Citation: Bonderson, Parsa, Michael Freedman, and Chetan Nayak. "Measurement-only topological quantum computation." Physical review letters 101.1 (2008): 010501.
Web: https://arxiv.org/abs/0802.0279
Tags: Universal-scheme, Modular-tensor-categories
This paper gives a universal scheme based on measurement of topological charge only, without any braiding. The construction looks basically the same as quantum teleportation. A series of three measurements swaps the entanglement between two distant sites. The only difference here is that "swapping entanglement" now means applying a braiding map.
This scheme is nice, but one issue with it is that it does not work nicely with the realities of many interferometry schemes. Namely, topological charge measurement will generally decohere information inside and outside the region measured. This decoherence is not considered in the present paper. It is, however, considered in a much longer and more extensive paper:
> Bonderson, Parsa, Michael Freedman, and Chetan Nayak. "Measurement-only topological quantum computation via anyonic interferometry." Annals of Physics 324.4 (2009): 787-826.
In a sense, the first paper is a "toy model" for this one.
A third paper in this series comes from Parsa Bonderson alone, who shows that generically two-anyon charge measurements can be obtained by tuning tunneling terms between adjacent anyons, and hence tunable interactions could be a primitive for universal topological quantum computation as well:
> Bonderson, Parsa. "Measurement-only topological quantum computation via tunable interactions." Physical Review B—Condensed Matter and Materials Physics 87.3 (2013): 035113.
A lovely quote from the second big paper: "In mathematics, also, unitary operators and projectors are dual. Bott periodicity states that a loop of unitaries corresponds to a projector and a loop of projectors corresponds to a unitary. In the integral quantum Hall systems, this perspective links the Chern class in the bulk to the energy current at the edge". I have no idea what this means.