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A family of high rate quantum error correcting codes adapted to the amplitudedamping channel is presented. These codes are nonadditive and exploitself-complementarity structure to correct all first-order errors. Their ratescan be higher than 1/2. The recovery operations of these codes can be generatedby a simple algorithm and have a projection nature, which makes thempotentially easy to implement.

Nonadditive quantum error correcting codes adapted to the ampltitude damping channel