PreprintCC BY 4.0HAL
The limits of magic-state distillation
Abstract
Magic-state factories are a major cost of fault-tolerant quantum computing, yet how few noisy inputs they need is known only for restricted protocols. We show that, for tolerating input faults, any stabilizer protocol, however adaptive, postselected or multistage, is no better than a projection onto one stabilizer code, and that for rational targets a fault pattern is harmful exactly when its complement is. Searches over all codes show that quadratic distillation of one T state needs exactly nine inputs and that the eight-input CCZ factory is optimal. At order d, one T state needs n ≥ 2d.
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BibTeX
@misc{gaggioli2026limits,
title = {{The limits of magic-state distillation}},
author = {Llorenç Balada Gaggioli and Jakub Mareček},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31115},
eprint = {2610.31115},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05837756v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The limits of magic-state distillation
AU - Llorenç Balada Gaggioli
AU - Jakub Mareček
PY - 2026
DA - 2026/10/22
PB - HAL
DO - 10.48550/arxiv.2610.31115
UR - https://hal.science/hal-05837756v1
AB - Magic-state factories are a major cost of fault-tolerant quantum computing, yet how few noisy inputs they need is known only for restricted protocols. We show that, for tolerating input faults, any stabilizer protocol, however adaptive, postselected or multistage, is no better than a projection onto one stabilizer code, and that for rational targets a fault pattern is harmful exactly when its complement is. Searches over all codes show that quadratic distillation of one T state needs exactly nine inputs and that the eight-input CCZ factory is optimal. At order d, one T state needs n ≥ 2d.
ER -