Runtime Compilation for Quantum Circuits with PQF-Enabled $R_z$ Synthesis

arXiv:2611.04075v1 Announce Type: new Abstract: In Fault-Tolerant Quantum Computing (FTQC) using surface codes, reducing $T$-count is critical for efficient computation due to the high cost of $T$-state distillation. Probabilistic Quantum Circuit with Fallback (PQF) synthesis significantly lowers $T$-counts compared to standard protocols like Gridsynth, but introduces high circuit dynamism through extra gates inserted at runtime. This dynamism invalidates static compile-time routing, as these new $T$ gates require dynamic lattice surgery routing to establish non-intersecting ancilla paths to $T$-state factories while minimizing total execution time. To address this, we introduce $\text{R}^2$-PQF, a Runtime Routing protocol for PQF-synthesized quantum circuits.