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I have been working with stabilizer codes and I understand the mathematical way that they are described and how to simulate such in a classical computer in order to check their performance.

However, lately I have been wondering how this class codes would be implemented physically in terms of Clifford gates in an actual quantum computer. I have not found much about such mapping in the literature, and less of an actual general algorithm (most of the things I have found are just examples, and not general algorithms that realize the task). Can anyone give some insight about this circuit synthesis problem? Are there any general algorithms that realize this circuit synthesis? Are there optimized versions?

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