PreprintCC BY 4.0arXiv
A three-eighths upper bound on the stabilizer-rank exponent of face-center magic states
Abstract
We give an explicit construction proving that the exact stabilizer rank of m copies of the qubit face-center magic state is O(23m/8). Two symmetry-related fifteen-term identities combine into a twenty-four-term decomposition at twelve copies. The balanced structure of this decomposition yields a substitution that adds eight copies at a cost of eight terms per existing term. The resulting bound γT ≤ 3/8 improves the previously published exponent log2(3)/4.
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BibTeX
@misc{bevins2026threeeighths,
title = {{A three-eighths upper bound on the stabilizer-rank exponent of face-center magic states}},
author = {Samuel Bevins},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17500},
eprint = {2610.17500},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17500},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A three-eighths upper bound on the stabilizer-rank exponent of face-center magic states
AU - Samuel Bevins
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17500
UR - https://arxiv.org/abs/2610.17500
AB - We give an explicit construction proving that the exact stabilizer rank of m copies of the qubit face-center magic state is O(2^3m/8). Two symmetry-related fifteen-term identities combine into a twenty-four-term decomposition at twelve copies. The balanced structure of this decomposition yields a substitution that adds eight copies at a cost of eight terms per existing term. The resulting bound γ_T ≤ 3/8 improves the previously published exponent log_2(3)/4.
ER -