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Quantum error correction summary

At this point, you have learned the concept of an error-correcting code and why it is useful to have additional qubits to protect our information. You have also learned the stabilizer formalism, a tool used to develop and analyse quantum error correction codes. The stabilizer formalism also tells us what kind of non-destructive measurements we have to perform in order to detect errors.

You have studied a simple code, the quantum repetition code, where you have put in practice the techniques of encoding and detection of errors. You have learned what to expect in the syndrome when certain errors act on the qubits. You have also learned about the disadvantages of this code, where it can only detect one type of errors.

This problem with the quantum repetition code can be solved by moving towards surface codes. These are scalable codes able to detect any kind of single-qubit errors. You have used the library plaquette to interact with a quantum code, explore various error patterns and learn how these errors produce different (or the same) syndromes.

Now that we know how to encode logical qubits into many physical qubits and how to perform measurements to detect errors, we might be interested in learning what can we do when we encounter these errors. In the next error correction module, we introduce decoders, which are algorithms that take as input a syndrome and use some arguments to create a correction operator that can be applied to the quantum code in order to correct the error and recover the original state of our code.

Bibliography

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  • D. Gottesman, “Stabilizer Codes and Quantum Error Correction,” May 1997. arXiv:quant-ph/9705052.

  • A. Y. Kitaev, “Quantum computations: algorithms and error correction,” Russian Mathematical Surveys, vol. 52, p. 1191, Dec. 1997. Publisher: IOP Publishing.

  • H. Bombin and M. A. Martin-Delgado, “Optimal resources for topological two-dimensional stabilizer codes: Comparative study,” Physical Review A, vol. 76, p. 012305, July 2007. Publisher: American Physical Society.

  • D. Lidar, and T. Brun, Quantum error correction. Cambridge university press, 2013.