标题： 开放量子系统中保真度非线性：高维量子计算中的门和噪声依赖性 显示英文标题

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

摘要： 高维量子计算由于其在解决传统基于量子比特系统所面临的可扩展性和错误校正挑战方面的潜力而引起了广泛关注。 本文研究了林堡形式主义中标记噪声下单量子比特系统的平均门保真度（AGF），通过开发一个全面的理论框架来计算高阶修正项，扩展了之前的工作。 我们推导了平均门失真（AGI）摄动展开的一般表达式，并以环境耦合系数的形式验证了这些表达式，通过广泛的数值模拟强调了从线性到非线性行为的转变在强耦合区域。 我们的发现突显了AGI对量子比特维度、量子门选择和噪声强度的依赖性，为优化量子门设计和错误校正协议提供了关键见解。 此外，我们利用我们的框架来识别强耦合区域中AGI的通用界限，并探讨了增强近期量子比特架构性能的实际影响。 本研究为高维量子计算的未来研究和发展奠定了坚实的基础，有助于推进稳健且高保真的量子操作的发展。 显示英文摘要

摘要： High-dimensional quantum computing has generated significant interest due to its potential to address scalability and error correction challenges faced by traditional qubit-based systems. 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.