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"Qudit surface codes and gauge theory with finite cyclic groups", Stephen Bullock, Gavin Brennen, 2007

Reviewed August 18, 2023

Citation: Bullock, Stephen S., and Gavin K. Brennen. "Qudit surface codes and gauge theory with finite cyclic groups." Journal of Physics A: Mathematical and Theoretical 40.13 (2007): 3481.

Web: https://arxiv.org/abs/quant-ph/0609070

Tags: Abelian-anyons, Expository, Error-correcting-codes

In the words of the authors: "This survey attempts to exhaust the topic of surface codes for topologically protected qudit memories". This means that the authors do not discuss the power of quantum computing with these abelian anyons, though they do assert without reference that these models are "not as powerful as fault tolerant models with non abelian anyons".

However, the authors do say that "It is also possible to generalize earlier discussions of stabilizer operations on topologically stored data while in code". The earlier discussions are about stabilizer measurements. Hence, it is likely that the authors are referring to a measurement-based scheme in the Pauli basis, which should be equivalent to the qudit Clifford group computational model.