A protocol uses the non-Abelian S3 quantum double as an intermediate to implement a controlled charge-conjugation (CC) gate between qubit and qutrit surface codes.
(a) In the bulk of Abelian codes, measure ver- tex and plaquette syndromes and apply stan- dard decoders for the qubit and qutrit surface codes
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Non-Clifford gates between stabilizer codes via non-Abelian topological order
A protocol uses the non-Abelian S3 quantum double as an intermediate to implement a controlled charge-conjugation (CC) gate between qubit and qutrit surface codes.