the implementation of several algorithms and, possibly, providing a foundation for optimised error correction. In this work, we propose a novel formulation of qudit gates that is universally applicable for any number of levels $d$, without restrictions on the dimensionality. By extending the mathematical framework of quantum gates to arbitrary dimensions, we derive explicit gate operations that form a universal set for quantum computation on qudits of any size. We demonstrate the validity of our approach through the implementation of the Quantum Fourier Transform (QFT) for arbitrary $d$, verifying both the correctness and utility of our generalized gates. This novel methodology broadens the design space for quantum algorithms and fault-tolerant architectures, paving the way for advancements in qudit-based quantum computing.

Quantum Physics (quant-ph); Quantum Algebra (math.QA)

arXiv:2410.05122 [quant-ph]

(or arXiv:2410.05122v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2410.05122 Focus to learn more arXiv-issued DOI via DataCite

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