{"ID":22955977,"CreatedAt":"2026-09-17T02:12:05.498442134Z","UpdatedAt":"2026-09-17T02:12:05.498442134Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.18922","arxiv_id":"2609.18922","title":"Exact logical error rates for magic state cultivation","abstract":"We compute exactly the acceptance and logical error rates for the distance $d=3$ and $d=5$ magic state cultivation circuits from Clifft [arXiv:2604.27058] and SOFT [arXiv:2512.23037] using Pauli propagation and binary tensor contraction. Actual $T$ gates are studied, not the $S$-gate proxy used for sampling. The calculation includes every fault order at several circuit-level noise strengths ($p$). We provide a series expansion form to the logical error rates, through order $(p/(1-p))^{10}$. The analytical results recover the numerical values from Clifft and SOFT at both $d=3$ and $d=5$ to within their sampling uncertainty. Then, we show that the $d=3$ and $d=5$ circuits actually have fault distances of $d_{\\text{fault}}=2$ and $d_{\\text{fault}}=3$ respectively, explaining the similar distance degrading effects from the companion code of [Quantum 10, 2134 (2026)].","short_abstract":"We compute exactly the acceptance and logical error rates for the distance $d=3$ and $d=5$ magic state cultivation circuits from Clifft [arXiv:2604.27058] and SOFT [arXiv:2512.23037] using Pauli propagation and binary tensor contraction. Actual $T$ gates are studied, not the $S$-gate proxy used for sampling. The calcul...","url_abs":"https://arxiv.org/abs/2609.18922","url_pdf":"https://arxiv.org/pdf/2609.18922v1","authors":"[\"Kwok Ho Wan\",\"Ainhoa Zapirain\"]","published":"2026-09-16T16:58:36Z","proceeding":"quant-ph","tasks":"[\"quant-ph\"]","methods":"[]","has_code":false}