Stabilizer code: Difference between revisions

Revision as of 14:40, 10 June 2023

Revision as of 14:45, 10 June 2023

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If there are no bit-flip errors, both operators <math>g_{1}</math> and <math>g_{2}</math> commute, the syndrome is +1,+1, and no errors are detected.

If there is a bit-flip error on the first encoded qubit, operator <math>g_{1}</math> will anti-commute and <math>g_{2}</math> commute, the syndrome is -1,+1, and the error is detected. If there is a bit-flip error on the second encoded qubit, operator <math>g_{1}</math> will anti-commute and <math>g_{2}</math> anti-commute, the syndrome is -1,-1, and the error is detected. If there is a bit-flip error on the third encoded qubit, operator <math>g_{1}</math> will commute and <math>g_{2}</math> anti-commute, the syndrome is +1,-1, and the error is detected.

If there is a bit-flip error on the second encoded qubit, operator <math>g_{1}</math> will anti-commute and <math>g_{2}</math> anti-commute, the syndrome is -1,-1, and the error is detected.

If there is a bit-flip error on the third encoded qubit, operator <math>g_{1}</math> will commute and <math>g_{2}</math> anti-commute, the syndrome is +1,-1, and the error is detected.

==Example of a stabilizer code==