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Misleading sentence in the Toric Code - Error Detection explanation in the Foundations of QEC course #4467

@matteo-piccolini

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@matteo-piccolini

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https://quantum.cloud.ibm.com/learning/en/courses/foundations-of-quantum-error-correction/quantum-code-constructions/toric-code

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  • typo
  • code bug
  • out-of-date content
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In the course Foundations of quantum error correction, lesson Toric code, section Detecting errors, when discussing closed loops of errors, it is state that

In particular, the different types of loops can be characterized as follows. 1. Closed loops of X errors with an even number of X errors on every horizontal line and every vertical line of qubits. (The example shown above falls into this category.)

It took me a while to make sense of this sentence, since the figure depicting the mentioned example shown above clearly shows horizontal and vertical lines of odd number of qubits (simply look at the red lines forming the loop borders). I only later realized that the sentence is referring to the lines forming the lattice grid: these are the lines which must contain even numbers of X-affected qubits.

Therefore, I suggest to change the incriminated sentence into Closed loops of X errors affecting an even number of qubits on every horizontal line and every vertical line of the lattice grid.

An analogous change should be applied to the subsequent sentence

  1. Closed loops of X errors with an odd number of X errors on at least one horizontal line or at least one vertical line of qubits.

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