{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T00:47:58Z","timestamp":1772758078670,"version":"3.50.1"},"reference-count":0,"publisher":"Rinton Press","issue":"13&14","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QIC"],"published-print":{"date-parts":[[2021,9]]},"abstract":"<jats:p>We investigate the $\\Lambda$-polytopes, a convex-linear structure recently defined and applied to the classical simulation of quantum computation with magic states by sampling. There is one such polytope, $\\Lambda_n$, for every number $n$ of qubits. We establish two properties of the family $\\{\\Lambda_n, n\\in \\mathbb{N}\\}$, namely (i) Any extremal point (vertex) $A_\\alpha \\in \\Lambda_m$ can be used to construct vertices in $\\Lambda_n$, for all $n&gt;m$. (ii) For vertices obtained through this mapping, the classical simulation of quantum computation with magic states can be  efficiently reduced to the classical simulation based on the  preimage $A_\\alpha$.  In addition, we describe a new class of vertices in $\\Lambda_2$ which is outside the known classification. While the hardness of classical simulation remains an open problem for most extremal points of $\\Lambda_n$,  the above results extend efficient classical simulation of quantum computations beyond the presently known range.<\/jats:p>","DOI":"10.26421\/qic21.13-14-2","type":"journal-article","created":{"date-parts":[[2021,10,7]],"date-time":"2021-10-07T16:47:57Z","timestamp":1633625277000},"page":"1091-1110","source":"Crossref","is-referenced-by-count":10,"title":["On the extremal points of the Lambda polytopes and classical simulation of quantum computation with magic states"],"prefix":"10.26421","volume":"21","author":[{"given":"Cihan","family":"Okay","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Zurel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert","family":"Raussendorf","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"10955","published-online":{"date-parts":[[2021,9]]},"container-title":["Quantum Information and Computation"],"original-title":[],"deposited":{"date-parts":[[2021,10,7]],"date-time":"2021-10-07T16:47:59Z","timestamp":1633625279000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.rintonpress.com\/journals\/doi\/QIC21.13-14-2.html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9]]},"references-count":0,"journal-issue":{"issue":"13&14","published-online":{"date-parts":[[2021,9]]},"published-print":{"date-parts":[[2021,9]]}},"URL":"https:\/\/doi.org\/10.26421\/qic21.13-14-2","relation":{},"ISSN":["1533-7146","1533-7146"],"issn-type":[{"value":"1533-7146","type":"print"},{"value":"1533-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9]]}}}