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## "Lattice Surgery with a Twist: Simplifying Clifford Gates of Surface Codes", Daniel Litinski, Felix von Oppen, 2018

*Reviewed August 24, 2023*

*Citation:* Litinski, Daniel, and Felix von Oppen. "Lattice surgery with a twist: simplifying clifford gates of surface codes." Quantum 2 (2018): 62.

*Web:* https://arxiv.org/pdf/1709.02318.pdf

*Tags:* Abelian-anyons

This paper introduces a really cute way of implementing 1-qubit Clifford gates in lattice-surgery based surface code models. Namely, you track which boundaries implement which logical operators. When you apply a single-qubit Clifford gate, you just change the names of your logical gates but leave them physically intact! What's nice is that this goes back to using the definition of Clifford gates, and hence easily generalizes to qudits. There is no physical overhead, because this tracking is entirely done in software.

This "edge-tracking" method doesn't apply to CNOT, because this tracking would end up losing locality, and error correction/other procedures would have to become multi-qubit, which you don't want. Hence, you perform CNOT with measurements as before.

This paper can be seen as making good on the promise of the Gottesman-Knill theorem: Cliffords don't need to be quantum.