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

Abstract

Fault-tolerant quantum computation in photonic architectures requires efficient preparation of high-fidelity logical magic states under realistic constraints of finite squeezing and photon loss. We present LiDMaS (Lightweight Density-Matrix Simulator), an architecture-level study of logical $T$-gate magic-state preparation in Gottesman--Kitaev--Preskill (GKP)-encoded photonic qubits using a repeat-until-success (RUS) injection protocol combined with outer surface-code protection. A density-matrix simulator based on standard numerical linear algebra is employed, mapping finite squeezing to effective logical dephasing, incorporating logical depolarizing noise, and treating photon loss as a heralded erasure process. Parameter sweeps are performed over squeezing values from $8$ to $16$~dB, baseline loss probabilities between $0.005$ and $0.03$, and surface-code distances $d=1,3,5,$ and $7$. Across this regime, RUS success probabilities range from about $0.90$ to $0.99$, with average injection overhead between $1.15$ and $1.21$ rounds per successful attempt. After outer-code protection, logical fidelities reach $F_{\mathrm{log}} \approx 0.765\text{--}0.796$, exhibiting weak sensitivity to moderate photon loss but strong monotonic dependence on squeezing. Sensitivity analysis identifies finite squeezing as the dominant continuous error source, while loss primarily impacts heralded failure rates. Phase-boundary diagrams determine minimum squeezing requirements to achieve success probability $\ge 0.95$ and logical fidelity $\ge 0.79$ as a function of code distance, providing quantitative design guidance for scalable photonic fault-tolerant architectures.