home | literature reviews

"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: Error-correcting-codes, Computer-scientific, No-go

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.