Quantum Computing with Equiangular Projections

We will investigate a common property of the measurements used in measurement-based quantum computing paradigms. We will show how this relates to the notion of equiangular planes. We will ask when a continuous collection of such planes can give a universal model. Surprisingly, in a sense that will be made precise, octonionic lines turn out to be the unique answer. This research is motivated by the challenge to construct a measurement-based model that exploits chemical protection given by the symmetries of certain molecules.  A joint work with Michael Freedman and Zhenghan Wang.