Gap-Priced |T⟩-States: Dynamic |T⟩ Post-Selection and Budget-Aware Factory Provisioning
Abstract
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× geometric mean speedup in logical cycle count and a 3.4× geometric mean reduction in space-time volume.
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BibTeX
@misc{poster2026gappriced,
title = {{Gap-Priced $|T\rangle$-States: Dynamic $|T\rangle$ Post-Selection and Budget-Aware Factory Provisioning}},
author = {Maxwell Poster and Sayam Sethi and Steven Hofmeyr and Yuhao Liu and Jonathan Baker and Costin Iancu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19299},
eprint = {2610.19299},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19299},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gap-Priced |T⟩-States: Dynamic |T⟩ Post-Selection and Budget-Aware Factory Provisioning
AU - Maxwell Poster
AU - Sayam Sethi
AU - Steven Hofmeyr
AU - Yuhao Liu
AU - Jonathan Baker
AU - Costin Iancu
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.19299
UR - https://arxiv.org/abs/2610.19299
AB - 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× geometric mean speedup in logical cycle count and a 3.4× geometric mean reduction in space-time volume.
ER -