摘要
There are two schools of“measurement-only quantum computation”.The first(Phys.Rev.Lett.86(22),5188-5191(2001))using prepared entanglement(cluster states)and the second(Phys.Rev.Lett.101(1),010501(2008))using collections of anyons which,according to how they were produced,also have an entanglement pat-tern.We abstract the common principle behind both approaches and find the notion of a graph or even continuous family of equiangular projections.This notion is the leading character in the paper.The largest continuous family,in a sense made pre-cise in Corollary 4.2,is associated with the octonions and this example leads to a universal computational scheme.Adiabatic quantum computation also fits into this rubric as a limiting case:nearby projections are nearly equiangular,so as a gapped ground state space is slowly varied,the corrections to unitarity are small.
