Theory of approximate quantum error correction and the error-set model
This paper develops a theory for approximate quantum error correction (AQEC) using an 'error-set model.' It defines conditions based on how errors interact with a fixed set of possible noise channels. The research establishes that codes can approximately correct these specific noisy channels if certain geometric distances, like the environment-leakage distance, are small. This framework connects exact correction to approximate correction across various quantum systems.