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

• URL: http://arxiv.org/abs/2410.05122v2
• Date: Tue, 8 Oct 2024 06:54:22 GMT
• Title: Generalised Quantum Gates for Qudits and their Application in Quantum Fourier Transform
• Authors: Francesco Pudda, Mario Chizzini, Luca Crippa,
• Abstract summary: We propose a novel formulation of qudit gates that is universally applicable for any number of levels $d$. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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