Zobrazeno 1 - 10
of 18
pro vyhledávání: '"Neil I. Gillespie"'
Publikováno v:
Nature Communications, Vol 14, Iss 1, Pp 1-8 (2023)
Abstract Large-scale quantum computers have the potential to hold computational capabilities beyond conventional computers. However, the physical qubits are prone to noise which must be corrected in order to perform fault-tolerant quantum computation
Externí odkaz:
https://doaj.org/article/fe534eed8b51446f8cf3c1746975769f
Publikováno v:
Quantum, Vol 7, p 994 (2023)
Rapidly improving gate fidelities for coherent operations mean that errors in state preparation and measurement (SPAM) may become a dominant source of error for fault-tolerant operation of quantum computers. This is particularly acute in superconduct
Externí odkaz:
https://doaj.org/article/951721aaab62457e971c7ccd1eefc94f
Rapidly improving gate fidelities for coherent operations mean that errors in state preparation and measurement (SPAM) may become a dominant source of error for fault-tolerant operation of quantum computers. This is particularly acute in superconduct
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7d4e0f284480a541d0bdef0800f4b012
http://arxiv.org/abs/2209.05391
http://arxiv.org/abs/2209.05391
Publikováno v:
Mathematics in Computer Science. 12:453-458
We give a new construction of the outer automorphism of the symmetric group on six points. Our construction features a complex Hadamard matrix of order six containing third roots of unity and the algebra of split quaternions over the real numbers.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ec6ec487f376a1b2e50a069b171cb4e6
https://doi.org/10.1007/s11786-018-0382-0
https://doi.org/10.1007/s11786-018-0382-0
Autor:
Daniel R. Hawtin, Neil I. Gillespie
Publikováno v:
Gillespie, N I & Hawtin, D R 2018, ' Alphabet-almost-simple 2-neighbour-transitive codes ', Ars Mathematica Contemporanea, vol. 14, no. 2, pp. 345-357 . < http://amc-journal.eu/index.php/amc/article/view/1240 >
Ars mathematica contemporanea
Ars mathematica contemporanea
Let X be a subgroup of the full automorphism group of the Hamming graph H ( m , q ) , and C a subset of the vertices of the Hamming graph. We say that C is an ( X , 2) -neighbour-transitive code if X is transitive on C , as well as C 1 and C 2 , the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f39738b6b4985bf26d7ba51321da4154
https://doi.org/10.26493/1855-3974.1240.515
https://doi.org/10.26493/1855-3974.1240.515
Publikováno v:
Gill, N, Gillespie, N I & Semeraro, J 2018, ' Conway Groupoids and Completely Transitive Codes ', Combinatorica, vol. 38, no. 2, pp. 399-442 . https://doi.org/10.1007/s00493-016-3433-7
To each supersimple $2-(n,4,\lambda)$ design $\mathcal{D}$ one associates a `Conway groupoid,' which may be thought of as a natural generalisation of Conway's Mathieu groupoid associated to $M_{13}$ which is constructed from $\mathbb{P}_3$. We show t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f76af89bc76fa2bfed5d576f7e7d1c03
https://doi.org/10.1007/s00493-016-3433-7
https://doi.org/10.1007/s00493-016-3433-7
Autor:
Cheryl E. Praeger, Neil I. Gillespie
Publikováno v:
Gillespie, N & Praeger, C E 2017, ' New characterisations of the Nordstrom–Robinson codes ', Bulletin of the London Mathematical Society, vol. 49, no. 2, pp. 320-330 . https://doi.org/10.1112/blms.12016
In his doctoral thesis, Snover proved that any binary $(m,256,\delta)$ code is equivalent to the Nordstrom-Robinson code or the punctured Nordstrom-Robinson code for $(m,\delta)=(16,6)$ or $(15,5)$ respectively. We prove that these codes are also cha
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8287df43d6a2e40e8696a22666e7c4c7
https://doi.org/10.1112/blms.12016
https://doi.org/10.1112/blms.12016
Publikováno v:
Finite Simple Groups: Thirty Years of the Atlas and Beyond. :91-110
In 1987, John Horton Conway constructed a subset $M_{13}$ of permutations on a set of size $13$ for which the subset fixing any given point is isomorphic to the Mathieu group $M_{12}$. The construction has fascinated mathematicians for the past thirt
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::78639441cc031f0b93adef3dabe5c8b8
https://doi.org/10.1090/conm/694/13962
https://doi.org/10.1090/conm/694/13962
Publikováno v:
Gillespie, N I, Hawtin, D R & Praeger, C E 2020, ' 2-neighbour-transitive codes with small blocks of imprimitivity ', Electronic Journal of Combinatorics, vol. 27, no. 1, P1.42 . https://doi.org/10.37236/8040
A code C in the Hamming graph Γ = H(m, q) is a subset of the vertex set V Γ of the Hamming graph; the elements of C are called codewords. Any such code C induces a partition {C, C1, …, Cρ} of V Γ, where ρ is the covering radius of the code, ba
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::04685b39cfdb3d2b1d28231782dc91a3
http://arxiv.org/abs/1806.10514
http://arxiv.org/abs/1806.10514
Publikováno v:
Gillespie, N I, Hawtin, D R, Giudici, M & Praeger, C E 2016, ' Entry faithful 2-neighbour transitive codes ', Designs, Codes and Cryptography, vol. 79, no. 3, pp. 549-564 . https://doi.org/10.1007/s10623-015-0069-3
We consider a code to be a subset of the vertex set of a Hamming graph. The set of $s$-neighbours of a code is the set of vertices, not in the code, at distance $s$ from some codeword, but not distance less than $s$ from any codeword. A $2$-neighbour
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b5e9147a6c1a4f40979ba8b1496d6362
https://doi.org/10.1007/s10623-015-0069-3
https://doi.org/10.1007/s10623-015-0069-3