{"paper":{"title":"Distillation with sublogarithmic overhead","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"J. Haah, M. B. Hastings","submitted_at":"2017-09-11T18:51:14Z","abstract_excerpt":"It has been conjectured [1] that for any distillation protocol for magic states for the $T$ gate, the number of noisy input magic states required per output magic state at output error rate $\\epsilon$ is $\\Omega(\\log(1/\\epsilon))$. We show that this conjecture is false. We find a family of quantum error correcting codes of parameters $[[\\sum_{i=w+1}^m \\binom{m}{i}, \\sum_{i=0}^{w} \\binom{m}{i}, \\sum_{i=w+1}^{r+1} \\binom{r+1}{i}]]$ for any integers $ m > 2r$, $r > w \\ge 0$, by puncturing quantum Reed-Muller codes. When $m > \\nu r$, our code admits a transversal logical gate at the $\\nu$-th level"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03543","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}