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"Universal fault-tolerant quantum computing with stabilizer codes", Paul Webster et al., 2022

Reviewed September 4, 2023

Citation: Webster, Paul, et al. "Universal fault-tolerant quantum computing with stabilizer codes." Physical Review Research 4.1 (2022): 013092.

Web: https://arxiv.org/abs/2012.05260

Tags: No-go, Error-correcting-codes

This paper proves the most general no-go theorem on universality of quantum error correction schemes. The result generalizes the Eastin-Knill theorem, established in

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

The Eastin Knill theorem only applies to transversal gates, whereas this paper has a much more general formalism.

One of the big points of the paper is that the most promising way of getting around the no-go result is to introduce some form of unitarity. It does seem like most of the fault tolerant quantum computing methods have some sort of non-unitarity built in.

This paper is also fantastic review of the literature on error correction schemes and no-go results. Perhaps the best general reference for the topic.