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

TL;DR

This paper develops a theoretical framework to analyze how the fidelity of quantum gates in high-dimensional qudit systems depends nonlinearly on noise strength and system parameters, with implications for optimizing quantum computing performance.

Contribution

It introduces a comprehensive perturbative expansion for average gate infidelity in high-dimensional qudits under noise, extending previous models and validating them with numerical simulations.

Findings

AGI exhibits nonlinear behavior in strong coupling regimes

AGI depends on qudit dimension, gate choice, and noise strength

Universal bounds for AGI in high-dimensional systems are identified

Abstract

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.