  There are two schools of "measurement-only quantum computation". The first
([11]) using prepared entanglement (cluster states) and the second ([4]) using
collections of anyons, which according to how they were produced, also have an
entanglement pattern. 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 precise 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.
