Nonlinearity of the Fidelity in Open Qudit Systems: Gate and Noise Dependence in High-dimensional Quantum Computing

High-dimensional quantum computing has generated significant interest due to its poten-
tial to address scalability and error correction challenges faced by traditional qubit-based sys-
tems. 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 thecalculation 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 dimensional-
ity, quantum gate choice, and noise strength, providing critical insights for optimising quan-
tum 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 practi-
cal implications for enhancing the performance of near-term qudit architectures. ... mehrThis 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.