Gap-Priced T-States: Dynamic T Post-Selection and Budget-Aware Factory Provisioning

Magic T-state preparation dominates the cost of fault-tolerant quantum computation on surface codes, yet cultivation and distillation are typically provisioned statically, leaving much of the program's error budget unused. We present Gap-Priced T States (GP T-S), a lattice surgery scheduler and factory allocator that co-optimizes both methods under a total T-error budget. GP T-S uses the complementary gap of each cultivated state as a fidelity estimate and dynamically adjusts the cultivation gap cutoff, converting budget slack into speed by giving the scheduler control over the cultivation post-selection. GP T-S also characterizes distillation factories by size, T-state production rate, and budget slack, and introduces cultivating factories that embed cultivation within routing channels, achieving fidelities otherwise requiring two-level distillation at a single-level footprint. GP T-S organizes these characterizations into a factory catalog, and performs distillation factory allocation over this catalog in tandem with the gap cutoff using dynamic-programming to achieve one of i) minimum spacetime volume, ii) minimum execution time, or iii) minimum space overhead, all within a user-provided T-error budget. Across sixteen benchmarks under high and low T-error budgets of 10-3 and 10-5 respectively, GP T-S consistently outperforms cultivation-only and single-factory baselines without exceeding the budget, achieving a 5.5 times geometric mean speedup in logical cycle count and a 3.4 times geometric mean reduction in space-time volume.