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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.11409 |
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| _version_ | 1866914536138735616 |
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| author | Ye, Boshuai Khan, Arif Ali Liang, Peng |
| author_facet | Ye, Boshuai Khan, Arif Ali Liang, Peng |
| contents | The efficient execution of fault-tolerant quantum algorithms is fundamentally limited by the production rate of magic states required for non-Clifford operations. While circuit optimization typically targets T-depth, static T-depth does not reliably predict executable performance under bounded T-state delivery. We introduce a model that captures demand-supply imbalance using two key quantities: slack ratio, a structural indicator of scheduling flexibility, and Delta_max, a measure of cumulative demand surplus. We show that Delta_max is a strong schedule-level indicator of execution slowdown and yields a provable lower bound on executable makespan for a fixed schedule. Empirical evaluation on constructed directed acyclic graph (DAG) families, with arithmetic circuits and exact quantum Fourier transform (QFT) traces providing additional grounding, shows that slack ratio is a stronger structural predictor than T-depth for stall and inversion risk, while Delta_max is the strongest predictor of slowdown. Across 4,904 instances, the lower bound shows zero violations, with 88.9% of cases within one cycle. These results highlight the importance of explicitly modeling delivery constraints in fault-tolerant quantum compilation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11409 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | When T-Depth Misleads: Predicting Fault-Tolerant Quantum Execution Slowdown under Magic-State Delivery Constraints Ye, Boshuai Khan, Arif Ali Liang, Peng Quantum Physics The efficient execution of fault-tolerant quantum algorithms is fundamentally limited by the production rate of magic states required for non-Clifford operations. While circuit optimization typically targets T-depth, static T-depth does not reliably predict executable performance under bounded T-state delivery. We introduce a model that captures demand-supply imbalance using two key quantities: slack ratio, a structural indicator of scheduling flexibility, and Delta_max, a measure of cumulative demand surplus. We show that Delta_max is a strong schedule-level indicator of execution slowdown and yields a provable lower bound on executable makespan for a fixed schedule. Empirical evaluation on constructed directed acyclic graph (DAG) families, with arithmetic circuits and exact quantum Fourier transform (QFT) traces providing additional grounding, shows that slack ratio is a stronger structural predictor than T-depth for stall and inversion risk, while Delta_max is the strongest predictor of slowdown. Across 4,904 instances, the lower bound shows zero violations, with 88.9% of cases within one cycle. These results highlight the importance of explicitly modeling delivery constraints in fault-tolerant quantum compilation. |
| title | When T-Depth Misleads: Predicting Fault-Tolerant Quantum Execution Slowdown under Magic-State Delivery Constraints |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2604.11409 |