LiDMaS: Architecture-Level Modeling of Fault-Tolerant Magic-State Injection in GKP Photonic Qubits

Abstract: Fault-tolerant quantum computation in photonic architectures relies on the efficient preparation of high-fidelity logical magic states under realistic constraints imposed by finite squeezing and photon loss. In this work, we study logical T-gate magic-state preparation in GKP-encoded photonic qubits using a repeat-until-success injection protocol combined with outer surface-code protection. We develop an architecture-level modeling framework based on a lightweight density-matrix simulator implemented with standard numerical linear algebra. Finite squeezing is mapped to effective logical dephasing, depolarizing noise is included at the logical level, and photon loss is treated as a heralded erasure process. This approach avoids explicit continuous-variable wavefunction simulation, hardware-specific photonic models, and quantum software frameworks, enabling transparent and computationally efficient exploration of architectural trade-offs. We perform systematic parameter sweeps over squeezing values from 8 to 16 dB, baseline loss probabilities between 0.01 and 0.03, and surface-code distances d = 1, 3, 5, and 7. Across this regime, we evaluate repeat-until-success probability, average injection overhead, and logical magic-state fidelity. We find that success probabilities exceed 0.94 across all studied parameters, with an average overhead close to unity. After outer-code protection, logical fidelities reach approximately 0.77 to 0.80 and show weak sensitivity to moderate photon loss but a strong dependence on squeezing. Phase-boundary analysis identifies minimum squeezing requirements needed to simultaneously achieve high success probability and logical fidelity. These results provide quantitative design guidance for scalable photonic fault-tolerant quantum architectures.