Flexion: Adaptive In-Situ Encoding for On-Demand QEC in Ion Trap Systems

Recent advances in quantum hardware and quantum error correction (QEC) have set the stage for early demonstrations of fault-tolerant quantum computing (FTQC). A key near-term goal is to build a system capable of executing millions of logical operations reliably -- referred to as a megaquop quantum computer (MQC). In this work, we propose a novel system architecture targeting MQC on trapped-ion quantum computers (TIQC), leveraging their ultra-high-fidelity single-qubit gates (1Q) and efficient two-qubit (2Q) logical CNOT gates enabled by the quantum charge-coupled device (QCCD) architecture with the ion shuttling feature. We propose Flexion, a hybrid encoding scheme that uses bare qubits for 1Q gates and QEC-encoded logical qubits for 2Q gates. This approach avoids fully encoding all qubits, eliminating the overhead of gate synthesis, teleportation, and magic state distillation for non-Clifford gates. To support this, we design (1) a low-noise conversion protocol between bare and logical qubits, (2) a bare-logical hybrid instruction set architecture tailored for 2D grid-based TIQC, and (3) a compiler that minimizes conversion cost and optimizes the scheduling efficiency. We evaluate our approach on VQA and small-scale FTQC benchmarks, showing that it achieves superior performance improvements with significantly reduced resource overhead, offering a practical path toward early FTQC on TIQC.