Efficiently estimating failure rates of fault-tolerant logical non-Clifford blocks
Abstract
Useful quantum computation requires the fault-tolerant implementations of a universal gate set which are generically not efficiently simulable. We devise an algebraic framework that allows for efficient sampling from the measurement distribution of fault-tolerant circuits that implement diagonal logic gates in the third level of the Clifford hierarchy. Upon successful sampling we also provide sufficient conditions for decoding success. The resulting estimate for the logical failure rate is an overestimate, which becomes more accurate for blocks that are fault tolerant against arbitrary local errors. The non-Clifford simulation overhead is independent of the number of logical qubits, making the method particularly attractive for large-scale simulations. The framework is based on viewing the non-Clifford gates in the circuit as a cohomology invariant of an underlying spacetime fault complex. The method can also be interfaced with Clifford simulators to simulate larger fault-tolerant circuits and algorithmic subroutines.
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BibTeX
@misc{fuente2026efficiently,
title = {{Efficiently estimating failure rates of fault-tolerant logical non-Clifford blocks}},
author = {Julio C. Magdalena de la Fuente and Thomas R. Scruby},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19485},
eprint = {2609.19485},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19485},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Efficiently estimating failure rates of fault-tolerant logical non-Clifford blocks
AU - Julio C. Magdalena de la Fuente
AU - Thomas R. Scruby
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19485
UR - https://arxiv.org/abs/2609.19485
AB - Useful quantum computation requires the fault-tolerant implementations of a universal gate set which are generically not efficiently simulable. We devise an algebraic framework that allows for efficient sampling from the measurement distribution of fault-tolerant circuits that implement diagonal logic gates in the third level of the Clifford hierarchy. Upon successful sampling we also provide sufficient conditions for decoding success. The resulting estimate for the logical failure rate is an overestimate, which becomes more accurate for blocks that are fault tolerant against arbitrary local errors. The non-Clifford simulation overhead is independent of the number of logical qubits, making the method particularly attractive for large-scale simulations. The framework is based on viewing the non-Clifford gates in the circuit as a cohomology invariant of an underlying spacetime fault complex. The method can also be interfaced with Clifford simulators to simulate larger fault-tolerant circuits and algorithmic subroutines.
ER -