Routing Techniques for Error-Corrected Silicon Spin Qubit Quantum Architectures

Silicon spin qubits have emerged as a promising qubit technology due to their favorable scaling and fabrication properties. However, efficiently compiling quantum circuits onto spin qubit platforms remains challenging, particularly when accounting for hardware constraints and the high sensitivity to static defects. Existing compilation approaches for spin qubits either largely ignore error correction, despite its critical role for large-scale quantum computation, or focus on low-level schedule constructions, missing a high-level compilation and routing for logical, error-corrected algorithms. To address this gap, we introduce a compilation framework for spin qubits based on the recent snakes on a plane model, which utilizes a 2D surface code and qubit teleportation to mitigate errors. Building on this model, we propose shortest-path and rotation-based algorithms as two novel classes of qubit-routing techniques, along with additional defect-handling and initial-mapping strategies. We evaluate both algorithms across diverse architectural settings and problem sizes, demonstrating that shortest-path methods excel in sparse, low-defect scenarios, while rotation-based approaches perform better in high-density environments. An open-source implementation of our framework is publicly available on GitHub as part of the Munich Quantum Toolkit (MQT) at https://github.com/munich-quantum-toolkit/spin-qubit-routing.