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This paper investigates the Average Gate Fidelity (AGF) of single qudit systems under Markovian noise in the Lindblad formalism, extending previous work by developing a comprehensive theoretical framework for the calculation of higher-order correction terms. We derive general expressions for the perturbative expansion of the Average Gate Infidelity (AGI) in terms of the environmental coupling coefficient and validate these with extensive numerical simulations, emphasizing the transition from linear to nonlinear behaviour in the strong coupling regime. Our findings highlight the dependence of AGI on qudit dimensionality, quantum gate choice, and noise strength, providing critical insights for optimising quantum gate design and error correction protocols. Additionally, we utilise our framework to identify universal bounds for the AGI in the strong coupling regime and explore the practical implications for enhancing the performance of near-term qudit architectures. This study offers a robust foundation for future research and development in high-dimensional quantum computing, contributing to the advancement of robust, high-fidelity quantum operations.<\/jats:p>","DOI":"10.22331\/q-2025-04-07-1690","type":"journal-article","created":{"date-parts":[[2025,4,7]],"date-time":"2025-04-07T10:51:18Z","timestamp":1744023078000},"page":"1690","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["Nonlinearity of the Fidelity in Open Qudit Systems: Gate and Noise Dependence in High-dimensional Quantum Computing"],"prefix":"10.22331","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1992-9675","authenticated-orcid":false,"given":"Jean-Gabriel","family":"Hartmann","sequence":"first","affiliation":[{"name":"Universit\u00e9 de Strasbourg, CNRS, Institut de Physique et Chimie des Mat\u00e9riaux de Strasbourg, UMR7504, F-67000 Strasbourg, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9550-6412","authenticated-orcid":false,"given":"Denis","family":"Jankovi\u0107","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Strasbourg, CNRS, Institut de Physique et Chimie des Mat\u00e9riaux de Strasbourg, UMR7504, F-67000 Strasbourg, France"},{"name":"Institute of Nanotechnology (INT), Karlsruhe Institute of Technology, P.O. 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