Citation: Dauphinais, Guillaume, et al. "Quantum error correction with the semion code." New Journal of Physics 21.5 (2019): 053035.
Web: https://arxiv.org/abs/1810.08204
Tags: Error-correcting-codes, Abelian-anyons
This is the first paper to flesh out the details of the semion code as a topological quantum error correcting code. The nice feature of this code is that it is based on the stabilizer formalism. That is, the procedure for running the code is that some family of commuting projectors are continually measured, a syndrome is obtained, and then some line operators are applied to return to the codespace. The projectors, however, are NOT pauli.
This model is good to keep in mind for several reasons. First, it adds some evidence to the assertion "topological phases of matter yield error correcting codes". Secondly, it serves as a good counter-example to some naive classifications of error correcting codes. Namely, we must remember that there are codes beyond the Pauli (or qudit Pauli) formalism.
Of course, saying that this paper fully fleshes out the details of the semion code as a quantum error correcting code is manifestly false. For instance, the question of decoding is left to future work. It would take a huge amount of work to go from this paper to a practical topological quantum computation code which could run on a real computer. This paper is a good first step, and does in a sense the hardest part of the problem. It seems relatively clear that there is nothing fundamentally in the way of making a semion quantum computer.