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## "Restrictions on Transversal Encoded Quantum Gate Sets", Bryan Eastin, Emanuel Knill, 2009

*Reviewed August 17, 2023*

*Citation:* Eastin, Bryan, and Emanuel Knill. "Restrictions on transversal encoded quantum gate sets." Physical review letters 102.11 (2009): 110502.

*Web:* https://arxiv.org/abs/0811.4262

*Tags:* Abelian-anyons, Computer-scientific

This paper introduces a no-go result: Any quantum error correcting code which can detect an arbitrary error on any single physical subsystem CANNOT have a universal transversal gate set.

In particular, we can have a theoretical reasoning for why there should be a Gottesman-Knill theorem for generalized normalizer groups. Generalizes normalizer groups are transversal gate sets for the group G surface code, and hence cannot be universal by the Eastin-Knill theorem. This doesn't mean that they will necessarily be simulatable by classical computers, but we know a-priori that the computational power will be at least in some sense limited.