Towards utilizing trapped-ion quantum computers with magnetic gradient induced coupling for quantum annealing

The Magnetic Gradient Induced Coupling (MAGIC) scheme in trapped-ion hardware is emerging as a promising quantum computing platform. Its inherent always-on all-to-all coupling between qubits makes it particularly suited for quantum annealing applications. However, like all quantum computing platforms, several technical challenges must be addressed before achieving large-scale, error-tolerant operations. We present a comprehensive analysis of noise sources in the MAGIC setup, including higher-order interactions arising from Coulomb anharmonicity and magnetic field curvature, while also examining errors specifically relevant to quantum annealing experiments. In our analysis, we identify operating regimes where these errors become negligible, while for regimes where errors remain significant, we propose specific mitigation strategies. This detailed characterization represents a significant step toward advancing magnetic-gradient trapped-ion technology for large-scale quantum applications.