Wrong Plot

[zhaomumu666]

URL to the relevant course

https://quantum.cloud.ibm.com/learning/en/courses/foundations-of-quantum-error-correction/correcting-quantum-errors/repetition-codes

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• new content request
• typo
• code bug
• out-of-date content
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Describe the fix or the content request.

There is a drawing error in the CNOT gates of the phase-flip 3-bit repetition code syndrome measurement circuit: the control qubit dots and target qubit crosses are reversed. The encoding qubits are incorrectly set as targets while the auxiliary syndrome qubits are set as controls, which would corrupt the encoded quantum state if executed as drawn.[

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[christopherporter1]

Hi @zhaomumu666! Thank you for your comment. The figure is actually correct, but you're certainly correct that it could use a bit of an explanation or pointer. The procedure shown in the figure relies on what is called "phase kickback". Showing it explicitly with math in the error correction course is probably not necessary; it would be tedious. But we should point out to where phase kickback is introduced, and saying something like: "CNOTs directly check/affect in the computational basis, such that when checking for bit flips we can directly move information to ancilla using them as targets. But when applying them to check for phase flips, it ends up leveraging the phase-kickback phenomenon, such that the CNOTs need to have their controls and targets flipped." The same structure of flipped CNOTs for phase checks appears in the 9-qubit Shor code, as well. If this explanation is unsatisfying, I recommend playing with the IBM Quantum Composer and building these circuits and checking their behavior directly.
I am linking a PR to add some explanation. #5339. Thanks!