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This research addresses the critical bottleneck of fault-tolerant quantum computation by dynamically optimizing the preparation and allocation of magic $|T\rangle$-states under strict error budgets. The proposed Gap-Priced $|T\rangle$ States framework significantly reduces spacetime volume and execution time through a scheduler that intelligently converts fidelity slack into speed, outperforming static provisioning baselines.
Gap-Priced $|T\rangle$-States: Dynamic $|T\rangle$ Post-Selection and Budget-Aware Factory Provisioning
arXiv:2610.19299v1 Announce Type: new Abstract: Magic $|T\rangle$-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 $|T\rangle$ States (GP$|T\rangle$-S), a lattice surgery scheduler and factory allocator that co-optimizes both methods under a total $T$-error budget. GP$|T\rangle$-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$|T\rangle$-S also characterizes distillation factories by size, $|T\rangle$-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$|T\rangle$-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$|T\rangle$-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.
Abstract:Magic $|T\rangle$-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 $|T\rangle$ States (GP$|T\rangle$-S), a lattice surgery scheduler and factory allocator that co-optimizes both methods under a total $T$-error budget. GP$|T\rangle$-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$|T\rangle$-S also characterizes distillation factories by size, $|T\rangle$-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$|T\rangle$-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$|T\rangle$-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.
arXiv:2610.19299 [quant-ph]
(or arXiv:2610.19299v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.19299 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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