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"Quantum error correction with imperfect gates", Alexei Kitaev, 1997

Reviewed July 25, 2023

Citation: Kitaev, A. Yu. "Quantum error correction with imperfect gates." Quantum communication, computing, and measurement. Boston, MA: Springer US, 1997. 181-188.

Web: https://link.springer.com/chapter/10.1007/978-1-4615-5923-8_19

Tags: Foundational, Computer-scientific, Error-correcting-codes, Universal-scheme

This is the paper which introduces the toric code. It defines the code, and gives circuit specifications for how syndrome measurement and error correction can be performed in a fault-tolerant way. As for logical operations, Kitaev makes an appeal to Shor's work which showed that CSS codes can be used for fault tolerant quantum computation:

> Shor, Peter W. "Fault-tolerant quantum computation." Proceedings of 37th conference on foundations of computer science. IEEE, 1996.

The toric code can be embedded into a large CSS code (like the Steane code) which is then used for some logical operations. Kitaev does not describe how to perform this method, instead opting to delay his treatment of fault tolerant quantum computation to

> Kitaev, A. Yu. "Quantum computations: algorithms and error correction." Russian Mathematical Surveys 52.6 (1997): 1191.

This paper is pretty short - it has a concept to introduce and a principle to demonstrate. It does that with little fluff.